Astrolabes in Medieval Cultures

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srlabs in Mdival ulurs

Astrolabes in Medieval Cultures Edited by

Jsna Rdríguz-rribas harls Burn Silk krmann Ryan Szpih

 | 

Originally publishd, in par, as Vlum 23, N. 1– (2017) f Brill’s jurnal Medieval Encounters. Library f ngrss aalging-in-Publiain Daa Nams: Rdríguz rribas, Jsna, dir. | Burn, harls (harls S. F.),  dir. | krmann, Silk, dir. | Szpih, Ryan, dir. Til: srlabs in Mdival ulurs / did by Jsna  Rdriguz-rribas, harls Burn, Silk krmann, Ryan Szpih. Ohr ils: Mdival nunrs. Dsripin: Lidn ; Bsn : Brill, [] | Originally publishd, in par,  as Vlum , N. –5 () f Brill’s jurnal Mdival nunrs. |  Inluds indx. Idnirs: CC  (prin) | CC  (bk) |    (Ebk) |   (hardbak : alk. papr) Subjs: CH: srlabs—isry. | srnmial insrumns—isry. |  Nauial insrumns—isry. lassiain: CC Q5 (bk) | CC Q5 .A  (prin) |  C 5/.—d C rrd availabl a hps://ln.l.gv/

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Contents Preface to the New Edition  Ryan Szpiech Preface to the First Edition Astrolabes in Medieval Cultures 1 Josena Rodríguez-Arribas, Charles Burnett, and Silke Ackermann Introduction Hic Sunt Dragones—Astrolabe Research Revisited 3 Silke Ackermann 1 Astrolabes as Eclipse Computers: Four Early Arabic Texts on Construction and Use of the afīa Kusūyya 8 Johannes Thomann 2 The Astrolabe Finger Ring of Bonetus de Latis: Study, Latin Text, and English Translation with Commentary 4 Josena Rodríguez-Arribas 3 Some Features of the Old Castilian Alfonsine Translation of ʿAlī Ibn Khalaf’s Treatise on the Lámina Universal 107 Emilia Calvo 4 From the Celestial Globe to the Astrolabe: Transferring the Celestial Motion onto the Plane of the Astrolabe 12 Flora Vafea 5 Knowledge in Motion: An Early European Astrolabe and Its Possible Medieval Itinerary 149 Petra G. Schmidl 6 A Monumental Astrolabe Made for Shāh Jahān and Later Reworked with Sanskrit Legends 198 Sreeramula Rajeswara Sarma 7 Saphaeae and Hayʾāt: The Debate between Instrumentalism and Realism in al-Andalus 263 Miquel Forcada

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cotet

8

Astrolabes on Parchment: The Astrolabes Depicted in Alfonso X’s Libro Del Saber De Astrología and Their Relationship to Contemporary Instruments 286 Laura Fernández Fernández

9

Fit for a King: Decoding the Great Sloane Astrolabe and Other English Astrolabes with “Quatrefoil” Retes 310 John Davis

10

European Astrolabes to ca. 1500: An Ordered List 37 David A. King

11

Too Many Arabic Treatises on the Operation of the Astrolabe in the Medieval Islamic World: Athīr al‐Dīn al-Abharī’s Treatise on Knowing the Astrolabe and His Editorial Method 367 Taro Mimura

12

Changing the Angle of Vision: Astrolabe Dials on Astronomical Clocks 406 Günther Oestmann

13

Astrolabes for the King: The Astrolabe of Petrus Raimundi of Barcelona 424 Azucena Hernández

14

A New Approach to the Star Data of Early Planispheric Astrolabes 447 Giorgio Strano Epilogue Reconstruction of the Plate of Eclipses according to the Description by ʿAlī ibn ʿĪsā 471 Flora Vafea Index 49

Preface to the New Edition Ryan Szpiech

Univrsiy f Mihigan [email protected]

This vlum was rs publishd in Mdival Enunrs 23.1‒ (2017) and was gus did by Jsna Rdríguz-rribas, harls Burn, and Silk krmann. I is nw my plasur as Edir-in-hif f h jurnal  publish ha spial issu in updad frm as a bk. Th nns f his vlum ar msly idnial wih hs f h jurnal issu, bu his bk als inluds a numbr f rrins and a fw impran addiins. mng h addiins ar brif pssrips addd by Jhn Davis and Günhr Osmann  hir arils ha disuss nw ndings and lariains f hir riginal pins. In addiin, imags and diagrams in sm arils hav bn rsizd and imprvd, a fw passags rwrin and updad, and sm rraa rrd. Ms signianly, a nw aril by Flra Vafa (whs wn riginal nribuin als rappars hr) has bn appndd  h riginal issu as an pilgu. Vafa’s pilgu prvids a rspns  h aril by Jhanns Thmann, “srlabs as Elips mpurs,” inludd in h riginal publiain and rprdud hr. Vafa prpss ha w f h xs nsidrd by Thmann as indpndn surs abu h pla f lipss, arding  ʿlī ibn ʿĪsā’s dsripin, shuld b nsidrd insad as w pars f h sam wrk. Vafa prvids a x and ranslain f h prpsd singl x and amps a rnsruin f h insrumn dsribd hrin. Wih his nw diin f h Mdival Enunrs issu “srlabs in Mdival ulur,” w fur dirs aim  dissmina his impran rsarh  a widr bdy f radrs and shlars and  fr hm a rrd and up-da vrsin f h rsarh i nains. I am ndn ha his vlum will prvid a uhsn fr nging rsarh in mdival asrnmy and srv as a fundain fr fuur sudis.

Preface to the First Edition

∵ Astrolabes in Medieval Cultures Josefna Rodríguez-Arribas*

Institut für Jüdische Studien Westfälische Wilhelms-Universität, Münster *Corresponding author, e-mail: [email protected]

Charles Burnett

Warburg Institute, Woburn Square, London WC1H 0AB,  [email protected]

Silke Ackermann

Museum of the History of Science, Broad St, Oxford OX1 3AZ,  [email protected]

This book, rst published as a Special Issue of Medieval Encounters, is based on the papers of the conference on “Astrolabes in Medieval Cultures” held at the Warburg Institute, University of London, on 24–25 April 2014, under the aegis of a three-year research project on “Astrolabes in Jewish Culture.” This project was supported by the British Arts and Humanities Research Council (/I003800) and based at the Warburg Institute (Josena Rodríguez-Arribas and Charles Burnett) with the participation of the British Museum (in its initial stages, Silke Ackermann) and the Museum of the History of Science, Oxford University (Stephen Johnston). The aims of the project were to produce a monograph on the place of the astrolabe in medieval Jewish culture, to draw up an illustrated catalogue of the instruments, and to edit and translate at least one of the Hebrew treatises on the use and construction of astrolabes. All three aims are nearing completion. In this context it seemed opportune to bring together scholars and students interested in the instrument, its history, and its literature, in which experienced and new scholars could update the knowledge so far available in this eld. We were interested in all periods and cultures, and in all kinds of approaches, but especially those that have received less attention. This meeting was an occasion for scholarly and friendly exchanges, and a source of inspiration for future research. Several participants brought

© koninklijke brill nv, leiden, �9 | doi:0.63/9789004387867_00�

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-, ,  

instruments they possessed or had made themselves, which were admired, displayed, discussed—and used! The general feeling was that astrolabe is still very much alive and there is still much to learn about its subtleties. After the conference, further articles were commissioned to ll out the subject matter of the book and it was decided to include David King’s list of European astrolabes (to ca. 1500 arranged by category) as a useful tool to place the astrolabes referred to in this volume in context. The editors would like to express their gratitude to the Warburg Institute, their staf and fellows, and to the British Museum and the Oxford Museum of the History of Science and their stafs, for supporting this research project and this conference in diferent ways. We would particularly like to thank Stephen Johnston for his part in preparing the conference and for the unstinted help and advice that he has always given us. We would like to extend our gratitude to Ryan Szpiech, the editor of Medieval Encounters, for accepting the proceedings of this conference into the journal. Last but not least we also thank all the participants in the conference “Astrolabes in Medieval Cultures” for sharing their knowledge and their enthusiasm for this intelligent, beautiful, and emblematic object and making this scholarly event a very special occasion. The Editors

Introduction

∵ Hic Sunt Dracones—Astrolabe Research Revisited Silke Ackermann

Mueum f e Hry f Scence, Bra Sree, Oxfr OX1 3AZ,  [email protected]

Hic sunt dracones (Here e ragn)  a  e e prae cmmny ue n meea map  ncae ank area a are awang furer expran an are u mewa angeru. n fac   n—ere appear  e ny ne ge a ear  prae n e eaern ca f Aa, u neeree e expren a aken n a fe f  wn, uner n a arey f cnex. Hic sunt leones (Here e n)  ue w a mar cnnan y rer Jrge, e e mnk n The Name of the Rose wen e  referrng  angeru knwege an agan, nw n e amguu ene, y e man caracer an er f e k, ranccan rer Wam f Bakere wen e n Afrca n a map n e rary.    ame Wam f Bakere w, prraye y Sean Cnnery n e Hyw me, rug an arae  e aenn f a wer puc—a r f ureac, f yu ke. Becaue   e w n ne f e key cene f e me furey reace fr an arae n  ag  ake me reang (wa e are we are neer ), anxu n e een  ue  nrumen nruce frm e amc—an u ereca, accrng  e curc aure—wr.

  enx ge, c. 103–10, New Yrk Puc rary, New Yrk, , .   Umer c, The Name of the Rose, ran. Wam Weaer (San eg, : Harcur Brace Janc, 1983), 421.   “The Name of the Rose” (Cuma Pcure, 198) y Jean-Jacque Annau.

© koninklijke brill nv, leiden, �9 | doi:0.63/9789004387867_003

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Arae ae n an ragn apeny, n fac a we menagere f em—e n a par f e zac, amng e ar-pner an n argca cnex; e ragn equay appear amng e cnean, fen guraey n e ree, n argca cnex an  expan ecpe. Bu equay reearc n e arae a  f n an ragn n e nn-ange ene. n pe f mre an 10 year f cary wrk ere reman many uncarere errre r e were ny e ca ae een expre. A cmmene an urae nenry f a urng arae a ge eyn a mere    uanng, n pe f a numer f ng ngng prjec. n e ecn ecae f e weny-r cenury ne wu w fr an nne arae pra a enae e uer  earc an away ncreang aaae y per an regn, maker an ae, curren (r a knwn) can, w ypernk  p, ecrpn, reean pucan an ngng cary cun an reearc prjec. A aaae a facae nercpnary reearc n a we arey f cnex n repec  ne f e m facnang nrumen a a eer exe—e  ar r pgy, crafmanp r ecngy, engy r cgy, ecnmy r aw, pc r regn—r a mxure f any f e ae. Te mre we knw, e mre we are aware w e we knw. Wa were e ega mpcan f ung an arae n e ecn af f e reen cenury? Wa prce were pa fr arae n enaance ay an wa  pe  make a ng ae n ? Hw are arae epye n m an eraure n e ecn af f e wene cenury an w  e auence “rea” ee? Wa  a Nuremerg czen knw au arae n e r af f e xeen cenury?  wmen make, ue, an eac e ue f arae n e amc Wr? T ume, a gy ree an upae ern f e peca ue f Medieval Encounters 23 (201), cann anwer a ee quen, f cure, u  nen   me f e ank area— ame a ea a few ragn (r n),   peak.   erek e Sa Prce an Sarn G, Computerized Checklist of Astrolabes (New Haen, : Yae Unery, 193).   Aan Breux an ranc . Man, Repertoire des facteurs d’ astrolabes et de leurs oeuvres (frcmng; a e me f wrng an fwng e ea f  aur ere are ncan a e eperre may acuay n e pue); a A. Kng, A Catalogue of Medieval Astronomical Instruments to c. 1500 (frcmng, e 199 ern  aaae a DF n p://aakng.acaema.eu/reearc#caaguefmeeaarnmca nrumen). See a A Kng’ arce n  ume.

stolb Rsh Rvisitd

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Pera Scm’ arce  cear eence nce agan (f  wa neee) w uefu  wu e  ae e afremenne arae pra  e ae  (re)examne e nrumen n ea an  (re)eauae earer reearc cam. Se w cnncngy a ce examnan f e acua eence can ea  urprng cncun—an a arae  n ny ae e u mng par, u  me emee (an eence fr  mn  een n e arae) a knwege  n mn eween e Arac an an peakng wr. Te necey f earnng  “rea” jec n e ame way a exua an pcra urce  emnrae amray y Jn a. Bae n cmparn w w umnae manucrp, e “Memee Treae” an a cpy f e “Secreum Secrerum,” a pu frwar an nrgung rca cnexuaan f e famu “Sane Arae” n e Br Mueum, e arge an m mpran f a meea ng nrumen, a a eacng  fr Prnce war f Wnr w wa n  ecme Kng war III, key  ae een cmmne, c. 132, y  ur car e Bury. He ugge a w er meea arae, nw n ège an n e nn Scence Mueum, are eee  e cey acae w e Sane nrumen an ere frm . A ur e frce afer wc quaref, wyern, r an’ ay n arae w neer agan e awe  e een a mere ecran. Te mprance f exua eence an e nnumerae urce a ae n een een appe ye, e ane ee an ranae,  emnrae ceary y ree arce n  ue. Janne Tmann cue, e, an ranae fur er unpue Arac ex f e nn cenury E n e cnrucn an ue f arae-ke nrumen fr wng e cnn f ecpe. Tee ex appear  e e eare ecnca ecrpn f ecpe cmpuer n any anguage. A ra Vafea prpe n er epgue a e en f  ume, w f e ex eang w e pae f ecpe a ecre y ʿAī n ʿĪā are, n er ew, acuay par f e ame ex. Se u pre an en mergng e w ex n ne an aemp a recnrucn f e nrumen ecre. Jena ríguez Arra epy er exceen cmman f Jew urce n e arae  make accee Bneu e a’ (Jac en mmanue Prenzae) reae n e arae rng (1492/1493), an nrgung an appareny unque jec a, accrng  a ea ne eye-wne accun, wa n ju a mn game, u , nee, ex n pyca frm. Te reae wa gy regare amng Bneu’ cnemprare an e nrumen epce n Bneu’ ke can e cnere, a e ae,  e ne f e a cnrun f Jew cuure  e ry f e arae.

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

By cmparng Kūyār n aān’ (en cenury E) Book of the Astrolabe w Aīr a‐īn a‐Aarī’ (. 122 r 12) Treatise on Knowing the Astrolabe, Tar Mmura w a  preuppe er wn arae wen wrng. He cncue a many Arac reae n e arae a er ney a ea guaranee y e unquene f a pecc arae a eac aur ue a  a. ae cerane can e mre amagng an n cerany a a. T  epecay rue n e cnex f e ang f arae y “cenc” me—me, a , a are a rca contradictio in se w e aa aaae a e me f prucn. Grg Sran cmpeeny examne, an en me ee me, remnng car a “meaurng e ar pn n e ree requre ne  ap e ame crnae yem ue urng e Me Age.” nee,  e, an Sran u nruce an aernae apprac ee n x meea arae a a wn remarkae reu, u muaneuy pen up a new e f quen. Bu e “an many er quen reea a e new apprac  e arae aa  n a ea en, u a ng pa f wc ny e r few ep ae een aken.” ace yur ragn, ne mg ay. Knwege f eregrapc prjecn  a e ear f arae cnrucn. Bae n er e, ra Vafea w a e eregrapc prjecn f e ceea ge n e pane f  equar  an eena prereque f e cnrucn f e panperc arae n rer  preere an ranfer a e funcn f e ge. W e repreenan f e ceea crnae n an arae  mre arac an furer reme frm e ree-menna me f e ceea pere a a ge repreen, e reung nrumen can e ue fr mre accurae meauremen.  funcnay u ge far eyn a f e mre acc re f e ge. Te reanp eween e e cmmn eregrapc prjecn frm e Nr Pe (reung n -cae uern arae) an eary arnmca cck wng me cnfungy n an an-cckwe mn,  expre y Güner Oemann, w  ae  cnrm a e knwege f aran f e eregrapc prjecn an peca arae cnrucn mu ae reace urpe frm amc area (pray Span) n e wef cenury, u prng eena knwege fr e cnrucn f arae cck a. ur paper n  ue fcu n e rc cuure f cenc excange an nrumen prucn n meea Span. Hw e we knw een au eemngy ac wrkp pracce an n f aur n e Me Age  amene y Azucena Hernánez. Se cue e ny gne an ae an arae knwn  ae ure frm meea Span an prpe an encan fr “Peru amun, a memer f e Hue f e

stolb Rsh Rvisitd

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Kng f Aragn” n e cnex f a we ynay f kng upprng cenc reearc, fcung my n  pracca menn: e cnrucn f cenc nrumen. Bu weer Peru amun wa ne n e cnrucn f e nrumen r n  cmmn reman, fr nw, an engma. ma Ca negae me feaure f e reae n e lámina universal, an arnmca nrumen ee y ʿAī n Kaaf, an eeen-cenury Anauī maemacan an arnmer w enge  e cenc crce f e qādī Sāʿ a-Anauī. Te ex  preere ny n e reencenury O Caan Afnne ranan. Mgue rcaa expre a numer f ex wren n a-Anau eween e wef an e eary fureen cenure a menn n a-Zarqāu r e “Tean arnmer.” Tee ex expre cary reacn  e cnrun f e crce f arnmer f eeen-cenury Te—an e exua eence reea aue rangng frm a mewa naïe amran  ar crcm. N e pyca nrumen emee, u “arae n parcmen” are e fcu f aura ernánez ernánez’ uy f fur ex reang  e cnrucn an ue f arae n e Libro del Saber de Astrología (L) cmmne y Afn e Sa n e ecn af f e reen cenury w a parcuar fcu n e ne an ampe uran. Se cncue a e rawng were egne n ce cnac w rea nrumen a we a e ue f urae manucrp. Here, , we n a we are nwere near cmpeey carere errry ue  e ack f a caague f umnae arae manucrp a wu facae  reearc, epecay n e g f e ue f earer urce frm e amc wr an e caran f Mum an Jew car n e crean f e arae caper f L. Te uy f arae a ene  e argey cenre n e re, manufacure, an ue f e nrumen n e caca wr, e Me a, an urpe, w a fcu n e Meerranean. Ta e rajecry  n ny g we arun e r Mennum, u a ea war na  a far e we uner ry. T a een aja Sarma’ reearc fcu fr many year an few can cam  ae uc a rug uneranng f  par f e wr. Here e argue a a uge arae, wc wa cmpeey rewrke a a aer age w Sankr egen, wa n fac rgnay pruce eween 148 an 18 y Ḍyāʾ a-īn Muḥamma f are fr e Muga mperr Sā Jaān. One cu ary magne a mre unnng manfean f e ynamc eepmen f a muc earer ran. Te preen ume eneaur  e furer g n wa reman ne f e m nrgung area f nrumen reearc.   a mean  encurage er  acke e area were we wu  cam hic sunt dracones.

 

Astrolabes as Eclipse Computers: Four Early Arabic Texts on Construction and Use of the Ṣafīḥa Kusūyya Johnnes Thomnn

epartet  Isac Stdes, Isttte  Asa ad Oreta Stdes, versty  Zrch, Rästrasse ,  Zürch, Swtzerad johnnes.thomnn@oi.uzh.ch

Abstract* The a tpc  ths artce cprses r pbshed Arabc texts  astrabeke strets r shw the cdts  ecpses. They are the earest techca descrpts  ecpse cpters  ay aae. The rst text s a treatse by ʿAī b ʿĪsā (th cetry)  a speca astrabe r ar phases ad ecpses. The secd text s a ays redact  the rst text wth se sss ad addts. The thrd text descrbes a sar stret wth a deret des, whch was veted by ḥaad b ḥaad asṭūs a-Asṭrābī  the year / . The rth ays text descrbes a pate r a raphca st  the sze  a ar ecpse. I the ccd part, ater Arabc descrpts  ecpse cpters are sarzed, se traces  these texts  rea astrabes are eted, ad ay se cparabe edeva Lat texts are reerred t. r Appedces cta a edt  the Arabc texts ad Esh trasats.

Keywords Aī b ʿĪsā ‒ Arabc treatses ‒ astrabe ‒ ecpse cpter – ḥaad b ḥaad asṭūs a-Asṭrābī

*  Edtrs’ te: See as ra aea’s epe t ths ve r a respse t ths stdy prps that tw  the r texts actay derve r the sae text.

© koninklijke brill nv, leiden, �9 | doi:0.63/9789004387867_004

  P MPU

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Introduction Ecpses  the s ad  are excepta evets ad have had a reat pact  ha scety thrht hstry. The predct  ecpses was e  the prary as  acet astry.1 The reprt abt Thaes  ets hav predcted the sar ecpse dr the batte at the rver Hays  the year   becae a parad  the trph  rata scece ver bd sperstt. Ecpses pay a prtat re  the reprts  Babya astrers t the k, ad  ther astrca recrds. The dscvery  the ecpse cyce awed r a easy way t predct pssbe dates  sar ad ar ecpses. Sch cyces ht have bee  se a terate ctres ad there are pret bjects that have bee preseted as caddates r ecd the. The st as ad the st dspted exape s the eathc et at Stehee. re recety, the s-caed “Berer dht,” e  r kw cca de hats kw r Brze Ae Erpe s ar, has as bee prpsed. Wred eh, the ate drectr  the “se ür r- d rüheschchte,” pbshed a eabrate terpretat  the patters  the hat as sar cyces, ad, add t hs aayss e ay say that the cyce   sydc ths st be csdered a vabe caddate r a ecpse cyce, sce  sydc ths are ast eqa t  dractc ths. re recety   a dsh d  the paace  Ksss has bee terpreted as a a ecpse cacatr.   Ceecy tee, Chsing Shdows. Mthemtics, Astronomy, nd the Erly History of Eclipse Reckoning (Batre, MD: hs Hpks versty ress, ).   haes Tha, “Zr achrech atker Sestersse,” Antike Nturwissen­ schft und ihre Rezeption  (): –; .R. Stephes ad Lay . ath, “Thaes’ redct  a Sar Ecpse,” Journl for the History of Astronomy . (): –; tr achek, “Thaes’s redct  a Sar Ecpse,” Journl for the History of Astronomy . (): –; Thas Wrthe, “Herdts’s Reprt  Thaes’ Ecpse,” Electronic Antiquity . ()  paat; .W. Rer, “Se Thhts  Thaes’ Ecpse,” Liverpool Clssicl Monthly  (): ‒; A.A. sshaer, “Thaes’ Ecpse,” Trnsctions of the Americn Philologicl Assocition  (): ‒; . O’Bre, “erved Lht ad Ecpses  the th Cetry,” Journl of the History of Astronomy  (): ‒.   h avd rth, Stonehenge. A New Interprettion of Prehistoric Mn nd the Cosmos (ew rk, NY: The ree ress, ).   Wred eh, Der Berliner Goldhut. Mcht, Mgie und Mthemtik in der Bronzezeit (Ber: Staatche see z Ber‒Stt pressscher Ktrbestz, ).   . Tskrtss, E. Thedss, .. aas, . ataraks ad . Tskrtss, “A a Ecpse Cacatr,”  5th Interntionl Conference of the Europen Society for the History of Science. Scientic Cosmopolitnism nd Locl Cultures: Religions. Book of Abstrcts, ed. . Katsapra (Athes: Isttte  Hstrca Research/ata Heec Research dat, ), .

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omnn

reek astrers becae aware that sar ecpses were prdced by the ar bdy ad ar ecpses by the shadw  the earth, ad cstrcted three-desa des  the sar syste. Ccer descrbed sch a de  Re, thht t be ade by Archedes, whch cd perr sar ad ar ecpses  the tre seqece  the rbta perds. The pr that sch cpex devces exsted  Atqty exsts  the as Atkythera echas. I a recety dertake ew read  the scrpt, yphs were deted as sybs r sar ad ar ecpses. espte the ceebrty sch devces had  Atqty,  techca text  the cstrct r se  the sees t have exsted. There are se sderearks  tey’s Almgest  physca des, bt these are ar r the srt  detaed descrpts  strets r astrca bservats that ake precse der recstrcts  the pssbe. Idepedet wrks  the cstrct  astrca strets are scarce; wrks by The, hps, ad thers  the pae astrabe are the y excepts. Ths chaed scaty  the Bahdada reassace  the sceces  the ehth ad th cetres. The ajrty  astrca texts as deat wth the descrpt  astrca strets. A ber  wrks  a-Khwārzī, Ḥabash a-Ḥāsb, a-arhāī, ad ther athrs  the eary Abbasd perd are extat.1 It was t y a te  acqst  acet techqes bt as a te  vat. Ḥabash wrte hs treaty  the e-shaped astrabe based  a -stereraphc prject wth eqdstat decat app.11    

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Ccer, On the Republic. On the Lws, tras. by Ct W. Keyes (Cabrde, M: Harvard versty ress, ), ., p. . Ty reeth, Aexader es, h . Steee, ad as Btsaks, “Caedars wth Oypad spay ad Ecpse redct  the Atkythera echas,” Nture  (): –. tey, “Aaest III.,”  Cludii Ptolemei oper que exstnt omni, ed. .L. Heber (vs. ‒), . B ad E. Ber (v. ),  vs. (Lepz: B.. Teber, ‒), vs. . ad . (, ), ; strets  bservat: see Aaest .. ea hp, Trité de l’strolbe (ars: Bees Lettres, ). raçs Charette ad etra Schd, “A-Khwārzī ad ractca Astry  thCetry Bahdad. The Earest Extat Crps  Texts  Arabc  the Astrabe ad Other rtabe Istrets,”   (): –; Rchard . Lrch ad a Ktzsch, “Ḥabash a-Ḥāsb’s Bk  the Sphere ad ts se,” Zeitschrift für Geschichte der rbisch­islmischen Wissenschften  (): –; Rchard Lrch, Al­Frghānī. On the Astrolbe (Stttart: Steer, ). Edward Stewart Keedy, a Ktzsch ad Rchard Lrch, The Melon­Shped Astrolbe in Arbic Astronomy (Stttart: Steer, ).

  P MPU

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ʿAlī ibn ʿĪsā’s Epistle on the Eclipse Plate () I the ctext  ths strs crce  Bahdad at the te  a-aʾū the srces et a certa ʿAī b ʿĪsā a-Asṭrābī as a eber  the tea red t easre e deree  eraphca attde.1 He s a sewhat shadwy re ad t ch s kw abt hs braphy.1 A treatse  the astrabe that bears hs ae was edted   ad trasated t era.1 Accrd t a-Qabīsī (ded  ) ʿAī b ʿĪsā wrte a Risāl fī ibṭāl ṣināʿt ḥkām l­nujūm (Letter  the vadat  jdca astry), aast whch a-Qabīsī wrte hs Kitāb fī ithbāt ṣināʿt ḥkām l­nujūm w­ nqd Risālt ʿAlī ibn ʿĪsā fī ibṭālihā (Bk  the vadat  jdca astry ad the shrtcs  ʿAī b ʿĪsā’s etter  the vadat  t).1 ether  the tw wrks has srvved. Besdes that, there s ather treatse ascrbed t h wth the tte Risāl fī mʿrift l­ʿml bi­l­ṣfīḥ l­qmriyy w­l­ḥuqq[] l­kusūyy (Epste  the kwede hw t se the ar pate ad the ecpse bx).1 As the tte dcates, devces r the dspay  the ar phases ad  ecpses were csey reated tasks. Whe the rst task  sar devces has receved se schary attet aready a cetry a, the stdy  the secd task—the dspay  the ecpse—s st  ts acy.1 The sar devce  

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avd K, “T ay Cks … A ew Acct  the Earest edetc easreets,” Suhyl  (): – (, , , ); . Tzv Laera, “The Bk  Bdes ad staces  Ḥabash a-Ḥāsb,” Centurus  (): – (). arv Bt, “ʿAī Ib ʿĪsā a-Asṭrābī,”  The Biogrphicl Encyclopedi of Astronomers, ed. Thas Hckey (ew rk, NY: Sprer, ), ; Brs A. Rseed ad Ekeedd İhsağ, Mthemticins, Astronomers, nd Other Scholrs of Islmic Civiliztion nd Their Works (7th–19th c.) (Istab: , ), . Ls Chekh, “Ktāb a-ʿaa b--aṣṭrāb -ʿAī Ib ʿĪsā,” l­Mshriq  (): –; Car Schy ad seph recker, “ʿAî b ʿÎsâ, as Astrab d se ebrach,” Isis  (): –. Chares Brett, Kej aat, ad ch a, Al­Qbīṣī (Alcbitius): The Introduction to Astrology (Ld: The Warbr Isttte, ), –. M Istab, Tpkapı Saray Kütüphaes, Ahet   . r–v, wrtte   . escrpts: at Sez, Geschichte des rbischen Schrifttums: Bnd VI Astronomie bis c. 430 H. (Lede: Br, ) ; eh Edhe Karatay, Arpç yzm­ lr ktlŏgu (Istab: Tpkapı Sarayı üzes, –), :; ax Krase, “Staber Hadschrte sascher atheatker,” Quellen und Studien zur Geschichte der Mthemtik, Astronomie und Physik; Abt.B: Studien  (): – (). r the ecpse pate see ra aea, “A-Bīrūī: The ate  the Ecpses,” Suhyl  (): rthc; haes Tha ad atthas e, Schttenspur. Sonnennsternisse in Wissenschft, Kunst und Religion (Base: atrhstrsches se, ),  ad

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omnn

Figu . The mter of ʿAlī ibn ʿĪsā.

descrbed by ʿAī b ʿĪsā s deret r ater exapes  eared echass. Its parts are stadard parts  a astrabe, bt have a deret des. The ater, whch s caed ḥujr (“b”), s dvded t r qadrats. The r  the pper ha s dvded t twety-eht parts. They crrespd t the twety-eht days dr whch the  s vsbe dr a ar th. The r  the wer rht qarter s dvded t tweve parts, whch crrespd t the tweve day hrs. The hrs are arked wth bjd etters. The r  the wer et qadrat s dvded accrdy, represet the tweve hrs  the ht. The scae  the wer ha  the b s desed t dcate the te  the sett  the  (see re .). The rete, caed ʿnkbūt (“rete”), has a crcar he  e ha. Its dess are t dcated  the text bt,  rder t  the descrbed task, the rat  ts rads t the dstace  ts cetre r the cetre  ts rete st be e t the sqare-rt  tw. I ths he the phases  the  are shw  the ar pate s sed, ad the atde  the ar ecpse,  the ecpse pate s sed.

–. r ar pates ad echass, see ad R. H, “A-Bīrūī’s echaca Caedar,” Annls of Science  (): –; Ehard Wedea, “E Istret, das de Bewe v Se d d darstet, ach a-Bîrûî,” Der Islm  (): –.

  P MPU

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The recstrct  the ar pate s sewhat prbeatc, sce the text  the Istab ascrpt sees t cta a aca  a crca passae. rever, at se pts there sees t be a cs  dacrtca pts. Arabc muḥrq (“bred”) s csed wth mukhriq (“perrated”). I the ater Istīʿāb l­wujūh l­mumkin fī ṣnʿt l­ṣṭurlāb  a-Bīrūī, the ersa express sīm­i sūkht (“bred sver”) s sed r the back cr.1 A aas Arabc express s bār muḥrq (“brt ead”) r a cpd  ead.1 Therere, the read l­ḍḍ l­muḥrq  the text  ʿAī Ib ʿĪsā sees preerabe. The express ht have eat a sver trate r ather cpd  sver. Eve s, thrh cpars wth ater texts, a tetatve recstrct ca be ve. O the ar pate are tw syetrcay arraed crces wth the sae dspst as the crcar he  the rete. They are ed wth a back cr. The tw crces are cected by a crcar path, whch s sver-bred. A thrd crce s caed “crce  the sphere  the s.” Ths crce st be ppste t the crcar path ad,  t has the sae sze as the ther tw crces, t st be taet t the tw crces. The prpse  the crce s t deed. The text dcates that the thrd crce s cse t the sspes  the stret, ad ths xes the retat  the etre pate (see re .). The ct  the rst tw back crces ad the svery crcar path  betwee the sees cear. The scaes  the r detere that ° derees crrespd t e ar th. Therere, by tr the rete by °, the phases  the  dr e th appear  the crcar he. O the ther sde  the pate ather ayt s descrbed  the text. A crce s eted that has a scae wth tweve ts  t by whch the ecpsed part  the  s easred dr a ecpse. Obvsy, these are the tradta tweve ers r dts by whch the atde  a ecpse s easred. Later the text reers t t as the sphere  the . It s sad that at the rht sde  the crce the vae  the dstace  the  r the de appears, bt  detas are ve. I the ast part  the text where the strct s ve ccer hw t detere the sze  a ecpse, t beces cear that there st be a speca scae  whch the dstaces  the  r the de are ayed t, ad that the rete st be tred t the pter caed “pter  the de” dcates the crrect vae (see re .). The text as ets a sphere  the dra that s sad t be vabe reatve t the sphere  the . It s a part  the rete ad has the ct    9 

A-Ḥsayī, Istīʿāb l­wujūh l­mumkin fī ṣnʿt l­ṣṭurlāb, ; c. Wedea, “E Istret, das de Bewe v Se d d darstet, ach a-Bîrûî,” . aba Käs, Die Minerlien in der rbischen Phrmkognosie (Wesbade: Harrasswtz ), v. , .

4

FGU .2 The plte of ʿAlī ibn ʿĪsā.

FGU .3 Other side of the plte of ʿAlī Ibn ʿĪsā.

omnn

  P MPU

5

cver the crce  the  by the desred atde. The y ther part  the stret descrbed  the text s a stadard dpter, sed r attde easreets, ad there s a shrt chapter  tekeep.  -stadard parts, ears, r ther re cpex echaca devces are eted. There s a expct stateet  the text that the psts  s, , ad ar de shd be take r a tqwīm, that s, a astrca epheers. I recet years, a ber  raets  Arabc epheerdes have bee dscvered  papyrca cects. The dest kw te s a epheers r the ersa year  (– ).1 The day psts  s, , paets, ad the ar de r a ersa th are sted  a dbe pae. The apprxate te  cjct r ppst  s ad  ca be cacated by spe terpat. The dstace  the  r the de s d by a spe sbtract  the vaes. Therere t ards  hher capabtes t predct the cdts  a ar ecpse. Ths s t pssbe  the case  a sar ecpse, sce ts cdts vary wth the bserver’s eraphca pst. The stret descrbed by ʿAī b ʿĪsā s ay a t r vsazat, t r cacat. It prvdes y a rh dea t the astrca pheea, ad precs s t teded.

0 

 

haes Tha, “A Arabc Epheers r the ear /  ad the eraphca Lattde  a-Bahasā/Oxyrhychs (.Stras. Iv. Ar. ),” Chronique d’Égypte . (): –; haes Tha, “A Arabc Epheers r the ear /   the ea apyrs Cect,”  Scientic Cosmopolitnism nd Locl Cultures: Religions, Ideologies, Societies. 5th Interntionl Conference of the Europen Society of the History of Science, Athens 1–3 November 2012. Proceedings, ed. aa Katsapra (Athes, Heec Research dat, ), –; haes Tha, “The Arabc Epheers r the ear /  (.Cabrde U Iv. chae. Chartae  ) ad the Arabc Baḫīṭas, reek Παχνίτης ad Cptc ⲡⲁϣⲟⲛⲥ,” Chronique d’Égypte . (): –; haes Tha, “Epheerde ür das perssche ahr  (/ . Chr.),”  Orkelspüche, Mgie und Horoskope. Wie Ägypten in die Zukunft sh, ed. A. Zdarsky (We: hbs, ), –; haes Tha, “Epheerde ür das perssche ahr  (/ . Chr.),”  Orkelspüche, Mgie und Horoskope. Wie Ägypten in die Zukunft sh, ed. A. Zdarsky (We: hbs, ), –; r a eera vervew see: haes Tha, “Astre d Astre  arabsche kete,”  Orkelspüche, Mgie und Horoskope. Wie Ägypten in die Zukunft sh, ed. A. Zdarsky (We: hbs, ), –. haes Tha, “A Arabc Epheers r the ear – ,”  From Bwīṭ to Mrw. Documents from the Medievl Muslim World, ed. A. Kapy, . tthast, ad C. Röer (Lede: Br, ), –.

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omnn

An Anonymous Redaction of ʿAlī ibn ʿĪsā’s Epistle () A ays text wth the tte Bāb fī ʿml bi­l­ṣfīḥ l­qmriyy (Chapter  the se  the ar pate) ctas  ts secd part r sects  a ecpse pate. It was deted wth ʿAī b ʿĪsā’s epste. Hwever, a cat  the tw texts reveas that the Car ascrpt ctas a redact  ʿAī b ʿĪsā’s epste  whch se passaes reappear wth y r varats, whe ther passaes are repaced by a deret text. I rder t prvde  trasparecy, the Car vers s edted ad trasated separatey  Appedx B. Nasṭūlus on the Eclipse Plate () A text  a sar devce s preserved  a se ascrpt  ba. Its tte, “Epste  the ractce  s the ae Lar Astrabe,” dcates that t descrbes ay the se  the stret, t ts cstrct. It s sad that the stret was veted by ḥaad b ḥaad, caed asṭūs a-Asṭrābī. asṭūs s kw as a prtat astrabe aker ad he s as credted as a vetr  a ecpse pate by a-Bīrūī. Three astrabes ad a astrabe-ke stret wth hs satre are preserved.  

     

 

 

M Car, ār a-Ktb, Zakī , . r–r, seveteeth cetry . escrpt: avd K, Fihris l­mkhṭūṭāt l­ʿilmiyy l­mḥfūẓ bi­Dār l­Kutub l­Miṣriyy (a-Qāhra: A-Hayʾa a-ṣryya a-ʿĀa --Ktāb, –), :–, :. Rseed ad İhsağ, Mthemticins, Astronomers, nd Other Scholrs, . I thak ra aea r prvd dta aes r a cr  M Zakī , as kept  the ār a-Ktb Lbrary  Car. M bay, a rz Lbrary,  . v–v, tweth cetry . escrpts: Edward Rehatsek, Ctlogue risonné of the Arbic, Hindostni, Persin nd Turkish Mss. in the Mull Firuz Librry (Bbay: a rz Lbrary, ), –; Sez, Geschichte des r­ bischen Schrifttums: Bnd VI, . I thak r. Sez r prvd cpes r a cr kept  the Isttt ür eschchte der arabsch-sasche Wsseschat, rakrt. ḥaad Akbar awādī a-Ḥsayī, Istīʿāb l­wujūh l­mumkin fī ṣnʿt l­ṣṭurlāb, llfhū Muḥmmd Ibn Aḥmd Abū Ryḥān l­Bīrūnī, d ed. (ashhad: ajaʿ a-Bḥūt a-Isāyya, ), . Kwat, Isac Archaeca se, v. . N , Iterata Istret Checkst () #; Car, se  Isac Art, v. . ,  # = #; see avd A. K, In Synchrony with the Hevens: Studies in Astronomicl Timekeeping nd Instrumenttion in Medievl Islmic Civiliztion,  vs.. . : The Cll of the Muezzin. . : Instruments of Mss Clcultion (Lede: Br, ‒), :–. rvate cect (Swtzerad), c. avd A. K, “Tw ewy scvered Astrabes r ʿAbbasd

  P MPU

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Figu .4 The Plte of Nsṭūlus.

I ctrast t the stret  ʿAī b ʿĪsā, where ° derees represeted e ar th, the ser s td t dvde the ar eat by three. Ths presppses a deret des. As t sees, the astrabe s sppsed t have a stadard scae  tweve zdaca ss wth ° each  ts r. A etre th the s represeted by a arc  ° deree. Istead  a partcar scae  days  the th, the ser s td t tpy the day  the Arabc th by r,  rder t et the desred arc  derees. rther, the ser s td t k p the ar attde  a zīj. Aa, a crcar perrat  whch the phases  the  are dspayed s eted. The des  the pate cssts  tw crces  back cr, ad a crce caed “sphere  the s,” whch s adjacet t the secd crce. The des s sar t that  ʿAī b ʿĪsā, bt the crces are saer  cpars wth the pate, ad cver a sectr  °. The sphere  the S s prbaby paced ppste t the rst back crce (see re .). Ths arees wth the des whch a-Bīrūī ascrbes t the stret  asṭūs  hs

Bahdad,” Suhyl  (): – (–). ha, se  Isac Art, v. . W., c. avd A. K, “A Istret  ass Cacat ade by asṭūs  Bahdad ca. ,” Suhyl  (): –.

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omnn

Figu .5 An nonymous plte for eclipses.

Istīʿāb. Hwever, a-Bīrūī’s descrpt ay cta addts by the ther vetrs eted by a-Bīrūī. A Graphical Device for Eclipses (V) The thrd text t be preseted here s preserved  a eeveth-cetry ascrpt  Lede that ctas a ber  wrks  a-Sjzī, Ḥabash a-Ḥāsb, ad ther athrs. Therere, t sees key that the ays text bes t the teth cetry. It s a shrt text cver e pae. rtatey there s a strat  the ascrpt, whch akes the recstrct easy (see re .). There s  stateet ccer the atera  the devce. It cd be ade  paper, eta, r ther ateras, sce t has  veabe parts. The perats are exected wth a cpass, ad psts  the scaes are arked, prbaby wth wax. The eat  the  r the ar de   9  0 

A-Ḥsayī, Istīʿāb l­wujūh l­mumkin fī ṣnʿt l­ṣṭurlāb, –. A-Ḥasa Ib ḥaad a-Ādaī ad ʿtārd Ib ḥaad a-Ḥāsb, see a-Ḥsayī, Istīʿāb l­wujūh l­mumkin fī ṣnʿt l­ṣṭurlāb, . M Lede, U Or. , . v–r, eeveth cetry . escrpt: Catae, avaabe e at https://scrates.edev. (accessed  Septeber ).

  P MPU

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has t be arked  the scae  the r. ext, the hrztay crrespd pt  the pper scae  the dde  the crce has t be arked. Ths s the ar attde. Ths vae has t be d  the wer cetra scae, whch s dvded t sxty arc-tes. The er ha-crce s caed “sphere  the dra” ad akes the t wth whch a tta ar ecpse ccrs. I the ar attde s reater, the ecpse w be parta, r,  t s reater tha sxty tes,  ecpse w ccr. The stret s spe ad desed r a se ted task. Aa, vsazat sees t be the a prpse, sce r hher precs a erca tabe wd d better ad wd t cver re space. Therere t sees key that t was sed r ddactc prpses. Later Texts on Eclipse Devices The cprehesve bk  the astrabe  a-Ṣūī (– ), whch exsts  three verss, was the sbject  ra aea’s h thess.1 Chapters –  ers T  ar ad sar ecpses cta detaed strcts  hw t d the cdts  a ecpse by eas  a astrca tabe ad a stadard astrabe. There s  descrpt  specazed strets r ecpses. ers S ctas  crrespd sect, ad  vers  chapters  ecpses ht have bee part  the st rst part. The bk  a-Bīrūī (– )  the cstrct  astrabes ctas tw chapters  a ar bx ad a ecpses pate. r the ecpse pate three creatrs are eted: asṭs a-Asṭrābī, a-Ḥasa Ib ḥaad a-Ādaī ad ʿṭārd Ib ḥaad a-Ḥāsb. The des s sar t that whch s descrbed  text , bt the descrpt  ts cstrcts s re detaed ad precse  a-Bīrūī’s text. I hs eta wrk  astrca strets, a-arrākshī (fl. thrteeth cetry ) cded a    

         

ra aea, Les trités d’l­Ṣūfī sur l’strolbe (h.. ss, versty ars —es dert, ). ra aea, “ʿAbd a-Raḥa a-Ṣūī: Stdy  the Lar ad Sar Ecpses wth the Astrabe,”  Nvigting cross Mthemticl Cultures nd Times, ed. I.. adaks ad L  (Sapre: Wrd Scetc, rthc). ḥaad ʿAbd a-ʿīd Ḫā, Kitāb l­ʿml bi l­sṭurlāb li­l­ʿllām ʿAbd l­Rḥmān Ibn ʿUmr l­Ṣūfī (Ḥaydarābād : āʾrat a-aʿār a-ʿthāyya, ), –. aea, Les trités d’l­Ṣūfī sur l’strolbe, –. A-Ḥsayī, Istīʿāb a-wjūh a-ka ī ṣaʿat a-aṣṭrāb, –; see ra aea, “A-Bīrūī: The ate  the Ecpses,” Suhyl  (–): –. A-Ḥsayī, Istīʿāb l­wujūh l­mumkin fī ṣnʿt l­ṣṭurlāb, . See abve ad Appedx C.

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omnn

paraphrase  a-Bīrūī’s chapter  the ecpse pate, bt dd t add ayth ew t t. A abts apprach t a ecpse cpter was ade by hyāth a-ī a-Kāshī (– ). I hs wrk  the eqatr, whch exsts  tw Arabc verss ad a ersa trasat, he descrbes a pate r a eetrca st r the atdes  ecpses ad ther drat. By eas  a rer, erca vaes ca be btaed. Hs a was t cstrct a devce whch ade the se  tabes sperfls, ad he tred t prvde des whch were desed r precs, t y r a cveet vsazat. At the sae te,  Erpe attepts  the sae drect were dertake by Rchard  Ward (– ). A se ate wth ecpse scaes  the qe edeva lbion, cstrcted ater the wrk  Rchard  Ward, has srvved.1 Specased strets desed excsvey r ecpses were descrbed by etrs hea (fl. – ). Based  astrca tabes avaabe ard   ars, he cstrcted a t-pate devce r ecpses, whch he caed eclipsorium. Islamic Astrolabes There s e Isac astrabe that ca ve a reastc press  the rete  the three rst texts: the as astrabe wth a ear echas  Oxrd.

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at Sez, Jāmiʿ l­mbādiʾ w’l­ghāyāt fī ʿilm l­mīqāt. Comprehensive Collection of Principles nd Objectives in the Science of Timekeeping by l­Ḥsn b. ‘Umr l­Mrrākushī,  vs. (rakrt: Isttte r the Hstry  Arabc-Isac Scece, ), : –. Edward Stewart Keedy, Plnetry Equtorium of Jmshid Ghiyth Al­Din Al­Kshi : n Ed. of the Anonymous Persin Mnuscript 75 in the Grrett Collection t Princeton University; Being  Description of Two Computing Instruments, the Plte of Hevens nd the Plte of Conjunctions (rcet, NJ: rcet versty ress, ), –. h avd rth, Richrd of Wllingford. An Edition of his Writings (Oxrd: Cared ress, ), : –, –, –. Re, Osservatre astrc d te ar, c. rth, Richrd of Wllingford, : pate XXV. rtz Saaby ederse, Oper Petri Philomene (Cpehae: Scetas ae et tterar acar, ), –; rtz Saaby ederse, Trcttus instrumenti eclipsium (Cpehae: Isttt d ye-âe rec et at, ), –. Oxrd, se  the Hstry  Scece, Iv. . .

  P MPU

2

The crcar pe s saer tha thse descrbed  the texts becase the ar phases are prdced by a eccetrc whee. Ccer the dspay  ecpses there are y at eches  the devces descrbed  the texts. A astrabe that was acqred by Wy Harter r the rakrt Isttte r the Hstry  Scece has  the back  ts ater a speca scae whch dcates the ar attde r a ve ar eat. As Ske Ackera pted t, ths astrabe was ade  the tweth cetry ad rewrked  the seveteeth cetry. There are tw re astrabes  Oxrd wth sar dess. Oe has the des  the back  the ater, as des the rakrt astrabe. The ther has t  a separate pate. Conclusion The r earest texts  astrabe-ke ecpse cpters tated a seres  attepts t trasr the cpex teac de  ecpses t spe ad easy-t-rasp des. e  these attepts see t reach the ety  Archedes ad hs as be. r ths, we have t wat t the sxteeth cetry  whe Erpea cckakers tred t trp each ther  cpexty. Hwever, eve  sch a tstad pece as the sa eqat cck by st Bür—the rst that prdced eptc veet—we ca dscver a dspay  the ar phases that s ast detca  des wth the ṣfīḥ qmriyy descrbed seve hdred years earer. Spcty ad cpexty ca ve  hary tether; ether  the shd be baed by hstras  scece.

 

       

rakrt, se ür aewadte Kst ( a r rakrt versty),  #, c., Ske Ackera, “tabr: e arbet ees tteaterche Astrabs  . ahrhdert,”  Ad Rdices. Festbnd zum fünfzigjahrigen Bestehen des Instituts für Geschichte der Nturwissenschften der Johnn Wolfgng Goethe­Universtat Frnkfurt m Min, ed. A. v tstedter (Stttart: raz Steer era, ), ‒, ; K as  . , : –. Ackera, . . Oxrd, se  the Hstry  Scece, Iv. .  (Isaha / ),  #; K as  . , : ; Ackera as  . , . Oxrd, se  the Hstry  Scece, Iv. .  (Isaha eary ehteeth cetry ),  #; Ackera, “Mutbor,” . rtz Stadacher, Jost Bürgi, Kepler und der Kiser. Uhrmcher, Instrumentenbuer, Astronom, Mthemtiker, 1552‒1632 (Zürch: era ee Zürcher Zet, ), .

22

omnn

Acknowledgements y warest thaks  t ra aea, wh heped e a t  read the Arabc texts ad prv the trasats. I as thak aes Weaver wh ade vaabe sests t ake the Esh trasats re readabe. Appendix A: ʿAlī ibn ʿĪsā’s Risāla Arabic Version ّٰ   . ّ ‫�ل‬ >‫ّلabc< characters erresy tted by the scrbe, restred r crrected by the edtr. Hwever, sce dts bew etters shd t be sed r Arabc texts, «abc» s sed stead r characters daaed r therwse cear  the text. The sperscrpt bers crrespd t thse  the Esh trasat  rder t actate t cpare t t the Arabc text. The Arabc text ws csey the ascrpt eve  cases where t devates r stadard raar, r awkward phrases ccr. Se r wrt eeets ke haza r shadda are razed accrd t stadard rthraphy.

  P MPU

23

.�   ‫ك‬ �   ،  ‫ ف‬� ، �  � 

  ‫ذ‬ ،�  ّ� ‫ي‬  �  �   ، �   

.�

.ّ �   ،� ‫ك‬  ‫د‬   ‫ذ‬  ،  ّ ‫ي‬  ‫ي‬ 

 ‫ف‬  ‫؛‬� � ‫و‬   ،‫ر‬   ّ  ‫ى‬ ،�  ‫ى‬ ،  . � ‫و‬   ، ‫ذ‬

 � ‫ك‬«    � ‫ك‬     ،� ‫ف‬ 

1 ،� }{   �  ‫ ف‬  .}� ‫ك‬  {  ، �  ‫ذ‬  ّ    ‫»؛‬� «  ‫ي‬ � ‫ظ‬�  ‫ؤ‬ ،� ‫ك‬ ‫ل>ل‬< �  ّ   ،� ‫ك‬  ‫ذ‬  ّ   

‫س‬�  ،      .�     ّ  ّ  ّ   ،�  >.-.< .ّٰ  ‫ء‬  � � 

     ، ‫شر‬    ،�  ‫آ‬ � ‫ف‬ |v|

�     ‫د‬     ‫ف‬  .    ،�  .�  ‫آ‬ � ‫ ف‬   1 ،‫�ل‬  �

   ‫ط‬ ‫ي‬  ،‫ط‬    ّ  � �   ‫ف‬ >< ‫ف‬  .ّٰ  ‫ء‬  ،         ،   �  ‫ض‬

،  ،‫ط‬  ‫ ف‬ ‫ا‬ ،}{     }{

  ،�  ‫ ف‬  ‫ى‬      .ّ‫�ظ‬ ‫س‬    ‫ف‬  .ّٰ  ‫ء‬    

.   ‫ ف‬:‫أو‬ ‫ا‬ 

� ّ  1 ، �     ، ‫ط‬  ‫ا‬   ، ‫ء‬  ّ  ،  �   .� ‫ر‬   ،

ّ �  ‫ظ‬ ّ ‫ث‬ |r| . � ‫ى‬  �  �  

.ّٰ  ‫ء‬  ،� ‫ذ‬      ، ‫ء‬  ،‫ء‬   

� ‫ ب‬ �  ّ ‫ز‬  ،ّ    �  ‫ض‬   ‫ ف‬:‫ثاني‬ ‫ا‬  .‫صر‬   ،    ‾

 ّ �    ،      ،   

  ّ   ّ  ،�  � ‫ ب‬  .  �  ‫غ‬

24

omnn

  ّ ‫�ظ‬    .   ‫ى‬  ‫ غ‬،  �   �

 ‫ط‬  ّ ‫�ظ‬   ‫ذ‬     1 ‫؛‬� ّ  ،�  

}‫ل‬{ .‾ ‫‾و‬ ‾ ‾ ‫ جـ‬ ‾‾  ّ   �     ،� �  ‫ط‬

�    ،  �  ‫ض‬   �  ،ّ‫�ظ‬   ‫ذ‬ ‫ـ‬

 ‾‾  ّ |v|   ّ َ ُ  ‫ ف‬�  � ‫ط‬ ّ  ،�        �  ‫ط‬ ّ  ،�    ‫إ‬  ‫‾؛‬ ‫‾و‬ ‾ ‾ ‫جـ‬

. ‾ ‫‾ط‬ ‾ ‫ ز‬ ّ   � ‾ ‾‫ا‬ ‾ .ّ‫�ظ‬  ‫ ف‬:‫ثا‬ ‫ا‬ 

  ،ّ‫�ظ‬     �  ّ  ‫ظ‬ ،‾ ‫ مه‬  ّ       ّ ‫�ظ‬    ّ ‫�ظ‬     ،‾   ‫س‬  ‫س‬ ّ‫�ظ‬  ‫ء‬  

 ‫إ‬{  ‫ذ‬ � ‫ ف‬ ّ ‫�ظ‬  ّ  ،‾ ‫ مه‬  ‫إ‬ 1 . ‫ذ‬ � ‫ف‬

    ‫�ظ‬  ،     ‫إ‬  .  ّ ‫�ظ‬ }‾ ‫ مه‬ ‾ 

‾ ‾ ‫ ق‬ ‫س‬ ‫آ‬ ،ّ � .ّٰ  ‫ء‬     ،‾

   .‫�ش‬ ّ   ‫ة‬�  ّ  ‫ ف‬�  �  ‫ظ‬   ‫ ف‬:‫ع‬‫لر‬ ‫ا‬ 

‫ك‬    ،� ‫ك‬}{ ><  ‫ك‬ ‫ل{لطل}ل‬ ّ  ،�  ،

   ‫ء‬ ‫ء‬�  ّ�  ّ   ،  ّ�  �  |r| 

� ‫ ف‬ ‫ء‬   ‫ء‬ �  ،    .�  ‫�ش‬ ّ    ،‾ ‫ح‬ ‾ ‫ه‬ ‫ب‬ ‫‾ط‬ ‫‾> و‬ ‫‾} ‾ ‫ل<       ،‫ء‬�  ّ� ،      �   1 ،    �   

1 ،�  � ‫ ف‬  ،‫ء‬�  ّ�   ‫ظ‬  ،�   ‫ك‬ ‫ى‬ ‫ظ‬ ّ ‫ ث‬11 .   

.‫�ش‬  ‫ة‬� ّ �     ‫ ف‬:‫سا‬ ‫ا‬ 1

  ،�    ‫ذ‬  ّ  - �     1   ‫ى‬ - � ‫ك‬ ‫ل{لطل}ل‬ ّ  1 ، ‫ك‬ ّ  |r| ،�    ‫ف‬ ّ  1 .‫حج‬   � ‫ ف‬  ‫ى‬ ‾   �‫ل>ـ‬
�

ّ  ،  ّ   .� ّٰ  1 ، �  ‾  

26

omnn

    11 ‫ل>ل‬‫ل}‫ل{ـ}ل‬‫ل}ل‬‫ل}hw ay derees there are betwee the < ad the asced r desced ar de. 1 I [the dstace] s reater tha  derees, 1 the  w t be ecpsed. 1 I t s ess tha  derees, the  w be ecpsed. 1 Sccess s wth d!

3

  P MPU

1 th Chapter: 1 I y kw that [the ] w be ecpsed, 11 ad y wat t kw hw ch  t w be ecpsed, 1 the tr psde-dw the pate  whch the brt sver s, 1 ad [se the ace]  whch the crce  the  s dvded t tweve parts.1 ext, adjst the rete  [ths] ace, 1 ad br the pe ad the hrse t ther ta psts. 1 Rtate the rete t the crce  the sphere  the s s adjsted  crece t the crce  the , 1 s that th s vsbe r t. 1 ext, rtate the rete t the dex  the dra as  the dstace betwee the  ad the ar de. 1 I [the prcess ] that, the crce  the s (recte  the dra?) s ved away r the crce  the , 1 ad the atde  the ecpse s shw  the crce  the ; 11 ths w be the atde  the ar ecpse. 1 derstad that! 1 I the crce  the  appears etrey bew the crce  the dra, 1 the  w be etrey ecpsed. 1 I seth  t reas cvered, ths s the at  what reas ecpsed  the . 1 Kw that, ad easre accrd t t. I t s etrey ecpsed, 1 the atde addta t that shw  the crce  the , crrespds t the drat  the ttaty dr the ecpse. 1  have eared by that the atde  the ecpse ad the [drat  the] ttaty wtht cacat ad pa,  d wshes. 1 Wth H s the dace ad the eadershp  the rht way. 1 He s scet r s; a st exceet arda. 11 The cetary  the se  the ar pate, attrbted t ʿAī Ib ʿĪsā a-Ḥāsb—ay the Exated d have ercy p h—has bee cpeted. Appendix B: Anonymous Redaction of ʿAlī ibn ʿĪsā’s Risāla Arabic Text1   ّٰ   

 � � �  

  ،ّ   ، ‾     ،     ّ   

‫؛‬ّ � ‫ى‬  ،    ‫ء‬  ‫ء‬ ‫ت‬    ، ‾   ‫ر‬  ‫ ف‬ّ �   ‫ذ‬  ّ   ّ ‫ ث‬1 .ّ‫ط‬ ١٤   

 

The sperscrpt bers crrespd t thse  Appedx A. assaes whch d t ccr  the rer text are dcated by a secd ber separated by a dt.

32

omnn

  �      ،‫آ‬ � ّ 11.�  ‫ظ‬   

  1 ،  ‫ذ‬    1 .� �   ‫ة‬� ‫ خ‬ 1 ،  ‫سر‬   1 � 1، ‾ ‾   � � ّ ‫ ث‬. ‾ ‫ و‬1.1  

 1. ، ١٢  1.1 �     ّ   1 ،  ‾  ‫ى‬   ّ ‫ ث‬1. ‫ة‬� ‫ى‬ ،‫ظ‬ ‫ة‬� ّ  �      ، ‫كد‬

 1،�  ‫ ف‬ ّ  ّ  1 ،   ١٢     ،�  . �  ‫ط‬ 

.‫م‬ � 1

."�   ‫ك‬"   ،‫ط‬�   ،  ‫ ف‬� � 

.�  � ،‫ء‬�  ّ� ‫ي‬  �  ‫ذ‬  ّ   �   

 ‫ذ‬  ،>  ّل‬‫ل}،  <    .�    ‫ء‬ ‫ء‬�  ّ�  ّ   ،  ّ�  � 

 ، ‫ ف‬،� ‫ ف‬ ‫ء‬   ‫ء‬ �  ،  ‫آ‬  ،>< ٣٠ ‫�ش‬   1 ‫؛‬� ‫�ش‬ ّ   ‫ي‬ �  

ّ   ،‫ئ‬  ‫ء‬ � ّ  >< ٢٩ ‫�ش‬    ، 

  ‫ظ‬ ،�  ‫ى‬  ّ �    ‫ذ‬   ّ   ‫ء‬   ‫ى‬ �    ‫ظ‬� ،   ّ �    . ‫ة‬� �  � ‫ف‬

 ّ  �  >< ‫ك‬      ‫؛‬ ‫ى‬ � ‫ ف‬ ّ ‫ ث‬ ‫؛‬

.� ‫ك‬

  ‫و‬   �   � ‫ ف‬�  � ‫ ف‬  ‫ ف‬ 1

  ،‫ر‬  ‫ ف‬ �     �    ،�   ،‫ء‬�  ّ�  �   ‫ك‬ ‫ ف‬    ‫؛‬�    

1 ،  ‫ ف‬�      ،   . �     

 ّ�    ‫؛‬�   ‫ك‬ ‫ى‬ ‫ظ‬ 11 ،   �  

.�  � ‫ ف‬  ،‫ء‬� |v|

.   �  ‫ ف‬ 1

 ‫ف‬    ّ  ْ �   1 ،‫�ش‬  ‫ة‬� ّ  

� ‫ء‬  - � � ‫ك‬ ‫ط‬ ّ  1 ، ‫ك‬ ّ ،� �     ‫ف‬ ّ  1 .‫حج‬   � ‫ ف‬  ‫ذ‬ ،‾  

34

omnn

1 ، ‫س‬  �   ّ  � ّ ّ‫ ث‬1 .‫ء‬  ‫ ف‬ 

  ّ  11 ‫؛‬�   ّ  ‫ة‬ ‫ى‬ ‫ظ‬ 1 ، �     

   11 . ّ  ‫ و‬111 :  ‫ ف‬  11.1 ،�    ‫حج‬  ّ ‫س‬   ّ  ّ  11 ، ّ    �    � ّ 

ّ      �    11 . �  ‫ �ل‬11 ،

‫؛‬ �     ،‫آ‬    ّ  ‫ة‬ ‫ى‬ ‫ظ‬ 11 ، .  �      11

�  �     ‫ ف‬11

 ّ  1 ،‫�ش‬ ّ   ‫ض‬   �   11 .‫�ش‬   1

 ‫ى‬   1 .  ١٢   1 ‫؛‬ �     1 ‫؛‬�  ّ  1 ،‫ ع‬   1 ،�  �  ّ ‫ ث‬، ‾ 

.‫ض‬    �

ّ     ‫ ف‬11

‫؛‬  ‫د‬  � � ،   �  ّ 1 ‫ي‬ � �  1،ّ  11 . ،ّ  ١٢   1 |r|

1 . ١٢  �   1 ،‫آ‬ � ‫ى‬ >  ّ�ل‬‫ل}ل‬‫ل}
ل‬‫ل}< \]..[/   >< }‫إ‬{ 1 .�  ‫ل>ل‬‫ل}I y wat that,< rtate the rete t the sphere  the dra as  the sphere  the s,  ad the dex  the ht  the   the bred sver,  ad th  the whte sver s shw r the he  the dex  the .  Whe y have de that, tr the rete by e  the parts atted  the rete,  ts r, a the dvss  that crrespd t the bers  the days  the ar th, 1 whe the th has 30 [days], ad  the ther sde  the r,  whe the th has 29 days. Whe y ve the rete by e  ts parts  a that the part s aed t the e  that es t r the sspes ad es twards the dde  the pate, the ht  the 

  P MPU

37

at e [partcar] ht w be shw t y.  Rtate [the rete] kewse t bserve the ht  the  each day, t t beces  .  Ater that t starts wa t essess.  The crce [dcat] the ht  the  ay tr, t t stcks t the sphere  the s. 1 Sect: T kw the ated [part]  the   the hrs at day r at ht  I ts rs s at a hr dr dayht,  pt the dex  the hrs  e  the dayht hrs atted  the et qadrat,  r [pt the dex]  what hr y wat. The [part]  whte sver that y have d t be vsbe  the crce dcat the ht  the ,  w be the extet  the ated [part]  [the ].  I the sae way,  y wat t kw the ated [part]  t [whe the  rses] dr the hrs  the ht, 1 pt the dex  the hrs  the hrs  the ht 11 ad k at the crce dcat the ht  the . The vsbe [part]  whte sver [depcts] the ated [part]  the . 1 Sect: T kw at what [te] the  sets I y wat the rst ht  the th, 1 pt the dex  the —that s, the e whch starts r the extretes  the pate  the rete ad passes thrh the sphere  the dra 1 t t cts the crce  the s dvdes the  t tw haves (recte the crce  the ht  the ?)—at the be  the ber   whch s at yr rht  the pper ha  the b. 1 Ths, the dex  the ht  the  ces t yr et straht ppste t t. 1 ext ve the rete t the dex  the  as p the dvs, 1  whch s wrtte “dex  the ht  the ” (recte “”?)1 ad bserve the tersect  the e  the rete; 11 t as p [the te] at whch the  sets. 11.1 It is written on the rst [comprtment] t your left: 111  [that s] sx-seveths. 11 Oe w prceed kewse by v the rete ad pac the dex  the   the ber  the days ad ther haves, 11 [r] each day, dvde the t  the b t tw parts, 11 s that the day cssts  tw haves. 11 Whe y pt the dex  the   the days ad ther racts y wat, 11 bserve  whch a the hrs ad ther racts the tersect  the e  the ther sde as; 11 what ths shws, w be [the te] whe the  sets at ht. 11 Sect: T kw at what [te] the  sets dr dayte 1 Ths happes ater the dde  the th. 11 t the dex  the   [the dvs crrespd t] what passed r the days  the th. 1 The e ppste t t as  the hrs ad ther racts. 1 Aways sbtract

38

omnn

tweve hrs r that.1  wrk sary p t the cpet  28 days, the the  es der the rays [ the s], 1 ad  wrk reas r t, 1 t t detaches tse r the s; 1 ater that the wrk prceeds wth that [sary]. 11 Sect: O the kwede  the r ad sze  the ar ecpse. 1 Lear rst r the astrca epheers hw ay derees are betwee the dra [ e sde] ad the s ad the  [ the ther sde] at the te  the ppst. 1 I there are 12 derees r ess, [the ] w be ecpsed.11 r d the atde  [the ecpse] 1 tr the pate  whch the bred sver s  the ther sde, 1 ad [se the ace]  whch the crce  the  s dvded t 12 parts. 1  adjst the rete  [ths] ace, 1 ad y br the pe ad the hrse t the ta pst. 1  rtate the rete t the crce  the sphere  the dra  the rete cvers the crce  the  1 cpetey, s that th s vsbe r t. 1 ext, rtate the rete t the r/extrety  the dra as  the dstace betwee the  ad the dra. 1 The crce  the dra ves away r the crce  the , 1 ad the atde  the ecpse s shw  the crce  the ; 11 ths w be the atde  the ar ecpse. 1 I the crce  the  appears etrey bew the sphere  the dra, 1 the  w be etrey ecpsed. 1 I seth reas cvered, [t shws] the at  what w t be ecpsed  the . 1 The atde addta t that shw  the crce  the , crrespds t the drat  the ttaty dr the ar ecpse. 1.1 Section: On the knowledge of how mny digits will be eclipsed 1. Look how much the sphere of the drgon cuts of on the divisions of the circle of the moon, which re . 1. Wht it is, will be the number of the eclipsed ngers of [the moon]. 11 [The chapter] eds—d kws best. Appendix C: Epistle on the Practice of Using the Plane Lunar Astrolabe Arabic Text ‫ …»ل‬« ‫ة ف‬

‫و‬‫ط‬  ّ  �  ‫ط‬�   ّ  ّ  1

    ‫ ف‬‫ط‬  �‫ط‬� 

ّ ‫ر ع‬     � ‫�ل‬ ‫ ع‬  

  P MPU

3

 ‫�ط‬        �  ‫ؤ‬

.ً    ��   

‫ء‬�   ‫ ف‬    ،�   �        �    ‫ظ‬ 1 ،     ّ  ‫ ف‬، ‫�ظ‬

.     ‫ ث‬11 .  ‫ء‬�   �    ‫ ف‬� ّ ‫ظ‬�  1 ،�    ّ  ‫ ث‬1

 ‫د‬  ‫و‬  ‫ى‬ 1    ، "� " ‫ي‬ ّ َ ُ

‫ى‬ ‫ظ‬ ،   1 .‫ظ‬ ‫ذ‬ �  ‫حج‬ 

>< ّ   ،    ّ  ‫ ف‬،� 

4

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ّ ،  ،     ، ‫ز‬

‫ظ‬ ّ ‫ ث‬ .ّٰ   ‫�ل‬    ،  

،     �    . � 

‫ذ‬       ‫ظ‬ ّ ‫ ث‬ .  �  ّ 

 ‫إ‬  ‫؛‬ �  ّ  ، ‫شر‬    ّ    ّ   . 

.ّٰ    �     .  ّ  ، ّ ‫ ث‬1 ،‫ظ‬ �‫لل‬�        ‫إ‬ 

�  ‫ظ‬    � ‫ ف‬‫�ل‬  

  . "�  � ‫ء‬" �  ‫ ف‬ ّ َ ُ

 ّ ‫؛ ع‬� ‫ك‬     ‫ك‬ ‫ى‬ ‫ظ‬ ، 

     ،�      ‫ذ‬   

[.v] ‫ك‬    .�    ‫ذ‬  � ‫ك‬

  ، ّ  ،  ،   ، ‫شر‬  �

   ،  ‫إ‬  .     ،  � 

   ،ّ   �  ّ  ، � ‫ك‬   ‫ك‬  ،  � ‫ء‬  ،    ‫إ‬  ‫؛‬ ‫ى‬ ‫ظ‬ ،  ‫إ‬ 1 .ّ     ،

‫ى‬ ‫ظ‬  ، ‫ك‬ ‫ ف‬‫ظ‬   ،‫ء‬    ّ َ ُ �  ‫ة ف‬ �    

  ‫؛‬ ‫ت‬  ّ   . "‫ء‬  " ‫ي‬

،‫�ل‬    ‫ص‬     

 ّ ‫ ث‬ .‫�ل‬ ‫ء‬     ،  

   .‫ء‬      ،‫�ل‬   

    ‫�ل‬ ّ   ،

 ‫ى‬ ‫د‬ ّ     .‫ؤ‬   ‫ غ‬ 

ّ‫ط‬     . ّ   ّ  � ‫ف‬

‫�ل‬ ‫ ع‬‫ي‬  1 ،‫ط‬ �‫ط‬    

.ّ  ‫ة‬   . ‫ل> ل‬ des t< vary wth the attde ad there s  dspte  the Zījes—start wth the adjstet  the te  the tre ppst  ad d t. I there s a ecpse, ths w be the te  the dde  the ecpse,  the cad  d.  ext, csder the attde  the  ad d t t.  I the attde s reater tha sxty-r tes, the  w t be ecpsed.  The bserve hw ay derees are betwee the deree  ppst ad the asced ad desced de.  I there are ess tha tweve derees, the  w be ecpsed,  ad  there are re, t w t be ecpsed.  Ths s eqvaet t yr rat abt the  ad s cred wth the ccess  d.  I y have d the dstace betwee the deree  the ppst ad the dra, reeber t, 1 the pt the dex  the ecpse  the pate at the eqvaet  what y have reebered a the eerat scrbed  t “derees  dstace r the  ad the de”  the er part  the pate.  Whe y have de that, k, hw ch the sphere  the dra has cvered  the sar dsc;what s cvered  t  w be (the part)  the bdy  the  that w rea t ecpsed,  ad the vsbe (part)  the sar dsc s that whch w be ecpsed  the bdy  the .   had dvded the sar dsc t tweve dvss,  ad these are dts that aw y t kw, wheever y set t p, what w be ecpsed  the   dts,  ad what reas w t be ecpsed.  Whe y ear that,  the sphere  the dra des t eaate/ stad t r the sar dsc, the  w be ecpsed etrey,  bt there w be  drat r the ttaty.  I there s se dstace r t, the ttaty w be easred  hrs by the easre  the derees that crrespd t the dstace r t, d w. 1 Whe y have de that, k at the dex  the hrs  ttaty ad eers,  whch s a spter  the sphere  the dra,  ad bserve where t as a the dvss  the hrs cstrcted  the er part  the pate,  whch “hrs  the ttaty ad eers” s scrbed.  I have detered the wth ther tes.  Sbtract the dcat  hrs ad tes r the te  the dde  the ecpse, that s the te  the ppst; the reader w be the te  the be  the

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  P MPU

ecpse.  The add t t the te  the dde  the ecpse;  the s w be the te ( the ed)  the eers.  Whe y have de that, y kw the atde  the ecpse, the te  the start ad ed ad the drat  ts ttaty wtht cacat ad rther act.  It s perata r the be  the ae/ae t ts ed at a attdes, ad t s adjsted t the wshes [ ts ser].  It s a vatve pate that ḥaad Ib ḥaad, wh s kw as asṭūs a-Asṭrābī, ade as a pa [pate]. 1 He added the perat ccer the ecpses ad the respectve kwede t t.  It was t ade bere the year ehty ad twhdred  the Hjra ( ).  The epste was cpeted wth the prase  d. Appendix D: A Graphical Device for Eclipses—Arabic Text . r:   �   ‫ظ‬    ، �    .  ّٰ   1

}{‫د‬  ‫ى‬      ،   .‫د‬ ‫ ف‬ ‫ط‬  ،‫ذ‬     .  �     ، ‫ء‬   

  >< }�{ ‫د‬  ‫ ف‬   ،  ،‫�ل‬ .‫د‬ ‫ ف‬، ّ   �   �    ،‫ظ‬ ‫ ث‬ .� ‫إ‬ 11 ‫ة؛‬  ّ   �  ّ  ،[] >‫ك‬<  �    1    ،   � ‫ظ‬ 1 ،‫�ظ‬   ‫ك‬    

    �  ّ  >< ّ‫إ‬ 1 .ّ  �  ،‫د‬   � 

،  1 ،   ،ّ   ّ  1 . ّ   ّ  

.‫ى‬ ّ ‫ء‬ 

English Translation A pate r whch e kws the attde  the  ad the atde  ts ecpse  a eetrca way (see re .) 1 I the ae  d, the erc, the Cpassate.  Kwede  the attde  the  ad ts ecpse.  [T kw] that, y k hw ch [the dstace s] betwee the  ad the asced r desced de, ad y seek ts eqvaet  the crce. Whe y ce t t, pt yr er  t.  Eter t [the scae that s ] the dde  the crces, whch [scae] s dvded t r ad ha derees.

44

omnn

 The ber y cae t s the [ar] attde.  I y wsh t kw the ecpse, take a cpass ad pt e  ts pts  the ceter  the crce pe t wth the qatty  the attde  the .  ext k  the crce, where the [ther] pt  the cpass as  [the scae ] the attde  the , whch s dvded t sxty tes [whch s] sde the crce. 1 I the attde  the  s sde the [crce ] the dra, the  w be ecessary ttay ecpsed. 11 I t as tsde the crce  the sphere  the dra ad the crce  the shadw, 1 k where the cpass as  t; ths w be the ecpsed part  the  crrespd t ths crce; t s stabe r a cates. 1 Kw that the  s t ecpsed ess ts attde s ess tha sxty tes. 1 The re t s ess tha sxty, the re the ar ecpse s reater. 1 Kw that—d the Ahty w!

 

The Astrolabe Finger Ring of Bonetus de Latis: Study, Latin text, and English Translation with Commentary Josena Rodríguez-Arribas

Istitut ür Jüis tui Wstäis Wims-ivrsität, üstr [email protected]

Abstract  sujt  tis rti is t trtis  t str ri (/) y tus  tis (J  Immu rvz).  trtis s t  ur-turis triti  Jwis trtiss  t str, writt miy i rw  mr rry i Ju-Ari, Ju-pis, pis,  ti,  pru msty i sutr urp  urky. tus’s txt is t s trtis writt i ti y  Jw, wi Arm i zr’s trtis  t pispri str (Ru ). y purps is t mpr it wit tr tmprry trtiss  simir istrumts  wit  itt rir trtis  t str i rw (y iyu   tt, tt tury) i rr t urst t triuti  tis istrumt  wy t trtis ws s iy rr m tus’s tmprris.  istrumt pit i tus’s kt   sir   t st triutis  Jwis utur t t istry  t str; ts triutis strt k t t rst rw writis  t istrumt i t twt tury.  ti txt  t is trsti r iu t t   t rti ttr wit t ti txt  trsti  t st vrsi  t itruti t t trtis.  tts  t trtis r xty t sm i  itis  tus’s txt, ut tr r tw vrsis  t itruti   is r  mr mpt t t tr. I v us t vrsis i my stuy, t  i t vrsi prit, m trs, i  (srtr)  t  i t vrsi  t trtis prit, m trs, i  (r).

Keywords tus  tis (J  Immu rvz) – str r ri – str – Jwis strs – miv  Riss strmy – tt-  sixtttury Rm Jws – Jwis siti itrtur i ti © koninklijke brill nv, leiden, �9 | doi:0.63/9789004387867_005

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-

Introduction tus  tis r J  Immu rvz m w kw i t Riss r  srt trtis   spi typ  str tt ws s  r ri.  v it t miuus ti m  Anulus astronomicus  it it t p Axr  (Rri ri) i /. tus ws r, s is m susts, i tts (r i Aix--rv, ri t sm), s t tpir  its mus s  mii, ru t yr , it  imprtt miy  pri rii.  wrk i rv s  pysii  mrt, ut i  r  tus mv t rptrs (t r rm tpir), pssiy u t t irsi prssur tt t rriv  my  t Jws xp rm pi ws putti up t Jwis muitis  sutr r. At tis tim  s puis is k Anulus astronomicus,   istrumt tt  pry ivt r vi r. It sms tt r i t rptrs  s sty i is r  yr, s  s si y im i vmr  iits. Ari t uzzti, t trtis wu v  writt, r t st is, i is,  ity i wi  wu s v m t tts ssry r vi t wrk prit i Rm, m tm ivi ri, s  p Axr ,  ivi  ii, w wu tr m p  X. tr tus t r, mv t Rm,  stt i t Jwis Qurtr  t ity,  t tr si  t ir (rstvr) r t riius ri,  m pysii t p Axr  (ri),  tr t p Juius  ( Rvr)  prps p  X ( ii). p Axr  rt im t rit t prtis mii s “rtium t mii tr” , s  ws  riius m rspt i is mmuity,  m t ri  pssiy s t ju (dayyan)  t Rm Jwis mmuity. I t strmi ri itrus us t tus s  iius spirit, is stri pritis (writt i ti  Iti) ut t ttti  t Jwis  risti mmuitis r y Rm, spiy is rst  t rriv  t ssi r t yr , prit i  i Rm. tus i, pry i Rm,   . uzzti, “t  tts  is  ,” Italia – (): –. 2  Rri t Jws i Ity, s Rrt , Jewish Life in Renaissance Italy (rky, C: ivrsity  iri rss, ), spiy –;  Rrt , Rabbis and Jewish Communities in Renaissance Italy (xr: xr ivrsity rss, ).   As rrs tus’s i  wrks, s ritz tisir, Mathematik bei den Juden,  . (isim: r ms, ), ; i Rt, The History of the Jews of Italy (ipi, P: Jwis uiti ity, ), ; i Rt, The Jews in the Renaissance (w rk, NY: rpr & Rw, ), –; R. . utr, The Astrolabes of the World (xr: xr ivrsity rss, ), :–; A. i, Il Ghetto Di Roma (Rm: trii, ), –, ; i ir  p, Archiatri pontici ebrei nel

T  Fn n  Bn  L

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smtim tr y , ri t spsit, r i  i t mm t  Rui’s ttr is t  pt. r is txtu vi tt wi i Rm,  ws i tt wit svr imprtt srs  t tim: t r ti  umist Jqus èvr ’Étps (. –); t rm umist  kist J Rui (–), w rss  ttr t im ski r t prtti  p  X;  rs  vs (–tr ), t r mtmtii  isip  èvr.  vs  ims  itru t tus uri is sty i Rm i , r  ws urius ut t strmi ri ivt y tus  wt t s it. Ari t is w txtu tstimy,  i s it, wi ms tt tr ws   ri Rinascimento (ttii rm: irii, ), –; . smit, “t  tis  i sui sritti tii  itii,” i Scritti in memoria di Enzo Sereni, . . rpi, A. i,  .  (i: rusmm, ), –; J. . ri, “t  tts, méii, stru t strm u pp,” i Ecumenismo della cultura, , L’umanesimo e l’ecumenismo della cultura. Atti del X convegno internazionale del Centro Studi umanistici, Montepulciano—Palazzo Tarugi 1977, . . rui (irz: ski, ), –; A spsit  i ri, “ str  i sui prstii: t  tts  Rm    Quttrt (i rzi  . ri),” Materia Giudaica: Rivista dell’associazione italiana per lo studio del Giudaismo . (): –; i rpi, “t tts,” Encyclopaedia Judaica, . r kik,  . (trit, M: mi Rr, ), :–;  iè Iu-Au, Régine-Catherine et Bonet de Lattes: biographie croisée (ris: r, ). I wu ik t tk Ams u, w prvi m wit  py  smit’s rti. tus’s stri pritis r t wi ri t t Gesamtkatalog der Wiegendrucke: rstik ür s Jr /, t. [Rm: Ars rit, it vr .., it  ..], °; rstik ür s Jr /, it. Rm .. [Vi: iysius rtus,  ..], °; rstik ür s Jr /, t. [Rm: trus  urr, vr ..], °; rstik ür s Jr /, t. [Rm: trus  urr, it vr .I., it  ..], °, tu vi i t ttp://smtktrwiruk./s/A.tm (ss  rury ).    tis ttr i is rw  ti vrsi i ri, “t  tts,” –.    t siti tivity  r Jws ivi i Ity  r, s rr R. sti, “ rw Astrmi riti: w urs,” Isis . (): –, spiy . u sti’s rti uss  ts Jws usi rw r tir txts, tr is s  ri mti  tus’s strmi wrk. 6  Questionum theologicarum libri septem, , . r (Dialogi de trinitate): “’mm [i.., tus] us répit qu ’u s truvit s s mis. t mm us ’ étis ps très éiés, us us y rîms âtivmt  s mpi pur y vir ’jt. Ars i srtit ’u ’u rt, t i m s vux” ( vs’s wrs i ri, “t  tts,” ). Ari t tis tstimy, tr wr t st tw str r ris:  tt tus r t t p   tt tus kpt r ims (vry iky t m) , wi  vs sw.

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-

mti t sripti i tus’s trtis, tu s r s I kw tr is  xtt ri mti it.  t tr , rri tus’s stri tivity, t Jwis rpr  pmiist Arm  rki riss (Avi –) viurusy ritiis is pritis i is Magen Abraham (Vikkuaḥ ha-dat). vr mtis i tmprry itrtur  tstimis ut tus’s strmi wrk iit is rt ppurity.  ppur r pt  pywrit irr riir (. –) rrs t im i is py La sottie du prince des sotz s  pysii  strr. im  rs s rrs t tus’s stri pritis i is Elucidaire d’astrologie (. ),  rçis Ris i t twty-rst ptr  is Gargantua and Pantagruel rrs t im s t Jwis pysii  t pp. spit t rmus ppurity  tus’s str trtis i urp  t my prits  tis wrk uri svr s, t triti  tus  is str trtis i rw surs is -xistt s r s I kw. The Treatise on the Astrolabe Finger Ring (1492/1493)  strmi kt  t str ri is writt i  iisyrti ti tt tus s mp t xus t t   is trtis, xpii tt is tiv u is rw: “r, prr, ruius qu sut rrt ti. x r mii st, iu ti mius.”  prs  miti struturs is stt truut t trtis wit t  xpti  t piu, wi is t rm iti  t txt t p Axr .  trtis ppr i svr itis  ws rprit svr tims  r wit tr strmi trtiss y irt utrs (Js rs, èvr ’Étps,  J ryr, m trs): i /, , ,    (Rm),  (Vi), , , , , , , , ,    ( i ris),  y i  (rur),    (ris).  umr  itis  t ir  t strmi wrks wit wi tus’s txt ws prit (s  .) iv us  i  t suss   

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 riss, s vi . Rurm, The World of a Renaissance Jew: The Life and Thought of Abraham ben Mordecai Farissol (iiti, OH: rw i  rss, ), spiy    (ri pritis  t rriv  t ssi i ). A. iy, Le jeu Prince des Sotz et de mere sotte (ris: mpi, ), . J-tri ut, Simon de Phares, Elucidaire d’astrologie, Recueil de plus célebres astrologues (ris: iriri ré mpi, ), :–. rçis Ris, Gargantua and Pantagruel, trs. ir ms rqurt  tr Aty ttux, itr. i R (w rk, NY: rs & , ), .

T  Fn n  Bn  L

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prsti  t wrk m is tmprris  v tr. r ur stuy, w v us t  iti, prit i ris y uium vt (tiv –)  simir t t iti   prit i rur, i wi tus’s trtis is u wit tr trtiss  anuli astronomici y irr usr (–), mm risius (–), J ryr (– ), urr itr (–), r ié (–),  Js Rimtus (–). tus’s trtis,  is istrumt, r t rst  t y  tir ki s r s I kw,  ty rmi uiqu i

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urr u rm is stuy  ry prit trtiss  strs tt tus’s trtis ws t txt wit t rst umr  itis i t tw--- turis w ks ut strs wr puis. urr ut it itis  t Auus, wit tölr’s uiti … strii immity tr it wit tirt itis. wvr,  s stts tt “t i umr  itis  tis srt txt rsuts rm it vi m ustmry t iu it i tis  trts  strmi sujts,” s A.J. urr, “rm rss t xt:  urp Astr i itrtur  rit,” i Astrolabes at Greenwich: a Catalogue of the Astrolabes in the National Maritime Museum, . Kr v mp (rwi: xr ivrsity rss  ti ritim usum, ), . I y s, t ri ws mus m tus’s tmprris, s  vs’s tstimy sws. Annuli astronomici: instrumenti cum certissimi, tum commodissimi, usus ex variis authoribus, Petro Beausardo, Gemma Frisio, Ioa[n]ne Dryandro, Boneto Hebraeo, Burchardo Mythobio, Orontio Finaeo; una cum Meteoroscopio per Ioa[n]ne[m] Regiomontanum & Annulo non uniuersali M.T. authore, Lutetiae: Apud Gulielmum Cauellat, 1557 (P. Beausardi Annuli astronomici usus—P. Beausardi Geometricae scalae usus—Usus annuli astronomici per Gemmam Frisium—Annulorum trium diversi generis instrumentorum astronomicoru[m] co[m]pone[n]di ratio usus … Per Ioan. Dryand.—De compositione meteoroscopi, Ioannis de Regio Mo[n]te epistla ‒ Boneti de Latis. Annuli astronomici utilitatu[m] liber—Compositio alterius annuli non universalis, sed ad certam polarem elevationem instructi authore. M.T.—Annuli cum sphaerici tum mathematici usus et structura, opera D. Burchardi Mithobii—Orontii Finaei. Compendiaria tractatio de fabrica & usu annuli astronomici). I wu ik t tk Kirst v r V  t ir irry  t istry  i  y t t mitsi usum  Amri istry (Wsit, D.C.), w st m  iit py  tus’s trtis.  Is ti, “ Astrmi irms i r ié’s Protomathesis (): ui  r riti?” Journal for the History of Astronomy . (): –, spiy . Annulorum trium diversi generis instrumentorum astronomicorum componendi ratio atque usus (rur: rvirus, ; r-puis i ris i  wit sm sm s: t rii iti  tus t t pp ws rp y  txt pssiy writt y t itr  ryr).  ri, “t  tts,” .

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svr rspts. is mks tm  xpti tstimy ut strs  strmi ris uri t i As  Riss, , mr ty, t txt is  vu sur  irmti ut Jwis si  utrsip  strmi istrumts, spiy strs. I t iti  , tus’s trtis s  srt itruti (mu srtr t t  i t / iti) iti t txt t Axr , pus tirty-tr ptrs xpii w t us t istrumt,   piu i wi tus prsts is wrk t t pp  piss r is  ti. is piu ( t  itruti i t iti  /) must v  writt r rrt y tr prs, r t u  sty r vry irt rm t rst  t txt, wi is istitiv r t miti ilu  its sytx.  trtis s ius  wut  t  

6 

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rs urtt irm m tt t t ritis irry tr is  trtis   rt istrumt ( rry r ri). It is  itt kt   is i t Ry ti  t ritis irry (Ry ..XX),  ty writt xpti  t us   “rry ri.”  iti is s ws: “rissim ivitissimi ris i mi izt Virii mius tur rtuqu tius rtissim uimus ukus prprtum ptt iittm.”  iipit  t itry pr is: “ si rti vtrs pispi…” uky s  t xpi tt  m r itrst i utur tur vts (isss, rps t.)  s v vis strmi istrumts t prit tm. “Itr qus uis rriis pstrmus us  rt triuus, prtim qui mm smpr t si msti i iitis prtri pssit.” is anulus, t, is ry mt t  wr s  ri.  itry pr s y ivi t p  t  writi: “x Ri trii i (Ki’s , mri) o  Apriis .”  txt is: “Quim ui rrii riququ uius ris strmi istrumt …” I tk rs urtt r prvii m t sripti qut v. I v us t tw pssi rms  t ti trm r ri annulus  anulus truut t rti, si t tw rms wr us i t Riss ( i ssi  iv ti txts). wvr, w I m t quti txtu surs, I prr t rm anulus (wi is y i t  itruti  tus’s trtis), wi is mr rrt.  Ar rut  Ati it, Dictionnaire étymologique de la langue latine. Histoire des mots (ris: Kiksik, ), –. wvr, utr ssi it m t Iti strs, r it ws si t  us i Ity.  Astrolabes of the World, . utr s stt tt it u  si tt tus ivt t quivt   wrist wt wit is str r ri. Ibid., . Wt ws r sm xmps wit rw sytti prs (i itis). ()  rptitiv us  t ti postea (ti: postea, rw aḥar kaḵ) t t ii  sts: “Postea sut mitrt qui sut i mitt irui supriris sripti, qurum quim itri pprt, quim imprti … Postea i mii i, qu st i ss  ru … Postea i iruitu suprii i spissitui ius …” (); rw pr (aḥar kaḵ): '‫עוד אחר כך תחלק הש“ס לי“ב חלקים והוא שתתן לכל חלק ל‬ ‫עוד אחר כך תוך אותה העגולה על זולת מרכזה אלא‬. ‫ עוד תכתוב עלהם הי“ב מזלות‬.‫מעלות‬

T  Fn n  Bn  L

51

rii str ri, wi sms t  t y xtt im  t ivti (iur .). is im  t sripti  t istrumt prv tt t str ri is quit irt rm t str strmi ris (iurs .–.) sri i tmprry txts, tu mst  tir ppitis r prtiy iti.

FGUE .1 Bonetus’s astrolabe ring (Dryander, Annulorum trium [...] ratio atque usus, Marburg, 1537).

 

‫במרכז קרוב למרכזה תעגל עגולה אחרת קטנה ממנה שהיא במקום גלגל יוצא המרכז של‬ ‫אחר כך תעשה מעצר אחד ישר בתכלית היושר‬. ‫( השמש‬it  t str, MS  , . ). ()  us  t sujutiv (ti: si velis, rw: ʼim raṣita) i t prtsis  t iti st: “Si velis sir um sis i qu si st t i qu rus ius i i i, p um supr im qum s, t t supr qum x rius sirum t um …” ( ); rw pr (ʼim raṣita): ‫ואם רצית לידע אי זה לוח‬ ‫( הוא לוח ארצך ספור המעלות שמהקו השוה עד האפק‬tt  t str, MS  , . ). ()  rptiti  t riti ti juti et (rw vav) t t ii  st: “Et iitium tv st ir su…. Et iitium im st ir qurt. Et iitium uim st ir quit. Et iitium uim st ir sxt (); rw pr (vav): ‫שים מקום השמש תחלה באופק המזרחי וסמן‬ ‫ וספור מה שביניהן‬.‫ ושים מקום השמש שניה באופק המערבי וסמן המורה בתא‬.‫המורה בתא‬ ‫( מהמעלות ותן לכל ט“ו מעלה שעה אחת‬tt  t str, MS  , . ),  s . I iti, t pututi  t ti txt s rvs t ilu  t rw u. Wut  t anulus astronomicus rm . r  t  iti  tus’s trtis (Dryander, Annulorum trium diversi generis instrumentorum astronomicorum componendi ratio atque usus, rur, ), urrty  t t iit tris, ürir ivrsitäts—u siitk i J. I  mprs tis wut wit t wut  t anulus i t r-prit  tis iti rm , wi ispys  sity irt im  t ri, t ttr is pprty mr urt (iur .), tu t tw ims prst prms  itrprtti.

5

-

FGUE . Standard astronomical ring (attributed to Arsenius, 1567, urtsy  t usum  t istry  i, xr, iv. ).

FGUE .3 Dryander’s astronomical ring (Dryander, Annulorum trium […] ratio atque usus, Marburg, 1537). 19

 

 ttp://www.ms.x..uk/tis/sr/ispyrr/?ivumr= (ss  rury ). © usum  t istry  i.

T  Fn n  Bn  L

53

FGUE . Ring dial in the form of a ring with seal (17th/18th century, English, urtsy  t usum  t istry  i, xr, iv. ).

 tts  t tirty-tr ptrs r str i str trtiss  s i trtiss  strmi ris.  . ispys t tts i tus’s txt  i iyu   tt’s trtis  t str, wi is  itt rir  ws writt i rw. TBLE .1

The contents in Bonetus’s text and in Montalto’s treatise on the astrolabe Bonetus de Latis’s ring

 2  4 

  2 

 sripti  t str.  psiti  t su y y.  y w  s t kw t t.  titu  t su.  st r  t st si.

Montalto’s astrolabe

 psiti  t su  t pts i t zi.

 titu  t su t   t titu  t pts t miit.  st, t st, t umiti si  t si i t wr mrii y y  y it.

 ttp://www.ms.x..uk/wp-tt/tms/ms--rspsiv/imu-mi .pp?ir= (ss  y ). r tt’s txts w v w MS  éru  s. –.  t us iyu   tt wit iyu tt, t rtuus marrano w ws r i st r  i i urs ().  ttr m t pysii  ri  éii  wrt svr trtiss  mii  rii ut t  trtis  t str. I m prpri  riti iti  trsti  iyu   tt’s txt.

5 TBLE .1

6  8    2  4 

6 

8

 2

- The contents in Bonetus’s text and in Montalto’s treatise on the astrolabe (t.) Bonetus de Latis’s ring

Montalto’s astrolabe

 twv uss  t sky. i t tim y t r mt.a i t tim i quiti urs. urs ps si suris.

 twv uss y y  y it.  quiti urs y y  y it.  quiti urs y y  y it.  iur  tur ss urs tt v ps. ri  vi twiits.  iur  t tur rs. rt  y iur r tur ss ur.  t quiti urs  t y tt v ps. vrsi  quiti urs it ss urs.

 urti  t y   t it.  urti  t y i ss urs.  urti  t quiti ur. i ss urs it quiti s.  titu  t su i t mrii.  psiti  t su w  s t kw t y. Wi y is qu t tr [i urti].  iti  t sis rm t quiti i (i.. t qutr).  titu  t p.

 titu r wi t ri s  m.  ssis  t sis i t spr rt.

 iti  y rtr r sutr r  t zi wit rspt t t qutr.  titu  t p y y  y it.  itu  t p y y  y it.  zimut is y y. irtis y it.  zimut is y it.

 ssis  t zi sis i t spr rt, y y  y it.

T  Fn n  Bn  L TBLE .1

2 22

2

24 2

The contents in Bonetus’s text and in Montalto’s treatise on the astrolabe (t.) Bonetus de Latis’s ring

Montalto’s astrolabe

 ssis  t sis i y ii riz. siti  t m i t zi witut usi its titu.  st  t t rvuti r  t rvuti  t wr.  rur  t ur y y  y it.  titu  t strs.

 ssis  t zi sis i y ii riz.

26

 r  t st y it.

2 28

 urti  t it.  r  t st witut usi t titu, witut strs y it  witut su y y.  r  t m witut usi t juti.  psiti  t pts. Wtr  pt is sutr r rtr. Wtr  pt is rtrr r irt.

2

  2

 prtis  t yrs  t wr  t tivitis.

 titu  y x str y y r y it.  tim  t risi  y x str y y  y it.  tim  t stti  y x str y y  y it.  tim  t umiti  y [x] str y y r y it.  [iur]  tur rs  y x str.  st, t st, t umiti si  t si i t wr mrii y y  y it.

 ii  t m t t   t mt i t mri.  titu  t pts.

55

5

-

TBLE .1



The contents in Bonetus’s text and in Montalto’s treatise on the astrolabe (t.) Bonetus de Latis’s ring

Montalto’s astrolabe

 it   twr r y tr ti.

 it  yti prpiur t t   t su r tr ti.  pt  yti pr t t sur  t rt.

  I r t iur pri ws ivi i  ur pris ii t miit   rsptivy. I Ity t iur pri ws ivi i  qu urs rk rm t mmt  sust, s ik Akrm  Rrt v t, ttp://www.ms.x..uk/ pt/rti.pp?ArtiI= (st ss  rury ).

As t ist  tts mks r, tus’s trtis is  istrumt-k spiy us  t us  t str ri. r is  xpti  its struti, tu tus mtis t t ii  t rst ptr tt it   m  , sivr, r tr mt, s is usu r ris.  t  tts prsts  miti  strmi  stri utis, wi is t  xpt rm  utr ik tus, w wrt svr prstitis  ws   t strrs wrki r p Axr . It is s kw tt p Axr   is tur wr mst itrst i stri pritis  vur stri sujts  prtis. I w mpr tus’s trtis wit str trtiss  t str i rw (su s tt’s), w  v  ut tt tr s   simpiti  t tts tt r str i tis r, ut tr is  rs r it. m  t typi mpts  str pispri strs r missi i t str ri (r ist zimut 22 

“ urts  Axr , Juius    X s  tir rsit strrs. I , Asti Vspui irm ivi tt tr wr ‘v r six trs’ i t ri urt w wr   isussi ptry  stry.   ts ws Axr ’s vurit strr. W Axr ws sti  ri,   rrty prit tt  wu  y  pp … tus  ttis  spr rr wr sr ri’s strrs.” ttr  Vspui t ivi,  Auust .  Aty J. r, The Machiavellian Cosmos (w v, CT:  ivrsity rss, ), . r tis ttr s Jms . Atkis  vi is (s.), Machiavelli and His Friends, Their Personal Correspondence (K, L: rtr Iiis ivrsity rss, ), ttr . spr rrs (Vi –Rm ) ws  pis isp w m t pysii  strr  p Axr   tr  p Juius .  wrt svr trtiss  mii.

T  Fn n  Bn  L

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is, twiit is, r irt pts  titu), wi mks tir xpti ussry. I iti, p Axr  prsumy wu t v  itrst i sm  t mr spi utis tt wr str i str trtiss. us, tt’s txt xpis w t msur t pt  y jt, t umitis, risis,  sttis  spi strs,  t itu   rti p,   wi r missi i tus’s txt. Axr  ws t  prtitir  strmy ut  Riss m r t ispy is tiv prtiipti i t utur  is tim, wi rtiy iu  si kw  strmy  stry.  tus rrs t t mst prti ppitis  strs i strmy  stry  mpts mst  t tirty-tr ptrs  is trtis wit r xmps usi tmprry strmi  ri t. It must   tt tus itrus mr xpiit stri irmti t tt s (.., t “rurs  t urs,” i.., t pts rui  ur  vry y, r w t  wtr  pt is rtr r sutr  rtrr r irt i its pt, psitis tt v spi itrprttis i stry). m  t uss  tus’s istrumt tt  t mr i tt’s txt r mm i tr str txts.  sripti  t str  t wy t srti t titu r wi t istrumt ws m (. XX i tus’s trtis) wr prt  t tts  my str trtiss,  Arm i zr rrr t t ttr i   is trtiss  t str. I t str ri sms t   str pispri str, wt is tus’s triuti t t   strmi istrumts? I w sir t  itruti i t / iti  t Annulus (Rm), tr r sm iumiti xptis ut t purps  tis spi typ  str  tus’s stimti  is ivti. I t  itruti t t trtis (s ur iti  trsti t t   tis rti), tr r six quttis rm t  stmt, wi r vry siit mi rm  Jwis writr. urtrmr, ty p tis Riss jt i t txt  t ursti  t si  t strs rtristi  t i As.  rst quttis r itru t uri tw ssti is: tr is  kw ir t t kw   (Jrmi :),  t vs r t wrk  ’s s (sms :, :,  :), s t stuy  t vs ps us sst t   t t kw  . “I w wt t kw , w must kw t si  t strs,” tus stts i is itruti. tr  s xpis wy  i t mk  str 2 

 tir rw vrsi  is trtis  t str, MS üzur , . .  s Js Rríuz-Arris, “iv Jws  iv Astrs: Wr, Wy, w,  Wt r?,” i Time, Astronomy, and Calendars in the Jewish Tradition, .  tr  rs urtt (i: ri, ), –, spiy –.

5

-

i t sp   r ri.  i rrs t svr ii quttis t supprt is i: t ri is  xt rmt  t s  pwru  iustrius m ik r  Jsp (sis :),  it is  rmir  t vs  t strs, “t wrk  is rs.” I iti, tus rts is anulus t t ri tt t i prist Ar wr  is rst ttr wit t rstpt  t p (xus :), t tur  purps  wi rmi  vry itriui  trvrsi mttr.  mst pprt vts  t istrumt r s mti, spiy t t   t trtis: it is  sm, prt istrumt, mu sir t mk t trs; it is  utiu  visi rmt, wys vi r us t y mmt;  it is w. tus ws immrs i t utur  t Riss, i wi iuity ws iy priz,  is str ri ws ivtiv i  rti wy  it ws prst t t p i  prsusiv  sutiv rm. Did Bonetus de Latis Invent a New Astronomical Instrument? tus’s txt ws svr tims iu i mi itis wit tr mus trtiss xpii w t mk /r w t us strmi ris, s i t str r ri wr   ts. r r tw typs  ris: t ri i, wi is siy  sui   r ri (s iur .),  t strmi ri i r uivrs quiti ri (s iurs .  .). Ari t rçis rtt, jm -ī’s 24 

2 

It is s  t Aquiti ri i, r it is si tt r  Aquiti r  t r us, ry   , i ut . I v t   t trk w  istri sur r tis ttriuti. Atr pssi m r t r rup  prt su is is pkt r “pk” i.  ttp://www.uk..uk/jys_sit/ps/ pkt_sui.tm (ss  rury ).  us t ri i  susps it rm t  i t su. A m  t su must t  tru t sm  pir i t ri t  smwr m t ur ivisis rv isi t ri.   is   s ri witi t ri s tt it   mv ri t t y  mt t wi t srvti is m.  quiti ri i, w it is ispy, rsms  rmiry spr (its mpts r sri i t xt tt).  ur ivisis r rv  t qutri ri  t mrii ri must  susp ri t t titu  t p.  sr m s tru t   t ir r iti ir  iits tim.  t strmi ri i t tis  t ritis usum (ttp://www .ritismusum.r/rsr/ti_i/ti_jt_tis.spx?jt I=&prtI=) (ss  rury ), © rusts  t ritis usum.  strmi ri sists  tr irs: t utr r t mrii, wit  sk t susp t sm ( urtr vpmt  t ri); t itrmit r t qutr;  t ir ir r t iti.  utr ir tis  r tw ss

T  Fn n  Bn  L

59

txt  t ri sui (rst   t urtt tury) sms t  t rist xtt umtti  tis istrumt i Ari.  t tr , MS  ()  t iitèqu uiip  Arrs sms t ti t st ti txt  t ri i (iipit Ad faciendum anulum, t urtt tury).  ivti  t strmi ri ws ttriut t t mis mtmtii mm risius (–) wit is De annuli astronomici usu (), ut it sms tt strmi ris  is wr i us w r t sixtt tury, ti k t t i As  v Rm  isti tims. ki t t im  tus’s str ri, w  rm tt it is rtiy itr  ri i (s it   mr t t t tim), r  uivrs quiti ri (wi s svr ppitis sis ti t tim  is uivrs). tus’s ri is t uivrs; it is m r  spi p (ik ri is),  ti t tim is just   its my ppitis (ik uivrs quiti ris). Is tus’s str ri  typ  ri sui? s  ; it is  sui (r it ts tim y ms  t su) ut it is i iti smti s.   prrm my mr utis wit tus’s ri t wit  ri sui, r ist: ti t tim y it, uti tim i quiti urs, us ivisi  t sky, iur 

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2  28 

2 

  rs.  qutri ir  ti t mts, t zi sis,  tw twv-ur ss.  ir ir  tur witi t mrii ir y ms  tw pivts t t twt ur. is ir usuy s s s tt it   us s t i   str  is rv wit t zi sis  sm  t x strs. rçis rtt, Mathematical Instrumentation in Fourteenth-Century Egypt and Syria: The Illustrated Treatise of Najm Al-Dīn al-Misrī (i: ri, ), . Ay  t mr t  ur strmi istrumts sri i t urtt-tury musript tt rtt it sws tt struti itrit istrumts ws  wy t ispy ’s itt  siti um i t i As  Riss,  triti i wi tus’s str r ri must  p. rtt, Mathematical Instrumentation, , . ,  vi Ki, The Ciphers of the Monks: A Forgotten Number Notation of the Middle Ages (tuttrt: tir, ), . u rs, “ pst-iu rtruvé: ’Usus annuli astronomici  mm risius, uvi t Avrs, ,” Quærendo . (): –. rs susts tt tis t  t editio princeps  tis txt, us t wrs “im u vtus”  t tit p () mk  tik tr ws tr iti prir t t yr . r  sripti  Arsius  simir ri is, s mu ssr, “ s  rit Ims r Istrumt-ki t t Arsius Wrksp,” Early Science and Medicine  (): –.  wis vs, “rt uis” i Ar tty, The Book of Sun Dials, t . (: r   s, ), – (t rst-tury sui i t sp   m u i ruum)  – (t urt-tury uivrs i i t sp   lt isk).

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-

tur rs, t. W  sy tt it is  miti   pispri str, s w s s i t  mmts  irms pp t t trsti.  mi ir tw tus’s ri  strs is tt t rmr s  pts t  ri t t titu  t p (iur .); rtr, it must  us i t p r wi it ws m, ik ri is. I iti, t sm siz  tus’s str must v m uti mu ss pris, wi ws  rqut r m miv strists i rti t str strs.

FGUE .5 Main components of Bonetus’s ring according to the image of the ring in the reprint of Bonetus’s treatise in 1557. (1) Ru; (2) Circulus Capricorni (ir  prir); (3) Almicantarat (mutr is); (4) Erraticae horae or horae inaequales (ss urs); (5) Gradus ad inveniendum altitudinem (titu ss); (6) Foramina (tr  i t str pt r t pi); (7) Rotula zodiaci or circulus signorum (zi ir); (8) Rotula mobilis (rt); (9) Horae aequales (quiti urs); (10) Linea meridiei, i.e., linea medii coeli et linea mediae noctis (mrii i sisti  t miy i  t miit i). Im rpru wit t prmissi  t ir irry  t istry  i  y t t mitsi usum  Amri istry i Wsit, ..

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Rri I zr’s r wit t ury  t uti wit strs, s Rríuz-Arris, “iv Jws  iv Astrs,” , –, ,  .

T  Fn n  Bn  L

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tus’s ri is, prpry spki,  str,  it su trr    “str r ri” rtr t  “strmi ri.” W v tri, witut suss, t  ims r xtt ris tt u mt tus’s sripti. xmps  strmi ris wr m i rmy i t sixtt  svtt turis, ut tr is  vi   str ri ik tus’s. I t istrumt xist, t y visu vi  it is t wut i t  iti  tus’s trtis  t sity irt  i its r-prit rm t yr  (iurs .  ., rsptivy).  us  prit ims  istrumts ws just strti, wi xpis t rptiti  t w vi ims.  puisrs rtr t t utrs us t prvi t wuts (r pprpts)  ty wr r-us i irt wrks.

 

 

 r rrik Kuz, Rings for the Finger: From the Earliest Known Times, to the Present, with Full Descriptions of the Origin, Early Making, Materials, the Archaeology, History, etc. (ipi, P: ippitt, ), – (i  i t ti  t Impri Kustwr usum i Vi, “  str ri, wi w s ks ik  riry ; ut w t t irs r p up, stituts  vrit str”);   (im   str ri i t Art ir ti i Vi). itr t im r t sripti  itr  ts tw ris mts tus’s ri; wvr, ri t  vs’s rprt i is Questionum, tus’s ri xist   sw it. ri i, i is Traité de l’astrolabe (ris: riux, ), , tut tt t iitis . . rv  tw xtt strs rrr t “rus tus” (t str   t t usum  t istry  i i xr  t str   t t ti usum  ui). wvr, it s  prv tt ts tw strs wr m y s mm,  w-kw str mkr w wrk i tr rmy i t tt tury. It sms tt t wuts i t iti    t rprit i  r t y ims  tus’s ri. is is t rs wy w v us t  iti, wi s prrri t txt i wt wu    t tw st   t itis  pritis (). r is  irt im i t Annulus astronomicus  t  tts prit y Ars rit i Rm i /.  ttp://tis.utwy.rvr.u/ viw/s/rii/.jp, m . yms ti  t st i irry (r ). wvr, tis t   im  t ri. r wr vry w prit istrumts i txts tw   , s Margaret Gaida, “Ri smrpi: Peter Api’s k-Istrumt yri  t Ris  t tmti Amtur i t ixtt tury”, Early Science and Medicine , (): –, r .



-

TBLE .

Table of contents of contemporary treatises on the astronomical ring (Paris 1558)

Petrus Bosardusa

 

sripti  t mpts.  psiti r t r  t su i t si.  titu  t p.  quiti urs y y, t irtis  t wr,  tr tis.  tur urs.  psiti  t p  t wi prt t strs ii.  tim i tr p.  suris  sust  t urti  t y  t it.  tim  suris  sust y tr mt.  ss r ptry urs.  tim si suris r sust.  titu  t su r t x strs.  titu  t su  t strs t y tim w t sky is uy.  iti  y r  t ipti.  itis  sm  t x strs.  mximum titu  t su r t x strs t   t titus  t ps.  psiti  t su  t y  t mt.  sm y srvi t titu  t su t miy,  t y ur  t y.  miimum visi titu  t su t y tim. Isrii t mrii i   p.  pit  t riz i wi t su r y x str riss r sts y y.  it ri t t t  t sw,  t sm y prprtis.  sw   stk r m. suri it wit  y srvti.  it  issi tis  t sm witut usi prprtis.  ist  smti w its it is issi.

rtius ius’s trtis  t us  t istrumt is t vi i t  iti, i wi y  ri xpti  t struti  t strmi ri is prit.

T  Fn n  Bn  L TBLE .

3

Table of contents of contemporary treatises on the astronomical ring (t.)

Petrus Bosardus

 t  tis tt r   i p  t sm y  sir mt.  msurmt  ists.  msurmt  pt.

Gemma Frisiusb

 mpts.  us  t ri  t si i wi t su is y y.  it  t p. i t tim. Wtr it is r r tr .  tur urs.  tur urs i  sir wy.  suris  t urti  t y. s r ptry urs.  tim si suris r si sust.  irtis  t wr.  titu  t su  t strs. si sws.  it w t ru is visi.  it  jts ut  r  t sm y  sir mt.  ist  i-t jts  t sm y  irt  sir mt. surmt  ist. surmt  pt.

Ioannes Dryandrusc mpts  t ri.d w t ri is pt t t it  t p.  urt it  t p [i.., t urt imt].  it  t p usi t titu  t su t .  it  t qutri ir v t riz. xpti  t it  t qutr   t p.  titu  t su t .  ur  t y wit t ri w t su is sii. Wtr t su is r r tr .  ur irtis  t wr.  mrii i wit t ri  t sm y  irt mt.

 TBLE .

- Table of contents of contemporary treatises on the astronomical ring (t.)

Ioannes Dryandrus

Burchardus Mithobiusf

ii t y wit t ri w t t is ukw.  psiti  t su w it is ukw usi t t.  iti  t su  its r i t zi. Itiyi t imt w  ts st i t s r i t srt.  it  t p. struti suis  y vrti r rizt sur usi t ri.e  msurmt  tis.  it s  t ri.  it  yti ssi p   uv ru,  t sm y  irt mt.  it  smti ri t its sw.  it  yti p i up usi t ri  witut i ’s p. uti  t ru t it  smti t wi ss r msuri it is t pssi.  it  smti p   muti, t tp  t s  wi r visi t t ys  t prs sti i  vy.  msurmt  t, i.., sur.  msurmt  pt.  tru psiti  t su  y y  t yr usi t t mti v.g Atr ru  t sr mti.  iur ur.  vti  t p. w mu t zit is sprt rm t p. Wtr t ur is r r tr . W t su riss  sts.  urti  t y   t it.  irtis  t wr. ki titus wit t ri.  wis.h

T  Fn n  Bn  L

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  y trsripti  t argumenta  t Prioris partis capita (–)  Posterioris partis capita (y ris ym si, –)  t iti  : Partium declaratio, Solis in signifero locum vel gradum invenire; Loci latitudinem quomodo invenias; Horas aequales interdiu, et mundi plagas, cum aliis nonullis, addiscere; Nocturnae horae inventio; Poli situm, et utram in partem stellae declinent, observare; Quota in alio tractu hora sit per diei ac noctis capienda; Ortus et occasus horam alia ratione investigare; De planetarum seu inaequalibus horis; Ab ortu vel occasu Solis, quota hora sit investigare; De Solis et stellarum altitudine; Solis et stellarum altitudines coelo nubilo ac quolibet tempore inquirere; Cuislibet gradus eclipticae declinationem supputare; Aliquot stellarum declinationes invenire; Solis meridiana vel stellarum maxima altitudinis observata, locorum latitudines indagare; Solis locum et mensis diem venari; Idem meridiana Solis observata altitudine etiam indagare; Idem diei quavis hora inquirere; Solis etiam minime conspicui meridianam altitudinem quolibet tempore obtinere; Meridianam lineam plano inscribere; Quo horizontis puncto Sol vel stella quolibet die oriatur et occidat; Altitudinum per umbras dimensio; Idem calculorum ratione addiscere; Stili seu gnomonis umbra idem investigare; Unica facta statione altitudinem dimetiri; De inaccessarum rerum altitudine capienda; Sine calculorum ratione idem obtinere; Quantum altitudine inaccessa absis, dimetiri; Rerum edito loco sitarum longitudines investigare; Idem faciliori modo obtinere; De distantiarum mensuratione; Profunditatum dimensio, s ttp://ks...uk/k s?i=V_AAAAAAJ&prits=rtvr&sur=s__summry_r&=#v=p &q&=s (st ss  rury ).   y trsripti  t contenta libelli (t  tts)  t iti  , : Declaratio partium; De usu annuli et signi inventione quod Sol quovis die occupet; Eleuatio poli quomodo inveniatur; Horae inventio interdiu; An sit ante meridiem an post; Horae nocturnae investigatio; Qua ratione horae nocturnae facilius inveniantur; De ortu Solis et quantitate diei; De horis inaequalibus sive planetarum; Quota sit hora ab ortu Solis vel occasu; Plagas mundi quomodo invenias; De altitudine Solis et stellarum; Altitudinum dimensio per umbras; De altitudine per solum visum; De altitudinibus rerum inaccessibilium; Facilius idem; De longitudine rerum in aedito sitarum; Aliter idem et facillime; Distantiae dimensio; De profunditatis mensuratione, s “ttp://ks...uk/ks?i=V_AAAAAAJ&prits=rtvr& sur=s__sumry_r&=” \ “v=p&q&=s” ttp://ks...uk/k s?i=V_AAAAAAJ&prits=rtvr&sur=s__sumry_r&=#v=p& q&=s (st ss  rury ).   y trsripti  t capitula (‒)  t iti   (Annuli astronomici compositio atque usus): De inscriptione meridiani atque aequinoctialis circuli; Aequinoctialis circuli divisio; Zodiaci circuli divisio; De calendario; De tertio sive ultimo annulo; Rimularum tam tertii quam quarti annuli formas hic poni vides; Canones, quibus annulus examinatur nunquid in compositione eius erratum sit; Canon pro rectificatione deferentis qui interior est annulus; Pro rectificationes signorum zodiaci, in deferentis concavitate, descriptorum; De rectificatione circuli latentis in concavitate deferentis, quem Solis indicem vocamus; Hactenus de annuli structura, sequitur eiusdem instrumenti usus; Partes ex quibus annulus constat, declarat; Quomodo optandus sit annulus ad certae regionis poli elevationem; Quarta polaris elevationis; Elevationem poli alia ratione ex Solis meridiana elevatione reperire; Aequatoris circuli elevationem supra horizontem, reperire; Theorica duarum

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-

elevationum aequatoris atque poli; Elevationem Solis meridianam, quovis tempore reperire; Quota sit hora diei splendente Sole ex annulo addiscere; Sol sit ne ante meridiem, aut post, addiscere; Quatuor plagae mundi, quomodo indagandae; Lineam meridianam investigare ex annulo; Idem aliter reperire; Tempus calendarii ignotum, quomodo ex annulo depraehendas; Si Solis locum nescias, quomodo ex calendarii noto loco deprehendas; Declinationem Solis, et cuiuscunque gradus zodiaci, addiscere; Si quis in mari aut solitudine erruerit, in quo mundi climate versetur, agnoscere; Elevatio poli; Horologia solaria, in quacunque, sive murali, sive horizontali planitie, adiumento annuli, construere; Horae nocturnae investigatio ex Gemmae Frisii libello; Qua ratione horae nocturnae facilius inveniantur [ex Gemmae Frisii libello]; De ortu Solis et quantitate diei [ex Gemmae Frisii libello]; De horis inaequalibus, sive planetarum [ex Gemmae Frisii libello]; Quando oriatur et quando occidat Sol ex D. Burchardi Mythobii traditione; De metiendis rebus; De scala altimetra annuli; Cuiuslibet rei accessibilis inaequali planitiae erectae, altitudo quomodo sit deprehenda; Idem alio modo; Altitudinem mensurandae rei, per umbram suam observare; Non mutato loco, altitudinem elevatae rei per annulum addiscere; In planitie, si negatur accessus ad rem metiendam, quomodo tum vestiganda sit altitudo; Altitudo rei super montem erectae, cuius altitudinis terminus inferior et summitas videntur, oculo existenti in vale, quomodo dimetiatur; De longitudine, id est, planitie mensuranda; De profunditate mensuranda, s ttp://ks. ..uk/ks?i=V_AAAAAAJ&prits=rtvr&sur=s__summry _r&=#v=p&q&=s (st ss  rury ).    trtis strts wit t struti  t istrumt: The inscription of the meridian and equinoctial circle; The division of the equinoctial circle; The division of the zodiac circle; The calendar; The third or last circle; The forms of the inscriptions placed on the third and the fourth circles. It tius wit rus r ki t ury  t istrumt.   r t utr itrus svr utis ri t tr surs: Finding nocturnal hours according to Gemma Frisius’ booklet; Finding the nocturnal hours in an easier way [according to Gemma Frisius’ booklet]; Finding sunrise and the duration of the day [according to Gemma Frisius’ booklet]; Seasonal or planetary hours [according to Gemma Frisius’ booklet]; When the sun rises and sets according to Burchardus Mythobius’ method.   y trsripti  t pitu (‒)  t iti   (trutur t usus ui sprii): Aequinoctialis circuli divisio; Appendix compositionis pro hora noctis; Solis locum verum quocunque die anni ex tabula suprascripta indagare; De Solis motu alius canon; Pro hora diurna; Pro elevatione polari; Quantum distet zenith a polo; An sit hora ante meridiem, vel post meridiem; Quando oriatur et quando occidat Sol; Longitudo diei et noctis; De plagis mundi investigandis; Quomodo altitudines per annulum dimetiri liceat; De ventis; Ex aeolia Ioannis Camerarii; Carmen Ausonii de imaginibus coeli; Instrumentum horarum inaequalium; Planetam horae temporalis per annexam tabulam invenire; Annuli mathematici compositio [i.e., a sundial ring]; Usus annuli mathematici; Quo tempore oriatur vel occidat Sol; Longitudo diei et noctis quomodo investiganda, s ttp://ks...uk/ks?i=V_AAAAA AJ&prits=rtvr&sur=s__summry_r&=#v=p&q&=s (st ss  rury ). itius ws wit t sripti  irt typs  ri tt r t strmi ris r sui ris, wi I v t iu i t ist.

T  Fn n  Bn  L

7

   trtis strts wit sm istrutis t ui t istrumt: Division of the equinoctial circle; Appendix on the construction for the nocturnal time.    txt itrus r tw pms xpii t wis (rm Is mrrius’ Aeolia  Ausius’ pm  t sttis  t sky),  tius wit t xpti  tr istrumts, m tm t y xpti, i ts itis,  t sui ri: The instrument of the seasonal hours; To know the planet of the seasonal hour with the attached table; Construction of the sundial ring; Use of the sundial ring; When the sun rises and sets [wit t sui ri]; How to nd the duration of the day and of the night [wit t sui ri].  ws is xpti wit tr strmi istrumts us r ti t tim.

Conclusions Wt ki  jt ws tus’s ri? i it ry xist s t trtis  t wut sust? i it wrk prpry? Ws it vr us? r is  rs t ut tt tus’s ri xist r tt it ws uti. rs  vs’s writt tstimy prvs tt it xist, r tus sw it t im i Rm, s s t kt wit istrutis t us it. I iti, t kt prst t p Axr  i t mk ss witut t ri  t ri t t sm tim.  kt is t  trti trtis ut  ri  is ist  istrutis t  t jt i irt situtis. urtrmr, t r prst t p Axr  ws t ri rtr t t kt, ut t rmr wu v  usss witut t ttr r y umiir wit strs. tus’s ri ws  pispri str wit sm strutur mitis t mk it  r ri; it ispy  str  its mpts, ry riz r y w sw it. It  t pwr   mmti jt: t strmi jw  t i As, t mst prstiius strmi istrumt, t i  strmrs  strrs. At t sm tim, tis ri u prrm mst  t utis tt  str r  strmi ri prrm. tus’s ivti rw t rt  istrumt mkrs, jii t sp  t ppitis   pispri str wit t sp  t uti   jw, i tis s  r ri, t ti  utiu  prt, sm yt smrt, siti jt.  str r ri ws r wit  t symism   str (wi rprst t pi  miv si)   ri (t ris  kis  pps  wys    t visi tks  tir tmpr /r spiritu pwr). Wit tis strmi jt   r  t wr i ’s , ut rtr  ’s r. tus rri t im  stp urtr t strmrs i miv tims  i rr

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-

t vy prty t i  ivmt  suss tt rtris Riss m. Appendix A: Bonetus’s Long Introduction to His Treatise According to the 1507 Paris Edition. Latin Text ti  tis ri mii prvzis Aui strmii utiittum ir  Axrum sxtum ptim mximum.  st ri siut ri titim tis i  st xtti supr xttim spitis prtis sus. m, ut it irmis prpt pitu : Non glorietur sapiens in sapientia sua, nec fortis in fortitudine sua nec dives in divitiis suis, sed in hoc solo glorietur qui gloriatur videlicet scire et noscere me. ius utm titi quiritur pr sitim strum, ut iquit smist psm : Celi enarrant gloriam dei et opera manuum eius annunciat rmamentum. m, um m rpr sti t mtum ssus t rssus tv spr  ptrum rumqu rumt vit, primm  mm t mirim usm ss sit, ut it smist psm : Domine dominus noster quam admirabile est nomen tuum in universa terra. Quoniam videbo celos tuos, opera digitorum tuorum Lunam et stellas que tu fundasti. x uius vris tri sut t. rimum qu prius ixit: videbo celosque Lunam et stellas, qui uivrsi sut is prius t qum siuri, ut vut Aristts prim pysirum. uum, um iit opera digitorum, qu itum vuit itii  iitis ypsis umirirum qu ypstur. rti qu i  u ttum,  utm   qui st  i t urtr mui mtim it, qui suum qum trm 4   

 trsripti  tus’s txts s  rmiz ri t str ti. rsripti  t ii  t Anulus astronomicus, wi ius t  itruti y tus justiyi t stuy  t strs  t us  its ri, ri t t iti prit i ris i   w t t iit tris, ürir ivrsitäts—u siitk i J (Textus De sphera Johannis de Sacrobosco. Cum additione (quantum necessarum est) adiecta: Nouo commentario nuper editio ad utilitate[m] studentiu[m] Philosophice Parisien[sis] Academie illustratus cu[m] Co[m]positione anuli astronomici Boni Latensis. Et Geometria Euclidis Megarensis, . r).  ttp://riv.tu.ui-j./isst/riv/isst_u_#t (ss  rury ). I v itru sisty   t pututi, pitizti,  rtrpy i t ti itrutis  t ti trtis t mk ts txts sir t w r  mr rr.

T  Fn n  Bn  L

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strum vi uiusmi psmum  t tvit.  vr t mir rti st qui mut rpr sti vitur  t t prptr  rum titim m ips vi m rpr  t vir vuit, t tu mxim um viss iitur m trrmmt mum ss t miri. i r i titim r sirmus, strum sitim r prtt. Qu mxim viris sistiis t utis um timtius vit. Quprptr, ptr tissim Axr sxt ptix mxim, tsi tum umittm (ivi umi ispirt) mium virtutum rrtm ivirumqu  umrum rrum titim r itim,  tu tm stittis um t miis xttim  rm t rim siurumqu tu uivrsi itii suitrum mmum t utiittm qum prvum istrumtum ivi pr qu strrum i rmmt xrum irumqu i prum stium ii qum viti titi ri ptrit. Qu prt tu tim  ispir tituii mii i prsusi ipsumqu  rmm ui rmum sui, um qui uus uiusmi mrum mirum t tissimrum virrum rmtum muum i st, ut pprt ir sis pit : Tulit rex Pharao anulum de manu sua et misit eum in manu Joseph, um tim qui quiuqu uum rs mus sus ituitur, uus rit ii ur t us um qu m t um t i rpr sti sirit, t tu it   prtm titim. ri  rx vi um   t vit t prspritur i si triumpti um ist u siut Ar ptix i tru um rtii t umri qu prtt supr ptus suum um quttur uis, ut iitur ir xi pit : Stringatur rationale anulis suis cum annulis superhumeralis vitta hiacinthina ut maneat t tr. t erunt in pectore Aaron quando ingredietur coram domino et gestabit iudicium liorum Israel [x. :]. Vitur im mii mpsiti istius ui mut iir strii mpsiti t qurti Isris t irum istrumtrum stri t mius tis, mxim qui st rmtum i  smpr visii i mius  sium ssri t st istrumtum vum. I prir  sus usus t utiitts qu purs sut. Imprimis utm  rtri i rtis imus. English Translation  k  t s  t Astrmi Ri  t  tts, rvç Jwis ysii t p Axr 

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-

r is  ry ik t ry  t  w kws , r is tr pri ir t t pri  t  w kws is wrks, s t prpt Jrmi sys i ptr : “ wis m s t ry i is wism, r t mity m ry i is mit, r t ri m i is ris: ut  w ris i tis , my, i kwi  risi m.” wvr tis kw is quir y t si  t strs, s t smist sys i sm : “ vs r t ry    t sky prims t wrks  is s.” r w m ss t vy is  t mti  ssi  rssi  t it spr  [t mti]  t pts s w s tir iitis,  kws t rst rt mir us, s t smist sys i sm : “ r, ur r, w xt is ur m  t w rt. W I sir ur vs, t wrk  ur rs, t m  t strs tt u u.” rm ts wrs, tr tis su  ti. irsty, tt  mti, “I wi s t sky, t m  t strs,” us uivrs tis r kw prir t iiviu tis, s Aristt sys i t rst k  is Physics. y, w  sys “t wrk  ur rs,” wt  wt us t urst y “rs” is t ips  t umiris w ty r ips. A tiry,  mti t m rtr t t su, wi is t   t sky  t rur  t wr, us, ri t  rti mstr  urs, vi s tis psm t it. ut t tru  t st rs is us mst  t vy is r visi t it. rr, vi wt t s ts is t it t   t srv tm,  mrvr us t tt tim  is si t v kw tt t m  t trrmmt ws rt  wru. 6    8   

Jr. : i t Ki Jms vrsi. A ii quttis iv r w tis vrsi. s. :. s. :  :. r is  u triti mri i tus’s sttmt rri Ki vi.  t  , vi s  sir t utr  sms, spiy ts sms tt i wit t rmu: “izmr -vi,” su s sm . Rri tis triti, s Rut ir, “A  r A ss? wrs  try  vi’s Ris s smist” [i rw], Studies in Bible and Exegesis (Iyyunei Miqraʼ u-Parshanut)  (): –, spiy , . .  t tr , tr is t mui triti tt vi s is sms t it (r ist t yi mu, rkt ). r  si summry  ts Rii tritis, s R. r Wiss, “Kir s vi -: st krt,” Daf le-Tarbut Yehudit  (): –;  uis izr, Legends of the Jews, :– . – ( sp. . ). I tk Ami Ksm  Isr m r tir vu irmti rri tis qusti.

T  Fn n  Bn  L

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I w wt t kw , w must kw t si  t strs,  it is prtiury pprprit t urm  t  ts w r . r tis rs, mst ss tr p Axr , tu t kw  ivi  um tis su [ us t] urst tt yur kiss (y t ispirti  t ivi spirit) is pk wit vry virtu, vrtss I v ivt  rti sm istrumt t pris yur iss  xt, ur  riy yur m r t vi  us   prs w is sujt t yur uivrs utrity, tru wi kw  t x [strs] i t rmmt  tr sti wrks     ti i  prt  sy wy. rtiy I m prsu tt yur titu wu t  isps y my isi  mki it i t sp   ri, t us  ri  tis ki is  xt rmt  t s  rt rs  iustrius m, s is si i t k  sis, ptr : “r tk  is ri rm is   put it  Jsp’s ,”  s us wvr wrs t ri  is   ks t it, t sp r is ys wi  r im s i  wr ki t t su, t m,  t tr vy is.   wi r  prt kw  . Just s ki vi w  wt tm y it  t triumpt ur prspr wit tis ri. A t i prist Ar, w wr it i t r wit t rstpt  t p up is rst, wit ur ris, s is si i t k  xus ptr : “y s i t rstpt y t ris tr ut t ris  t p wit    u, tt it my sty …” A “ty s  up Ar’s rt, w  s i r t r;  Ar s r t jumt  t ir  Isr”. I tik tt t struti  tis ri is mu sir t t struti  t str, Isr qurt,  tr stri istrumts,  ss tius, spiy si it is  spi rmt, wys visi  t  t kw wt is ssry,   w istrumt. rr, I v t

4  4    4 

. :. x. :. x. :. is is  rr t t quadrans novus r azafea sri y Azrqui (vt tury). J  kir i i (tirtt tury) trst its sripti it rw  tr r s svr vrsis  it i ti.  J. . iás Virs, Don Profeit Tibbon: Tractat de l’assafea d’Azarquiel (r: Arts ràqus, ), wi tis t rw, ti,  t vrsis.

7

-

iss its uss  ppitis, r ty r my. irst  , w tk , rtr  t vs. Appendix B: Annuli Astronomici, Boneto Hebraeo, Lutetiae 1557 (103b–117b). Latin Text () Boneti de Latis Hebraei medici provenzalis annuli astronomici utilitatum liber ad Alexandrum sextum Ponticem maximum. Vitur mii mpsiti istius ui mut iir Astrii mpsiti t qurti Isris t irum istrumtrum stri t mius tis, mxim qui st rmtum i  smpr visii i mius  sium ssri t st istrumtum vum. I prir  sus usus t utiitts, qui purs sut. Imprimis utm  rtri i rtis imus. () De declaratione annuli. Cap. . t qu uus t ri  ur v rt ut i r mti  mum siii  prtum i iit t ius rti tis st. upr iruitu ui sut  si i suis rtrius: primum st Aris, suum urus, t it ips. Quit sium tit  rus, ivi  quiqu i quiqu rius pr quit put. Itm sut uim mss i itris, rtius i ist itr m. Apriis vr i ist itr . t si  iis. t quiit msis iviitur   i  is pr put, t iitium rtii st i  ru sii isium, t pr ists mss t rtrs sirum situr us is mi i. Itr uum sut  rus   i  iis  ivium tituim is t strum. t iitium umri istrum  ruum st i i mii rmiis, i qu itrt rius is  sum ius tituim. Itm i supri ui rt t p (qu st supr uum) sut trs irui, qurum primus st miimus t st iruus ri, mius quitiis, mximus vr rum, iruus priri, qui st utimus i () irurti iius suprii rt t p.

44 

is st prrp is t srt itruti  t trtis i t itis tt  t v t  itruti I v rpru r.

T  Fn n  Bn  L

73

st sut mitrt, qui sut i mitt irui supriris sripti, qurum quim itri pprt, quim imprti, qurum primus riz i u iviitur mispri, t iti irui mitrt tit  rus, t sut i summ  rus  prim usqu  trum iriris rum, qu zit pitis mitur. st sut  rrti r ir mitrt. st i mii i, qu st i ss  ru, uius prs  tr i qu st rm iitur i mriii, t i iitur uus trr t i mi tis. st i iruitu suprii i spissitui ius sut  r sit i iis. st squitur rtu miis psit supr im suprim, i qu sut si  rtrius um zi stitut t iitur rtu zii. Itm sut i it rtu zii  put, qu  sts xs siit. rimus putus siit Ar t st i su ru sii mirum. uus siit r is t st i  ru sii is. rtius siit r rpiis t st i su ru sii ittrii. Qurtus siit um priri t st i  ru sii Aqurii. Itm i rtu zii sut  i, qurum sptm  si tit t siit  msis u. i () squitur rm, qu st i mi i rtu zii, qu trsit pr put Aritis t ir, i qu st xis tis rtum um u t rstris m. st sut u rmi, uum st i mi ui  suspum uum t m um , trum rm st i summitt ui pr itritu rii is  sium tituim ius. st st uus prrtus, qui itrt i rm tituiis is, tum st miis t  st smpr um u isi  t pr tituim strum. st st um  suspum uum. Ad inveniendum locum Solis in omni die. Cap. . i vis sir um is i qu si st t i qu ru ius i i i, p um supr im qum s t t supr qum x rius sirum t um, i tt um is i i i. xmpum: i st  msis rtii.  r um supr imum msis rtii, t qui supr primum rum Aritis it um, i i ru st  i. () Ad sciendum diem ignotum. Cap. . i im itum ivir sirs, sis i qu ru st , t i i ru i qu st p um, t t supr qum x ius msium t um; i tt im msis iti.

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-

xmpum: i  st i prim ru sii Aritis, p um supr ium rum, t t supr im  rtii. t si irvris um is,  siut itur i pitu . Ad inveniendum altitudinem Solis. Cap. . i tituim is sir sirs, susp uum  mu tu xtr pr um ius t p um  m  pr rm trst rius is, t i supri itris ui vi i qu ru x  rius t rius t i st titu is. Ad inveniendum gradum ascendentis et signum ascendentis. Cap. . i rtituim stis vuris sir, sis prim um is; pst sis tituim is; pst qur () rum i rtu zii i qu st , t p supr mitrt tituiis x prt ritis, si urit t mium im, ut x prt itis, si pst mium im pisti tituim, t i rus qui irit supr im riztis (qu st prim i mitrt) st rus stis, t sium iius rus st sium ss, i st, ris. Qu vr i iti, is. Qu utm irit i i mii i st i mi i t ius ir i u trr. xmpum: i us is st i prim ru Aritis, t titu is t mriim st  ruum.  primum rum Aritis x prt riti supr mitrt  ruum, t supr primum mitrt t suus rus sii mirum; i rus suus mirum st rus stis, t sium mirum st sium ss. Ad inveniendum duodecim domos coeli. Cap. . um uim ms i vuris qur, qur prim rum stis, t i rus qui irit supr im riztis st prim mus. st si rum qui irit supr () im mii i, i qu i, vv rtum zii, p rum ir ii rui mii i, t pst vi i prt i itis rum rrsptm r prim rrti, t i rus st iitium su mus. i immt rtu zii, 4 

I kp t rm nadair, r it sms tt tis rm ws iruti i tis pri ttr wit t mm nadir (s tr i t txt). I i ikwis wit t rms almicantarat  almucantarat, t rquty us i t miv pri  tr,  prst i tus’s txt.

T  Fn n  Bn  L

75

vi rum rrsptm r rrti su t i rus st iitium trti mus. st vi rum rrsptm i mii i t i rus st qurt mus. st vi rum rrsptm r rrti trti t i rus st iitium quit mus. st vi rum rrsptm r qurt rrti t i rus rit iitium sxt. Iitium utm sptim mus st ir stis. t iitium tv st ir su. Iitium ququ  st ir trti. t iitium im st ir qurt. t iitium uim st ir quit. t iitium uim st ir sxt. xmpum: rus stis st suus rus sii mirum siut itum st t st prim mus, t rus qui iit supr im mii i st  Aqurii. Vv rtum zii t p  is rum supr im mii i t rus rrsps r prim rrti st  mirum t st su mus; t rus rrsps r su rrti st  ri t st iitium trti mus; t rus rrsps mi i st  () is t st iitium qurt mus; t rus rrsps trti r rrti st  Viriis t st iitium quit mus; t rus rrsps qurt r rrti st  ir, qui st iitium sxt mus; rus ir prim mus st  ittrii t st sptim mus; t rus ir su mus st  ittrii t st tv mus; t rus ir trti st  priri t st  mus; t rus ir qurt st  Aqurii t st im mus; t rus ir quit st  isium t st uim mus; t rus ir sxt st  Aritis t st uim mus. Ad sciendum quot sunt horae ex horis xii sicut est in Gallia. Cap. . um sir vuris qut sut r  ris uim, sis prim is tituim, t p rum is supr mitrt tituiis x prt ritis si urit t mriim, t p supr ium rum is um, t vi i iru rrum supr qum rm irit um, t umr  i ui trr qu st mi tis usqu  im rm i qu um it, t is qut () sut r  ris . xmpum: i us is st i prim ru Aritis t titu ius st i  ru; p primum rum Aritis zii supr mitrt  ru x prt ritis, supr u rum p um t t i iru rrum supr rm  umr x i mi tis. t si urit pst mriim p rum is x prt itis t umr  i mii i qu st mriis, t sis qut sut r pst mriim siut st i ptri i, i qu tus sum.

7

-

Ad sciendum quot sunt horae ex horis viginti quatuor. Cap. VIII. i sir vuris qut sut r x ris  p rum is supr im riztis x prt itis, t  sium i iru rrum um ; pst vv rtum zii vrsus uum trr t p ium rum is supr mitrt tituiis x prt ritis, si urit t mriim, ut x prt itis, si pst mriim pisti tituim. i  sium um  i iru rrum, t umr i m pr vim ui trr  i si prim usqu  sium suum, t is qut   siut st () i Iti. xmpum: i us is st i prim ru Aritis t ius titu  rus; p primum rum Aritis supr im riztis x prt itis, t  ii sium i iru rrum um  t i r st prim. st vv rtum zii t p rum primum Aritis supr mitrt  rus x prt ritis, qui u st t mriim, t  sium um , t umr  prim si qu st prim r pr vim ui trr usqu  suum sium I t rut  r. t si st pst mriim, p rum ium  rus i mitrt x prt itis t rut  r. Ad sciendum quot sunt horae ab ortu Solis. Cap. X. i sir vuris qut r qus trsirut  i, ip rum is t ius tituim, t p um supr mitrt tituiis, t tu si um i iru rrum; pst vv rtr rum is usqu  primum mitrt x prt ritis, t su t um iusm i it iru; pst umr  i si prim usqu  suum t is qut sut r  rtu is. t si st pst mriim () p ium rum is x prt itis supr mitrt tituiis, t umr  i si prim usqu  suum pr vim mii i. xmpum: i us is st i prim ru Aritis t titu ius st i  ru; p ium rum  rus supr mitrt x prt ritis, qui st t mriim; pst p ium rum supr riztm, t  sium t umr  prim si usqu  suum, t rut  r qus qu trsirut  i. t si st pst mriim, p ium rum x prt itis, t rut  r  rtu is qu trsirut  i. Ad sciendum quantitatem diei et noctis. Cap. X. i vuris rum ii sr, p rum is supr primum mitrt x prt ritis, t  sium i iru rrum. st vv rtum

T  Fn n  Bn  L

77

zii pr vim mii, t p ium rum i i riztis x prt itis, t t ius um i iru rrum um , t r t prts rum qu sut  u t i im st rus ii; riqu vr prs irui st rus tis, qui ttus iruus tit  rs t qutittm ii t tis. xmpum: i  st i prim ru Aritis; p primum rum Aritis supr riztm () x prt ritis; pst p ium rum x prt itis supr riztm, t umr prts rrum pr vim mii i qu sut  u t i im, t sut  r. r  r st qutits ii i. Ad sciendum quantitatem horae erraticae diei. Cap. X. i vuris sir rum r iquis ii, sis prim rum ii siut itum st, t rs iius qutittis mutipi pr , t im summm ivi pr , t is umrum ruum r iquis ii. Qum si sutrxris  , rmit umrus ruum r tur, qui r iquis iur um r iqui tur it  rus i mi i, qu sut u r qus. xmpum: i qutits ii st  r; mutipi s pr  t rut ; qum umrum ivi pr  t rut  rus t  miut. r  rus t  miut st rus r rrti ii. i sutr itum umrum   t rmut  rus t  miut, t st umrus ruum r rrti tur. t  put st pprim ssrium i Astri  sium mium r, ut iitur i pit . () Ad sciendum quantitatem horae aequalis. Cap. X. i vuris sir rum r quis, ivi  pr  rs qu sut i iru rrum, t is umrum ruum r quis  i t  t, qui i r irui rrum sut qus t quit tit  rus. Ad reducendum horas erraticas ad aequales. Cap. X. um vuris rur rs iqus  rs qus, sit rus rrum iquium qut sut t ivi rus rum pr  t is rs qus. xmpum: qutits r rrti st  rus t  miut t sut , qui sut  rus; ivi pr  t rut  r qus.

7

-

Ad sciendum altitudinem Solis in meridie. Cap. X. um sir vuris tituim is i mi i, qu st iitium rssiis, p rum () is supr im mii i, t umrus ruum mitrt   is i rizt st titu iusm mi ii, umm uus sit tus  tituim imtis i qu quris tituim. xmpum: i  st i prim ru Aritis; p primum rum Aritis supr im mii i, t umr  rit usqu  mitrt i qu ppitur i rus supr im mii i, qut sut rus, t rut . r titu is i mi i iius ii st  rus. At sit qu iruus sirum iviitur i us smiirus, qurum uus st  pit priri i put ri t ius  pit ri i put priri. t put priri st sstitium ym, t put ri stiv. it tim qu ms qu istts rus  iqu rum sstitirum sut uius itiis vrsus spttrim v mriim, t is rum v ts sut qus, t umr t tituis qus i mi i. Ad sciendum locum Solis sine notitia diei. Cap. X um sir vuris rum is it i, p tm supr tituim mi ii i m- () -itt qum sumpsisti prius pr rm qu st  sium tituim is, i vv rtum zii, tqu u rus supr ipsm tm, qurum uum sis ss rum is, qu it sis im msis. xmpum: i titu is st  i mi i; vv rtum t vi rum sirum zii tm supr mitrt tituiis ruum, t rit primus rus Aritis v primus rus ir, t qui st tmpus ym, r  st i prim ru Aritis.  um i iru msium supr primum rum Aritis, t t supr imum msis rtii, t pr  put is um is t im itum. Ad sciendum quae dies sit aequalis alteri. Cap. X. um vuris sir qu is tri sit quis, sis  pr rus qu istts  sstitiis, qui rum is sut qus, siut itum st. xmpum: is  msis vmris st quis i  msis mris, qui sstitium ym st qu  st i pit priri, qu st i i uim msis mris, t si  iis.

T  Fn n  Bn  L

79

() Ad sciendum declinationem signorum ab aequinoctiali linea. Cap. X. i sir vuris itim uiusuqu rus sirum, p um supr im mii i t sit ius tituim  rizt. st sit tituim pitis Aritis v ir i m i, t irti uiusmi tituium st iti uius rus  quitii. i utm urit rus spttriis, spttriis st iti, si mriiis, mrii. xmpum: p primum rum sii ri supr im mii i, t umr  rizt usqu  mitrt tituiis ius, t rut i Rm  rus, t titu primi rus Aritis st ; r iti primi rus ri  quitii i st  rus, qui sut irti utrrumqu ipsrum tituium. Ad sciendum latitudinem civitatis. Cap. X. i vuris sir tituim ivittis qu st istti zit pitis ivittis ius  qui- () -tii i, sir tituim is i mi i, qum mius   si urit  i iiti Aritis v ir, qu st i  i rtii v ptmris, t rsiuum st titu ivittis; tu im rit mtus is i quitii i. i vr i i ru urit  t i i i, tu ius rus sir itim pr put prs, qum mius  titui is i mi i, si urit spttriis, v  im si urit mrii, t is tituim iitii Aritis i i ivitt; qum sutrs (siut prius itum st)  , t qu rmsrit rit istti riis  quitii i. xmpum: qu  st i prim ru Aritis v ir, titu is tu st  i mi i; qum mius   t rmut ; r  st titu ivittis Rm. xmpum: i iis ius qu  st i i si siut i r, sir itim primi rus ius, qu st , t miu im itim x titui ius, qu st , t rmut ; v  supr tituim primi rus priri, qu st , t rut ; sutrs    t rmut . I umrus  st titu uius ivittis Rm. () Ad sciendum ad quam latitudinem annulus factus est. Cap. XX. i vis sir  qum tituim tus st uus, vi qut mitrt sut i iru quitii usqu  zit, v  x  riztm  46 

is umr su  , tu t umr  sms t  sistty rpru i  t itis I v sut.

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-

spttrim, t supr ttm tituim tus st uus,  im sut qui; i tus st  tituim Rm. is tm tii uum  tituim qum vuris um mutti suprii mitrt, ut ptt i tuis strii istrumti. Ad sciendum ascensiones signorum in circulo directo. Cap. XX. i ssis sirum i iru irt sir sirs, iitium uiusvis sii supr im mriim p, t  sium i iru rrum um , t mv rtum zii  is sii sit supr im mriii, t  itrum si i iru rrum, t rs qu rut itr us ts mutipi pr  t is umrum () ruum ssium iusm sii. t simiitr is  qumit prtitim irui, qui quit r tit  rus, siut itum st. xmpum: p iitium sii Aritis supr im mriim, t pst mv rtum zii, t  sium i iis uus is, t r qu sut itr u si sut u r t qutur prts uius. utipi pr  t sut ; r ssis sii Aritis i iru irt sut  rus. Ad sciendum ascensiones signorum in circulo obliquo. Cap. XX. i  sir vuris, mv rtum zii  iiti sii  m iusm supr primum mitrt, t rus rrum i iru rrum rut ssis sii i i ri, qui quit r tit  rus. () Ad sciendum in quo signo sit Luna sine altitudine eius. Cap. XX. um  sir vuris, sis prim um is, pst sit im i qu uit iuti u, t umris   is supr rtum zii pr is qu sit  msis u tt qut sut is qu trsirut  i iutiis u. t iu sium qu iuis pr itum umrum, stt im i qu rit u. xmpum: i  st i prim ru Aritis, t  i iutiis u usqu  prstm im sut is . umr   is is  t p um supr im  t ivis im i  sii priri, i qu st us u i. Ad inveniendum ascendens revolutionis anni natalis vel mundi. Cap. XX. um sir vuris u rum stis i trsti, supr riztm i rit p rum is t i iru rrum  tm um . st

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T  Fn n  Bn  L

 ium rum mv  - () -m  pr rs  t quitm prtm uius r, qu sut  rus, t rus qui irit supr riztm st rus stis iusm i. i utm purs urit i, pr uququ  us ium rum pr sx rs t quitm prtm, qu sut it tri. t rus xists i prt riti st ss ipsius. xmpum: ss rvutiis istius i st  rus sii priri; p um supr riztm i rit; i mv ipsum pr  rs t quitm prtm uius, t primus rus mirum rit ss i uturi. Ad inveniendum dominum horae de die et de nocte. Cap. XX. i  sir sirs sis rm rrtim tis iius ii pr put , qui quit r rrti t suum mium uum x  ptis suum rim rum i , viit i i ti mius prim r st turus, mius su st Iupitr, t si pr rim usqu  , qui quuqu is sit v x  v rvis, tit  rs iqus t supr qutittm iius r rrti ivt, mi- () -tur uus pt. t  mpius pprt i tu irius sript.

x mii is mii x u is u x rtis is rtis x rurii is rurii x Ivis is Ivis x Vris is Vris x ti is ti

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6

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  I  V m s   I  V m s

 V m s   I  V m s   I

s   I  V m s   I  V m

I  V     I  V    

m s   I  V m s   I  V

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  I  V m s   I  V m s

 V m s   I  V m s   I

s   I  V m s   I  V m

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m s   I  V m s   I  V

, rurius. , u. s, turus. I, Iupitr, m. rs. , . V, Vus.

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-

Ad sciendum altitudinem stellarum. Cap. XX. um  sir vuris, susp  mu tu xtr pr um, t pr uum pr- () -rtum vi stm, t i supri itris ui vi i qu ru   rius t uus, t i strum st titu. Ad sciendum gradum ascendentis de nocte. Cap. XX. um  sir sirs, ip tituim uius st x  iis qutur qu sut i putis i rtu zii, t p rum i qu st i st x i mitrt su tituiis, x prt ritis si st st i ritis prt, v x prt itis si st i it, t i rus qui irit supr im riztis qu st prim i mitrt st rus stis. xmpum: i us ris is st st i ru  sii is, t titu ius st i prt ritis st  rus; p rum  is supr mitrt  rus, t supr riztm t  rus sii Viriis. I rus  Viriis st rus stis. () Ad sciendum quot sunt horae de nocte. Cap. XX. i  iius titim prvir vuris, ip tituim uius st x x iis qutur qu sut i rtu zii, t p rum i qu st i mitrt su tituiis x prt ritis, si st i rit, v x prt itis, si st i it. st p um supr rum is, t  sium i iru rrum. st vv rtum zii t p itum rum is supr primum mitrt itis, t  sium um  i iru rrum, t umr rs qu sut itr us ts; tt rut r tis. t si vuris sir qu rit mi x, vi qut sut r x prim si  im mi tis. t si vuris sir qut sut r  , umr x i mii i usqu  rum is i iru rrum pr vim i itis, si rus is st t im mi tis, t si st pst, umr  i mi tis pr vim ritis usqu  im mii i. xmpum: rus ris is st  is t ius titu  i it, t  st i i prim ru Aritis; p  is supr mitrt su tituiis, t  sium supr primum rum () Aritis. st vv rtum zii, t p primum rum Aritis supr mitrt primum itis, t umr rs qu sut itr us ts, t rut r  t  miut, t pst mim tm rit u r t  miut  ris .

T  Fn n  Bn  L

3

Ad sciendum gradum ascendentis sine latitudine et stellis de nocte et sine Sole de die. Cap. XX. i  iius titim prvir vuris, sis qut sut r; pst p rum is i i put r i iru rrum, t i rus sirum zii qui irit supr primum mitrt i prt ritis st rus stis. xmpum: i  st i prim ru Aritis t u sut trs r pst mriim; p rum is rrsptm ii r i iru rrum, t t supr primum mitrt  mirum, t i st rus stis. () Ad sciendum in quo gradu signi sit Luna sine notitia coniunctionis. Cap. XXX. um  sr upis, sir tituim u, t m t i mitrt i qu prt urit; i iqum qutur strum qu sut i rtu zii tii tm p supr sum tituim i m r um titui u pt i prt i qu urit, t rus irui zii qui irit i mitrt supr tm tituiis u rit rus ius. i utm pprurit i i, im is um titui iius t titui is. sir iitur uius sii sit rus i. xmpum: u titu u st i it  rus, t titu st ris is i rit st .   rum is i qu st st supr mitrt i rit  rus, t qui sx rus isium it supr mitrt tituiis u, qu psit st , i i iitur ru st u. () Ad inveniendum locum planetarum. Cap. XXX. um vuris sir um ptrum, is siut itum st i pit prti  sium um u; si tim tituis rum i t ptris ir. Ad sciendum quando planeta sit australis vel septentrionalis. Cap. XXX. i i prr vuris, vi tituim pt qu rit i i mrii, t si st quis tituii rus is, tu st i vi is. i utm urit mir titui rus is, tu pt st spttriis  vi is; si mir, ustris. t ttum it  vi is, qutum titu urit mir v mir.



-

Ad sciendum an planeta sit retrogradus vel directus. Cap. XXX. trum utm pt sit rtrrus ut irtus si sr vis, qur ius tituim () um titui st x, t ms mm mmri. i pst trtim tm v qurtm issiiis st qu st mtus xpt quusqu st t m qum prius tituim, t tu rursus tituim pt sir; qu si urit mir titui su prim, rit pt irtus, si urit i prt riti; t si urit i prt iti, rit rtrrus. i vr su titu pt urit mir prim, st rtrrus, r pt tituiis sistt i prt ritis; t si urit i prt itis, rit irtus. t ppsitum st  u. Ad sciendum altitudinem turris vel aliarum rerum. Cap. XXX.  uum prrtum supr rum  i umr , qui st pr titui is t strum, t ip tituim turris  imv uum  i ru . t im st titu turrus um titui tu, qut st titu qu st itr t t rim ri. t si st impssii msurr im tituim qu st itr t t rm, vi si mut um i trr, t msur   tu usqu  um trr qum vi- () -isti, t tt st titu ri. Bonetus de Latis Provenzalis Alexandro  Pontici Maximo  sut, tissim ptr, ui strmii put prri, u mum  sts tus ps umiim t, qu psitis supriiis iri vutu, ut sps vt, ripis.  mirum si rmmti mts qui rus sum tiittis xprs uqum xssrim, s uti pr iuti vitiri. ui tii rsus i vii, qum urtis ut ium i pris rr sprtu, ut qu  sutm tum ttiusqu Ripui mmum miumqu rrum piis um utii mprt sut,  umim txtum vurum  mittrtur. Qui ptius su summ tu mistt tqu utritt  mius mpius srtur. r, prr, ruius qu sut rrt ti. x r mii st, iu ti mius. I  AI RAI AVI ARII II.

4 

 st prrp is mpty irt rm t sty  u  t rst  t txt. It s  ry writt y  mr xprt tiist t t.

T  Fn n  Bn  L

FGUE . n .7

Ring in perspective (above) and divisions of the altitude scale on the shank of the ring (below).

5



-

English Translation k  t s  t Astrmi Ri y t  tts, rvç, rw ysii t p Axr  () I tik tt t struti  tis ri is mu sir t t struti  t str, t Isr qurt,  tr stri istrumts,  ss tius, spiy si it is  spi rmt, wys visi  t  t kw wt is ssry,   w istrumt. rr, I v t iss its uss  ppitis, r ty r my. irst  , w tk , rtr  t vs. () Chapter : On the Description of the Ring Kw tt t ri must  i , sivr, r tr mt, ik  ri t wr  t r,  tis is its sripti.  twv syms/rprsttis  t sis r ru t primtr  t ri: rst Aris, t urus,  s sussivy.   t sis s  rs, vry v sprt wit  t.  sm s rrs t twv mts wit tir [iiti] ttrs: r is rprst wit t ttr , Apri wit t ttr A,  s wit t rmii.   t mts is ivi it ys, vry v [sprt] wit  t.  ii  r is i t twtit r  t si iss.  kws t psiti  t su vry y tru ts mts  t syms  t sis. Isi t ri tr r ity rs, vry v [rs] sprt wit  i, wi r us t  t titu  t su  t strs.  ii  ts ity rs is  t i  t tr  tt t ry  t su trs t  its titu (iur .,  umr ).  t lt strit sur  t ri, wi is  t tp  it, tr r tr irs.  rst  smst is t ir  r, t itrmit is t quiti ir,  t rst is t ir  prir, wi is t utrmst ()  t irumr  tis lt strit sur. 48  4 

   

t  tts (J  Immu rviii), Astr r ri (ris, ), –. is is  sripti  t k  t str pt wit its zi  r ss rtr t  t sk  t ri, wi t trm circuitu annuli sms t sust (s iur .). w tus strts t sripti  t titu s. tus w itrus t sripti  t rt  t str pt wit its istitiv rvis (s iur .).

T  Fn n  Bn  L

7

Atr tis tr r t mutrs, wi r  t uppr   t ir sri, sm  wi ppr mpt  sm impt.  rst  tm, t riz, is ivi it tw misprs.  mutrs  t rsi ir r vry t rs, [mki] ity rs i tt rm t rst  t t tr  t smst , wi is  t zit. w t mutrs tr r ur ss urs (iur .). Atr tis is t i  t miv, wi is t i i w rm t rss; t [uppr] prt rm t  [] t t tr is  mrii  t tr prt is  t   t rt r t i  miit.   t rim [it. tikss]  t irumr ur urs r rv wit is.   turi w [rotula mobilis] is p  tt sur  wi t twv syms  wi t zi sists r rv. It is  t w  t zi [i.., t rt (rotula zodiaci)].  tis w  t zi tr r ur pits tt iit ur x strs.  rst pit iits Ar, wi is i t s r  mii.  s iits t rt  , wi is  t twty-tir r  .  tir iits t rt  rpi, wi is  t  r  ittrius.  urt iits prir’s i, wi is  t tt r  Aqurius. r r twty-it is  t w  t zi,  wi vry sv ti tr sis; ty iit t twtyit msis  t m. 2    4 

 

6 

 

itry, “  t ir ir.” r rrt: “t riz ivis t wr it tw misprs.” r r rmy  ss urs  t wut sws tm . wvr, tis puzzi mti  y  urs is sistt i t irt vrsis  tus’s txt tt I v sut. A pssi xpti is tt tus is usi ur ivisis tt mpss tw urs, s tt tr r ur ivisis ( r t st   urs,  r t r  t,  r t t  t,    t t  t), wi,  t t tw urs p t  si  t wr mrii, mks  tt   ivisis  tw urs  (s i iur .). is mit v  ssry us  t tiy siz  t str r ri. is umr su   (quiti urs)  t wuts sw  urs ( + ), s iurs .  .. wvr, t irt itis  tus’s txt v  urs r t. I su s mti tt t sripti r s t iu y mti  t ir   rs just isi t ur ir, wi is s visi i t wuts. tus strts t sripti  t tiy rt  tis prtiur str, wi y ispys ur x strs (Ar, t rt  , t rt  rpi,  prir’s i).  ur msis r usuy ispy  t k  strs. tus’s sripti is usi  impis tt t ur msis r rv  t zi  t rt, wi t .



-

() r is s   (s iur .,  umr ), wi is i t tr  t i  t zi w tt rsss t ii  Aris  ir, i wi t xis (i.., t pi) i ttr  ii st t w  t ri is p.  tr r tw s,  i t mi  t ri t susp t ri rm  tr i rt  t su (s iur .,  umr ), t tr i t uppr prt  t ri t mk t sr ry tr it t kw its titu (s iur .,  umr ).  tr is  w stik, wi is isrt it t   t titu  t su [s iur .  iur .,  umr ]. It is mv  is t wys wit t ri uss y it r tki t titu  t strs.  tr is  stri t susp t ri. Chapter : To Find the Position of the Sun Any Day I yu wt t kw t psiti  t su, i wi si it is  i wi r  it y y, p t tr  t y yu v,  mrk  wi r  t si t tr s . It iits t psiti  t su tt y. xmp: y is r tt, p t tr  t tt y  t mt  r. As t tr s  t rst r  Aris, t su is i tt r ty.

8   

6  6 

62 

 ri s t  susp wit t is vrti s tt t titu s  t ir sur  t sk prts rrty (s iurs .  .). is is  w siti tu tt is  rmv ssry. It s t  k tru t spt  str  yt t t sm tim iit t str’s titu  t si ri. r  xpti rri t us  tis w stik  t psitis i t str r ri  t tr s mti i t txt, s my mmts  irms t t   t is trsti  t trtis. is mit r mit t impy tt w t w stik is i us, t ri is priv  its suspsry prt ( umr tr, p  t str pt).  rs  t i  t rur s pitrs  utrs i str strs r py r y  tr us t mrk t msurs  t ss  ivisis rv  t k  t rt  t str pt   t rt, wi t r  t i s  visu t is py y t w stik (s iur .)  t  tt I v umr  (s iur .).  tr is us r s  i.

T  Fn n  Bn  L

9

() Chapter : To Find the Date I yu wt t kw t t, trmi i wi r t su is.  t tr  t r i wi it is  mrk  wi  t ys  t mt t tr s . It iits wi is t y  t mt tt yu  t kw. xmp: y t su is i t rst r  Aris, p t tr  tt r, it wi   t tt  r. I yu  t kw t psiti  t su,  s is xpi i t tt ptr. Chapter V: To Find the Altitude of the Sun I yu wt t kw t titu  t su, susp t ri rm yur rit  y its stri,  p it i wit t su s tt t ry  t su s tru t  ( umr  i iur .).  t ir sur  t ri [ t titu s], k  wi  t ity rs t ry s , it is t titu  t su. Chapter V: To Find the Ascendant Degree and the Ascendant Sign I yu wt t kw t st wit ury, rst  t psiti  t su.   t titu  t su  k r () t r  t zi w i wi t su is.  it m t str mutrs  titu i yu v tk t titu r , r m t wstr s i yu v  it tr .  r tt s  t riz i, wi is t rst mutr i, is t st r  t si  tt r is t st si, i.., i t st, wi t si i t st [r] is i t wst.  si utti t miv i is t si i t miv, wi its ir is i t   t rt. xmp: y t p  t su is i t rst r  Aris  t titu  t su r  is tirty rs.  t rst r  Aris  t mutr  tirty rs i t st, t s r  mii wi   t rst mutr.  s r  mii is t st r  mii is t st si. Chapter V: To Find the Twelve Houses of the Sky I yu wt t ut (it. “quis”) t twv uss  t sky,  rst t risi r.  r i  t riz i is t rst us.  6 

ir is  ti trm tt ms “t imtr ppsit.”

90

-

mrk t r i  () t [uppr] miv i. uri t zi w/rt, p  tis i (i.., t uppr miv i) t r tt is t ir  tt r t t miv.  k t t r  t wstr i tt s  t rst ss ur, tis r is t usp  t s us. Kpi t zi w sti, k t t r i  t s ss ur, tis r is t usp  t tir us. k t t r i  t i  t [wr] miv, tis r is t urt us.  k t t r i  t tir ss ur, tis r is t usp  t t us. k t t r i  t urt ss ur, tis r wi  t usp  t sixt. wvr, t usp  t svt us is t ir  t st; t usp  t it [us] is t ir  t s ;  t usp  t it is t ir  t tir.  usp  t tt is t ir  t urt, t usp  t vt is t ir  t t,  t usp  t twt is t ir  t sixt. xmp:  st r is t s r  mii s s  si,  it is t [usp  t] rst us.  r i  t i  t [uppr] miv is t urtt r  Aqurius. ur t zi w  p t urtt r    t i  t [uppr] miv.  r i  t rst ss ur is t twty-sixt  mii  it is t [usp  t] s us.  r i  t s ss ur is t twtit  r  it is t usp  t tir us.  r i  t [wr] miv is t urtt ()    it is t usp  t urt us.  r i  t tir ss ur is t tirtt  Vir  it is t usp  t t us.  r i  t urt ss ur is t urtt  ir, wi is t usp  t sixt us.  r tt is t ir  t rst us is t s  ittrius  it is t [usp  t] svt us.  r tt 64 

6 

 ur ivisis rmi  prm i tis ptr s w. r sm t  y tw ss ur is tw t mrii  riz, mki  tt  ur urv is w t riz ri t tus’s wrs.  ivisi  t uss usi t str twv ur is rv  strs is si ut mki s i t str ur ivisis tt r t xpi ywr i t trtis. r  pssi xpti  t ur ivisis  tis str, s t . wvr, tus xpti r ivii t uss sms t wrk  tw itis: t uti  t urs must  m i rvrs (strti rm t wst rtr t t st, s i ts ivisis wr just ivisis rtr t urs), , tr i t risi r, t rt s t mv t  t  t usps  t rmii uss, ts r r   t ur ivisis.  sripti s t wrk.  t r  mii is v t riz  it is t ut  rs titu t t wst. wvr, it wrks i t s xpi i t prvius t r itru.

T  Fn n  Bn  L

91

is t ir  t s us is t twty-sixt  ittrius  it is t [usp  t] it us.  r tt is t ir  t tir is t twtit  prir  it is t [usp  t] it us.  r tt is t ir  urt is t urtt  Aqurius  it is t [usp  t] tt us.  r tt is t ir  t t is t tirtt  iss  it is t [usp  t] vt us.  r tt is t ir  t sixt is t urtt  Aris  it is t [usp  t] twt us. Chapter V: To Find How Many of the Twelve Hours Have Elapsed according to the French Method W yu wt t kw w my  t twv urs v ps,  rst t titu  t su. I it is r , p t r  t su  t [rrspi] mutr  titu i t st.  t tr  t r  t su  k  wi ur  t rry ir (i.., t ur s) t tr s . ut rm t i  t   t rt, wi is miit, t t ur  wi t tr s   yu s v () t tim. xmp: y t psiti  t su is i t rst r  Aris  its titu is tirty rs.  t rst r  Aris  t mutr  tirty rs i t st.  t tr  tis r  it wi   t it ur  t rry ir (i.., t ur s), uti rm t miit i. I it is tr , p t r  t su i t wst  ut rm t miv i, wi is t mrii. u s kw wt t tim is i t tr ri t t mt i r, wr I ws r. Chapter V: To Find How Many of the Twenty-Four Hours Have Elapsed I yu wt t kw w my  t twty-ur urs v ps, p t r  t su  t riz i i t wst. rk wit t tr  t rry ir (i.., t ur s)  tur t zi w/rt twrs t   t rt.  t r  t su  t [rrspi] mutr  titu i t st i it is r , r i t wst i yu tk t titu tr .  mrk wit t tr  t rry ir (i.., t ur s)  ut  it rm t rst mrk t t s  pssi tru t   t rt. u s t w my  t twty-ur urs v ps () ri t t Iti mt. 66 

 rr r is t  pt wit mr t ur ur ivisis, wi is ry i triti t tus’s pprt sttmt i ptr .

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-

xmp: y t psiti  t su is i t rst r  Aris  its titu is tirty rs.  t rst r  Aris  t riz i i t wst  mrk tr wit t tr  t rry ir (i.., t ur s). is is t rst ur.  tur t zi w  p t rst r  Aris  t mutr  tirty rs i t st, us w it is r . rk wit t tr  ut rm t rst mrk, wi is t rst ur, t t s mrk pssi tru t   t rt. is is t urs. I it is tr , p t r  t tirty-r mutr i t wst  tis wi  twty- urs. Chapter X: To Know How Many Hours Have Elapsed since Sunrise I yu wt t kw w my quiti urs  t y v ps, tk t r  t su  its titu,  p it  t [rrspi] mutr  titu. rk t psiti  t rry ir (i.., t ur s)  mv kwr t r  t su up t t rst mutr i t st; mrk its psiti  tis ir.  ut rm t rst mrk t t s  yu s v t urs tt v ps si suris. ut i it is tr , () p t r  t su  t [rrspi] mutr  titu i t wst  ut rm t rst mrk t t s pssi tru t miv. xmp: y t psiti  t su is i t rst r  Aris  its titu is tirty rs.  tis r  t tirty-r mutr i t st, r it is r .  p t r  t riz, mrk [it],  ut rm t rst mrk t t s. is wi  tr quiti urs tt v ps  t y. I it is tr , p t r i t wst, t urs tt v ps  t y si suris wi  i. Chapter X: To Know the Duration of the Day and of the Night I yu wt t kw t iur r, p t r  t su  t rst mutr i t st  mk  mrk  t [rrspi] rry ir (i.., ur ivisi).  tur t zi w/rt pssi tru t miv  p tt r  t riz i i t wst. rk wit t tr tis psiti  t [rrspi] rry ir (i.., ur ivisi).  urs  tir prts, wi r tw t tw mrks, r t iur r. Wt rmis  t ir is t tur r, r t mpt ir s twty-ur urs, wi is t urti  t y  t it ttr.

T  Fn n  Bn  L

93

xmp: y t su is i t rst r  Aris, p t rst r  Aris  t riz () i t st.  p tt r  t riz i t wst  ut t ur ivisis tw t tw mrks pssi tru t miv. y r twv urs, s twv urs is t urti  t yit ty. Chapter X: To Know the Duration of the Day in Seasonal Hours I yu wt t kw t iur r i ss urs,  rst t iur r s s  xpi. utipy t urs  tis urti y t  ivi t rsut y twv. u s v t umr  rs   ss ur  t y. I yu sutrt it rm tirty, t rmir is t umr  rs   tur ur, r t iti  y iur ss ur wit [its] tur ss ur mks  rs y y, wi r tw quiti urs. xmp: y t urti  t y is urt urs, mutipy tm y t  t rsut s  . ivi tis umr y twv  yu wi t svt rs  v miuts.  svt rs  v miuts is t r   ss ur  t y.  sutrt tis umr rm tirty  t rmir s  twv rs  ty-v miuts, wi is t umr  rs   ss ur  t it. is ptr is ssry miy i stry t kw t rur  t ur, s is xpi i ptr twty-ur. () Chapter X: To Know the Duration of the Equinoctial Hour I yu wt t kw t r  t quiti ur, ivi  it t twtyur urs  t rry ir  yu s v t umr  rs  t quiti ur y y  y it, us t [quiti] urs  t rry ir r qu    tm s t rs. Chapter X: To Change Seasonal Hours into Equinoctial Ones W yu wt t  ss it quiti urs,  w my t rs  t ss urs r  ivi tir rs y t, t yu s v t quiti urs. xmp:  urti  t ss ur is svt rs  v miuts,  tr r twv urs, i..,  rs. ivi tm y t  t quiti urs s  urt.

9

-

Chapter XV: To Know the Altitude of the Sun at Noon W yu wt t kw t titu  t su t , wi is t ii  its i w, p t r ()  t su  t miv i.  umr  rs  t mutr rm t psiti  t su  t riz is its titu t , s  s t ri s  m r t titu  t imt i wi yu r sri t titu. xmp: y t su is i t rst r  Aris.  t rst r  Aris  t miv i  ut w my rs tr r tw t st  t mutr  wi tis r  t miv i is p. y r , s t titu  t su t  tis y is rty-it rs. rviusy, kw tt t ir  t sis is ivi it tw smiirs,  wi  is rm t ii  prir t t ii  r  t tr is rm t ii  r t t ii  prir.  ii  prir is t witr ssti  t ii  r is t summr . Kw tt  t rs  t sstiti urs quy istt rm  ssti v t sm iti itr rtr r sutr  tir ys  its r qu, s r tir sws  titus t . Chapter XV: To Know the Position of the Sun without Knowing the Date I yu wt t kw t r  t su  yu  t kw t t, mk  mrk t t titu  t su t   () t  [ t pt] tt yu us r wit t  t tk t titu  t su (s iur .,  umr ).  tur t zi w/rt  tw rs s   tis mrk. u s kw tt   tm is t r  t su. W yu kw tis, yu wi kw t y  t mt. xmp: y t titu  t su is rty-it t , tur t w,  k t r  t zi i  t mutr  titu. It s  t rst r  Aris r t rst r  ir. As it is spri tim, t su is i t rst r  Aris.  t tr  t rst r  Aris i t ir  t mts  it s   t tt y  r. Ari t tis ptr, yu s v t psiti  t su  t t tt yu i t kw. Chapter XV: To Know which Day is Equal to Another I yu wt t kw wi y is qu t tr, yu my kw tis tru t rs tt r quiistt rm t sstis, us tir ys r qu s s  si.

T  Fn n  Bn  L

95

xmp:  tirtit y  vmr is qu t t twty-t y  mr, us t witr ssti tks p w t su is i t ii  prir, wi pps  t twt y  mr,  t sm s rrs t rmir ys. Chapter XV: To Know the Declination of the Signs from the Equinoctial Line I yu wt t kw t iti  y  t rs  t zi, p it  t miv i   its titu rm t riz.   t titu  t ii  Aris r ir i tis i.  ir tw ts tw titus is t iti  tis r wit rspt t t qutr. I t r is rtr, t iti is s rtr; i it is sutr, sutr. xmp:  t rst r  r  t miv i  ut rm t riz t t mutr  its titu. is, r i Rm, is svty-tw rs.  titu  t rst r  Aris is , s t iti  t rst r  r wit rspt t t quiti i is twty-ur rs, wi is t ir tw ts tw titus. Chapter XV: To Know the Latitude of a Place I yu wt t kw t titu   p, wi is t ist  t zit  tis p rm t quiti () i, tk t titu  t su t . I t su is t t ii  Aris r ir, wi is  r tt r ptmr tt, rsptivy, yu s sutrt it rm ity.  rmir is t titu  t p.  [t t quixs] t mti  t su is  t quiti i. ut i t su is i  irt r,   irt y, t tk t iti  its r ri t t prvius ptr. u s sutrt it rm t titu  t su t  i it is rtr; r s  it t t titu i it is sutr,  yu s v t titu  t ii  Aris i tt p. u s sutrt it (s s  prviusy xpi) rm ity,  t rmir s  t ist  t ri rm t quiti i. xmp: W t su is i t rst r  Aris r ir, t titu  t su is rty-it t . u s sutrt it rm ity; t rmir is rty-tw, t rty-tw is t titu  t ity  Rm. xmp:  tr ys, w t su is i tr si, su s r, tk t iti  its rst r, wi is twty-ur. utrt tis iti rm its titu, wi is svty-tw.  rmir wi  rty-it. r yu s

9

-

 it t t titu  t rst r  prir, wi is twty-ur  t rsut wi  rty-tw, r sutrt it rm ity  t rmir s  rty-tw. is umr rty-tw is t titu  tis ity, Rm. () Chapter XX: To Know the Latitude for which the Ring has Been Made I yu wt t kw t titu r wi t ri is m, k w my mutrs tr r rm t quiti ir up t t zit r rm t p up t t rtr riz; t ri s  m r tt titu, r ts r qu. is ws m r t titu  Rm, wvr yu s mk r yurs  r t titu tt yu wt just y i t mutrs s pprs  t titu pts  t str. Chapter XX: To Know the Ascensions of the Signs in the Sphaera Recta I yu wt t kw t ssis  t sis i t sphaera recta, p t ii  y si yu ik  t mrii i  mrk wit t tr  t rry ir (i.., t ur s). ur t zi w s tt t   t si is  t mrii i. rk i  t [rrspi] rry ir (i.., ur ivisi)  mutipy y t t urs tw t tw mrks.  yu s v t umr ()  t rs  t ssi  t si. u s  t sm s rrs y prt  t ir, r vry ur s t rs, s s  si. xmp:  t ii [ t ]  Aris  t mrii i, tur t zi w,  mrk  ts tw ps.  urs tw t tw mrks r  ur  ur prts   (i.., /). utipy tm y t [rs pr ur], wi is twty-sv [rs].  t ssi  Aris i t spr rt is twty-sv rs. Chapter XX: To Know the Ascensions of the Signs in any Inclined Horizon I yu wt t kw tis, tur t zi w rm t ii  t si t its   t rst mutr.  rs  t urs  t rry ir [i.., t ur s] wi  t ssis  t si i tt p, us vry ur s t rs. 6  68  6 

ury tis su  rty-it (iti  + titu ), ut t umr rty-tw sms t  sistty rpru i  t itis I v sut. rsumy t s mrk is tk wit t ii  Aris s w. [ + /]· =  + / =  +  = .

T  Fn n  Bn  L

97

() Chapter XX: To Know in Which Sign the Moon is Without Knowing its Altitude W yu wt t kw tis, rst  t psiti  t su  t t y  wi t m ws i juti [wit t su] (i.., t w m). u s ut rm t psiti  t su  t zi w (i.., t zi ss  t k  t str pt) w my ys v ps si t y  t ur juti usi t is iiti t twty-it msis  t m.  si up wi yu s m wit tis uti s sw t i  wi t m is. xmp: y t su is i t rst r  Aris. wty-tr ys v ps si t y  t ur juti up t t prst y. ut twty-tr is [ t s  t ur msis] rm t psiti  t su  p t tr  t twty-tir i. u s m up t i t t   prir, wi is t psiti  t m ty. Chapter XX: To Know the Ascendant of the Natal Revolution or the Revolution of the World W yu wt t kw t r  t st  t prst yr, p t r  t su  t riz i t st. rk  t [rrspi] rry ir (i.., ur ivisi) wit t tr. Atrwrs, mv tis r rm tis () psiti pssi tru six urs   t  ur, wi is ity-tr rs.  r i  t riz is t r  t st  tis yr. I t yrs r my, yu s ppy tt r t vry si yr wit t six urs   t, wi r itytr [rs].  r i t st is t st  tt yr. xmp:  st  t rvuti  tis yr is it rs  prir.  it  t riz i t st.  mv it tru six urs   t  ur.  rst r  mii s  t st  t xt yr.

 

W tus sys “p t r  t su  t riz i t st”  ms “p t [kw] r  t su [r t prvius yr’s st]  t riz i t st,  t tur tru  rs t t t st  tis yr.” is stri prur is str i str trtiss. , r ist, rè Viri i ru, El “Kitab al-amal bi-l-asturlab” d’Ibn al-Samh/ Llibre de l’us de l’astrolabi (r: Istitut ’stuis ts, ), –.

9

-

Chapter XXV: To Find the Ruler of the Hour by Day and by Night I yu wt t kw tis,  t ss ur  t it  tt y usi [t istrutis iv i] t s ptr, r y ss ur s its rur,   t sv pts ri t tir rr i t vs.   tury t rur  t rst ur is tur, t rur  t s ur is Jupitr,  s  ri t t rr uti twv, us y ytim, wtr its it is  r srt, s twv ss urs   pt y rus t urti  tt spi ss ur. () is is ry visi i t t w:  Hour

uy it uy y y it y y usy it usy y Wsy it Wsy y ursy it ursy y riy it riy y tury it tury y

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6

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8

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 u Ju  V    u Ju  V  

 V    u Ju  V    u Ju

  u Ju  V    u Ju  V 

Ju  V    u Ju  V    u

   u Ju  V    u Ju  V

u Ju  V    u Ju  V   

V    u Ju  V    u Ju 

 u Ju  V    u Ju  V  

 V    u Ju  V     Ju

  u Ju  V    u Ju  V 

Ju  V    u Ju  V    u

   u Ju  V    u Ju  V

, rury; , ; , tur; Ju, Jupitr; , rs; u, t su; V, Vus.

 

 vi usi wit t ri  t t w v i t rp t iiti ttrs  t ti ms  t pts i t rii wit t rst tw ttrs  tir is trstis.

T  Fn n  Bn  L

99

Chapter XXV: To Know the Altitude of the Stars W yu wt t kw tis, susp it [t ri] rm yur rit  usi t stri  k t t str () tru t w stik. k  wi  t ity rs  [t titu s ] t itrir sur  t ri t stik s . t is t titu  t str. Chapter XXV: To Know the Degree of the Ascendant by Night W yu wt t kw tis, tk t titu    t x strs m t ur tt r  t pitrs  t zi w/rt.  t r  wi tt x str is  t mutr  its titu, i t st i t str is str, r i t wst i it is wstr.  r i  t riz i, wi is t rst mutr i, is t st r. xmp: wys t psiti  t str rt   is i t twty-tir r    its titu is tirty rs i t st.  t twty-tir r    t tirty-r mutr, t t twtit r  Vir s   t riz. is twtit r  Vir is t r  t st. () Chapter XXV: To Know How Many Hours the Duration of the Night Is I yu wt t rriv t tis kw, tk t titu    t x strs m ts ur  t zi w/rt.  t r i wi it is  t mutr  its titu, i t st i it is str, r i t wst i it is wstr.  p t tr  t r  t su  mk  mrk  t [rrspi] rry ir (i.., ur ivisi). ur t zi w/rt  p tis r  t su  t rst wstr mutr. rk wit t tr  t [rrspi] rry ir (i.., t ur ivisi)  ut t urs tw t tw mrks.  urs  t it r s my s tm. I yu wt t kw w it is i t  miit, k w my urs tr r rm t rst mrk t t miit i. I yu wt t kw wi  t twv urs it is, ut rm t miv i t t r  t su  t rry ir pssi tru t wstr i i t r  t su is r t miit i. I it is tr, ut rm t miit i t t miv i pssi tru t st. 2 

tus is w usi t siti t  is str r ri tt is spiy r srvi t sky t it.

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-

xmp:  r  t rt   is t twty-tir    its titu is tirty i t wst.  su is ty i t rst r  Aris.  t twty-tir    t mutr  its titu  mk  mrk  t rst r ()  Aris.  tur t zi w/rt  p t rst r  Aris  t rst wstr mutr. ut t urs tw t tw mrks; ty s  sv urs  rty-v miuts,   t twv urs [ it-tim] it wi   ur  rty-v miuts tr miit. Chapter XXV: To Know the Degree of the Ascendant without the Latitude, without Stars by Night and without the Sun by Day I yu wt t rriv t tis kw,  wt is t tim.  p t r  t su  t pit  t [rrspi] ur i t rry ir (i.., t ur s).  r  t zi i  t rst mutr i t st is t r  t st. xmp: y t su is i t rst r  Aris  t tim is w tr urs tr .  t r  t su rrspi t tt ur  t rry ir, t t tt  mii s   t rst mutr.  r  t st is r. () Chapter XXX: To Know in Which Degree of the Sign the Moon is without Knowing the Conjunction W yu wt t kw tis, ispt t titu  t m  mrk it  t mutr  t prt [ t riz] i wi it (i.., t m) is.  p   t ur strs rv  t zi w  its titu t tt ur, w t titu  t m s  tk i t prt i wi it is.  r  t zi w/rt i  t mutr  t mrk  t titu  t m s  its r. ut i it is visi y y,  t sm wit its titu  t titu  t su,  ispt  wi si t r is. xmp:  titu  t m is ty tirty rs i t wst  t titu  t str t rt   is rty i t st.  t twtytir r   i wi t str is  t mutr  rty rs i t st. As t sixt r  iss s  t mutr  t titu  t m, wi ws  tirty, t m is i tis r.

T  Fn n  Bn  L

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() Chapter XXX: To Find the Position of the Planets W yu wt t kw t psiti  t pts,  s s  si i t prvius ptr t  t psiti  t m. u  s  tir titus y it i tis wy. Chapter XXX: To Know When a Planet is Southern or Northern I yu wt t kw tis, srv t titu  t pt w it is  t mrii i. I it is qu t t titu  t su, t it is  t sr pt (i.., t ipti). ut i it s  titu rr t t su’s, t t pt is rtr wit rspt t t sr pt. I it s  smr, it is sutr. It prts rm t sr pt s mu s its titu is rr r smr. Chapter XXX: To Know If the Planet is Retrograde or Direct I yu wt t kw wtr t pt is rtrr r irt,  its titu () ttr wit t titu   x str,  kp t i mi. Atr tr r ur its t mti  t str is iisri; wit uti t str s t sm titu s r. Ispt i t titu  t pt. I its titu is ss t its prvius , t pt is irt i it is i t st. I it is i t wst, it is rtrr. wvr, i t titu  t pt is rtr t t prvius , it is rtrr s  s t tim t wi t titu is tk rmis t sm. I it is i t wst, it is irt. t ppsit s rrs t m. Chapter XXX: To Know the Height of a Tower or Any Other Thing  [ xtrmity ] t w stik  t r rty-v  t ity rs us r tki t titu  t su  t strs. k t it  t twr witut mvi t stik rm t r rty-v, r t it  t twr wit rspt t yur it is ik t ist tw yu  its s. I it is impssi t msur tis ist tw yu  t jt, kpi yur psiti  t p k  msur [t ist] tw yur psiti [ t ru]  t psiti  t ru tt yu () v srv; tis is t it  t jt. Bonet de Lattes Provençal to Pope Alexander V ss tr, ts r t istiuis pits  t strmi ri tt I umy prst t yur y t ttr wit mys. y yu riv tm

10

-

wit  ru xprssi  yur yrws, s  tt p wrms. It is t surprisi i I, i  Jw  ixpri i ti, v smtims wr utsi t us  ti rmmr, rusi t sti t usu wit t uusu. I v prrr t r yu itt rss i  p [vs] rtr t tts r  r i  sty it skt, s tt ts tis wi r u t  usu r yur t, r t t  t stt  r t pris  t kr  vryti su t  mitt  ut  t um wvi  t wrs.  t trry, ur yur i mjsty  pwr vryy s urst tm ttr. r, I pry, t ru tis wi r rrrs r  ti.  Jwis w s t m, ut t s mu t ti u.     ARIA RI   JWI   A. Notes on Chapters  and V of the Latin Text and the English Translation ptrs –  tus’s trtis  t str r ri itru us t t qusti  w t istrumt wrks, wi i t txt is irty rt t t rit itrprtti  sm  t trms  xprssis us i t sripti  t istrumt  sm  its uss. r is mti i ptr I  tr s r prrtis i t str r ri.  psiti  t rst  is r, it is t tr  t pt  is p  t xis  t quixs tt ivis t pt it tw qu vs (  i iur .).  psiti  t s prrti is “i t mi  t ri,”  its purps is “t  t ri rm  tr i rt  t su.” I t pt must tur r t titu  t su t  r usi t tir  mti i t txt, r t titu  t strs wit t w stik x i t str pt, t s prrti su srv t  t pt ( t ri)  p it vrti t t titu s (ri t t titu  t str, t su, r t m).  tis prrti must v   t im  t str (ik t tr  str pispri strs), i.., i t uppr rr  t pt (  i iur .). A stri p tru it mit v  u t susp t w vi i  rsy st wy. tr ty (  stri) stitut t suspsry prt  tis vry prtiur str. Ari t ptr , t tir  is “i t uppr prt  t ri”  srvs “t mk t sr ry tr it t kw its titu.” is is t mst iut prrti  t tr t t (  i iur .). Its purps is u: t tk t titu  t su  t x i it t w stik sri i t txt tt is ssti  spi t tki t titu  y

T  Fn n  Bn  L

103

x str. As rrs t w stik, tus xpi tt tis is  rmv pi iisps r tki t titu  t strs t it. is t is ry xpi i t trtis  pry rprst  t wuts. It must v wrk s  i   rur wit tir tw mi utis:  siti vi (wit tw siti vs)   iitr (ttr wit t tr mti r  tr i t txt).  w stik must v  sm mpt (iur .) tt w it t  just i t tr   t ri r   t titu (iur .,  ), s t rst ptr  t trtis xpis. I tis s, t str pt mit r mit t v  rmv t p t w stik i it, ut tis psiti wu v  ivit: witut t str pt t ri wu v  priv  its suspsry prt ( umr )  must v   irty wit t rs.  wuts i tus’s txt ispy  t  t rt tt ks ik  i, ut tt must  itrprt s   rprstti  t w stik r s  rur t mti i t txt (s iurs .  .).  xt qusti t sv is w t w stik ws us t tk t titu  t strs. is tur  t istrumt is mti wr i tus’s txt  must  u rm tr tis  t sripti. A prt  t w stik is p tru t   t xis i t sk ( ) s tt t titu   r  t ir prt  t   t ri. It is pprt tt t xis must   t tur  w   t xtrms  t w stik t pit t t str wi t tr pits t t titu s (s iurs .  .).

FGUE . Hollow stick.

10

-

FGUE .9 Front of the astrolabe plate.

FGUE .10

Back of the astrolabe plate.

T  Fn n  Bn  L

105

is xis is s t ky r t psiti  t tir   t str r ri.  tir prrti is  t uppr prt  t sk, wi is m i su  wy s t mk it pssi r t str pt t tur  it t msur titus.  tir prrti is p  t mi  tis xis  srvs t tk t titu  t su  t p  it t w stik t tk t titu  t x strs (s iur .  .). W v t u tt t trtis ws writt i  stritrwr sty wit my xmps, mki it sy t w t istrutis r usi t istrumt. wvr, witut si t pysi ri, y prs t miir wit t mpts  t istrumt wu v u it iut t prrm sm  t utis, spiy ts tt rquir t str t  susp, t pt t tur  its xis,  t w stik t  psiti i its p t msur titus.  wuts  t prvi y tis ut ts mpts  t trtis s t mu xpi tm. s ik m

FGUE .11

The ring side view.

10

FGUE .1

-

Complete ring.

w vr sw tus’s ri must v  t u tis irmti usi t txt  tir prvius kw  w str pispri strs wrk.

 

Some Features of the Old Castilian Alfonsine Translation of ʿAlī Ibn Khalaf’s Treatise on the Lámina Universal Emilia Calvo

Departet o Setc hloloy, verty o Barceloa, Gra Vía ,  Barceloa, Spa [email protected]

Abstract he a o the paper  to preet oe eatre o the treate o the lámina universal, a atroocal tret deved y ʿl  hala, a eleveth-cetry dal atheatca ad atrooer who eloed to the cetc crcle o Ṣāʿd aldal. ʿl  hala wa a coteporary o  al-Zarqāllh (al-Zarqāl, zarqel), alo a atheatca ad atrooer work der Ṣāʿd’ patroae, ad the vetor o the tret kow a azafea. Both tret, the lámina universal ad the azafea, are veral tret deved to overcoe the ltato o the tadard atrolae. he oly text decr ʿl  hala’ tret  the thrteethcetry old-Catla loe tralato, whch ha ot ee tded  detal p to ow, althoh oe prelary tde have ee plhed. he preet tdy deal wth oe ltc ad techcal dclte o the text.  ay paae, t ee to ollow lterally the raatcal trctre o the rac laae whle  other, the lack o techcal ter orced the tralator to reort ether to a lteral tracrpto o the oral rac teroloy or,  oe cae, to approxate tralato that ake the text oewhat dclt to ollow. he paper provde addtoal orato related aly to the atroocal paraeter ad the techcal vocalary ed  the tralato.

Keywords loo  El Sao – loe tralato – ʿl  hala – Andalusi atrooer – atrolae – azafea – lámina universal – Ṣāʿd al-dal – oledo – veral atroocal tret

© koninklijke brill nv, leiden, �9 | doi:0.63/9789004387867_006





Introduction he a o th paper  to preet oe eatre o the treate o the lámina universal. h ae reer to a atroocal tret deved y ʿl  hala, a eleveth-cetry dal atheatca ad atrooer who eloed to the cetc crcle o Ṣāʿd al-dal. he latter wa a htora o cece ad dea ad a atheatcal cett wth a pecal teret  atrooy.  1, Ṣāʿd wa appoted che relo jde (qāḍī) o oledo, a oce he held tl h death. H teret  the htory o cece, ad cece tel, epecally atrooy, led h to patroze the work o coteporary cett a well a to copoe everal cetc work hel. Ṣāʿd’ oly extat ook, Al‐Taʿrīf bi‐ṭabaqāt al-umam (Exposition of the generations of nations), ro 1, deal wth the “htory o cece,” decr the acheveet o the da, era, Chaldea, Eypta, Greek, al‐Rū (“Byzate” ad other Chrta), ra, ad Jew. ʿl  hala wa a coteporary o  al-Zarqāl (zarqel), alo a atheatca ad atrooer work der Ṣāʿd’ patroae ad the vetor o the tret kow a azafea. Both tret, the lámina   ū l-Ḥaa  ḥar al-Ṣaydalā. See Ṣāʿd l-dal, Tabaqāt al-Umām, ed. Ḥayāt Bū ʿlwā (Bert: Dār al-Ṭal’a, 1). rech tralato y Ré Blachère, Livre des catégories des nations (ar: aroe, 1). Elh tralato y Seaʿa Sale ad lok ar, d ed. (t, T: verty o exa re, 1), 1; Davd . , “O the Early Htory o the veral trolae  lac trooy, ad the Or o the er ‘Shakkazyya’  Medeval Scetc rac,” Journal for the History of Arabic Science  (1): –, reprted  Islamic Astronomical Instruments (odo: lderhot, 1); Jlo Saó, Las Ciencias de los Antiguos en al-Andalus (Madrd: Mapre, 1), 1–1; Roer , “ Jala al-Ṣaydalā,”  Biblioteca de al-Andalus (lería: dacó  ayl, ), :–; Roer , “ʿl  Jala,”  The Biographical Encyclopedia of Astronomers (hereater B.E.A.), ed. hoa Hockey et al. (ew ork, NY: Sprer, ), –. O Ṣāʿd, ee tz RchterBerr, “Ṣāʿd al-dal,”  B.E.A., 1–1.   ū ḥāq rāh . aḥyā al-aqqāh, kow a  al-Zarqāllh or al-Zarqāl. See Ṣāʿd l-dal, Tabaqāt al-Umām, 1; Joé M. Mllà Vallcroa, Estudios sobre Azarquiel (Madrd-Graada: Coejo Speror de vetacoe Cetíca, 1–1; repr., oledo: Dptacó rovcal de oledo: ttto oltécco .. zarqel, 1); Ja Veret, “al-Zarqal,”  Dictionary of Scientic Biography, ed. Charle C. Gllpe, 1 vol. (ew ork: Screr, 1–1), 1:–; Jlo Saó, Las Ciencias de los Antiguos, 1–; Jlo Saó, “al- Zarqāl,”  The Encyclopaedia of Islam, 1 vol. (ede: Brll, 1–1), 11:1– ; Ela Calvo, “ al-Zarqāllh,”  Encyclopaedia of the History of Science, Technology and Medicine in Non-Western Cultures, ed. Helae Sel (Dordrecht: lwer, 1), 1–1; Roer , “Zarqāl,”  B.E.A., 1–1. O the azafea, ee Joé M. Mllà Vallcroa, “ ejeplar de azaea árae de zarqel,” Al-Andalus  (1): 111–11.

ʿ Aī Ibn Kf ’ s Tis n  Lmin Unis

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universal ad the azafea, are deved to overcoe the ltato o the atrolae: they are veral—that  to ay, el—or ay ve lattde. Both are cotrcted  the ae projecto yte, relt  a lar de. hey are aed o a dal tereoraphc erda projecto o each celetal hephere that perpoe the projecto o oe hal o the celetal phere oto the projecto o the other hal. However, there are oe eatre that deretate the o that they t e codered a two copletely deret tret. Maye the ot evdet derece  that, whle zarqel’ azafea doe ot eed a rete to e ctoal, ʿl  hala’ tret e a rete that dplay hal o a coordate yte toether wth oe tar poter. he treate o the e o zarqel’ azafea  preerved  everal oral rac cope  addto to the loe Catla tralato ad, thereore, t charactertc are well kow ad have ee tded thorohly. Qte the oppote  the cae o ʿl  hala’ tret. he oly text decr t  the thrteeth-cetry Old Catla loe tralato, ce, to or kowlede, there  o extat copy o the oral rac text o th treate, ad thereore, the loe tralato cottte t oly wte. h Catla tralato ha ot ee tded  detal p to ow, althoh oe prelary tde have ee plhed.  a prevo paper, the a

3  O the projecto o the azafea, ee Roer , Al-shakkāziyya de Ibn Naqqāsh al-Zarqālluh: Edición, traducción y estudio (Barceloa: verdad de Barceloa ttto “Mllá Vallcroa” de Htora de la Ceca ́ rae, 1), . O the lámina universal, ee Ela Calvo, “a láa veral de ʿl  Jala (S. I) e la veró aloí y  evolcó e treto poterore,”  Ochava Espera y Astrofísica, ed. Mercè Coe, Hooro Melo, ad Jlo Saó (Barceloa: verdad de Barceloa ttto “Mllá Vallcroa” de Htora de la Ceca ́ rae, 1), 1–. or a coparo etwee the, ee Jlo Saó, “Sore el trazado de la azaea y de la láa veral: tervecó de lo colaoradore aloíe,” Al-Qanṭara  (1): –; Davd , “veral Solto to role o Sphercal trooy ro Malk Eypt ad Syra”  A Way Prepared: Essays on Islamic Culture in Honor of Richard Bayly Winder, ed. arhad aze (ew ork & odo: ew ork verty re, 1), 1–1 at 1–1; ad raçoe Charette, Mathematical Instrumentation in Fourteenth-Century Egypt and Syria: The Illustrated Treatise of Najm al-Dīn al-Miṣrī (ede: Brll, ), 1–1.   O the azafea, ee alo Roer , “Cocer the ṣaḥa šakkāzyya,” Zeitschrift für Geschichte der arabisch-islamischen Wissenschaften  (1): 1–1; Roer , “El aql ʿalà rālat al-ṣaḥa al-zarqālyya de  al-Baāʾ de Marrakš,” Al-Qanṭara  (1): –; Roer , Los Tratados de Construcción y Uso de la Azafea de Azarquiel (Madrd: ttto Hpao Árae de Cltra, 1); ad Ela Calvo, “a Risālat al-ṣafīḥa al-muštaraka ʿalà al-šakkāziyya de  al-Baā de Marrākš,” Al-Qanṭara 1 (1): 1–.

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e reard the cotrcto o the tret were aalyed. he preet tdy wll provde addtoal orato related aly to the paraeter ed ad the techcal vocalary o the tralato. More peccally, t wll deal wth oe ltc ad techcal dclte o the text.  ot paae, t ee to ollow lterally the raatcal trctre o the rac laae. Bede, the lack o techcal ter  the taret laae at the te o tralato orced the tralator to reort ether to a lteral tracrpto o the oral rac teroloy or,  oe cae, to approxate tralato that ake the text oewhat dclt to ollow. King Alfonso the Learned and His Quest for Enlightenment loo  wa or  11 ad wa k o Catle ro 1 Je 1 tl  prl 1. He wa a elhteed oarch who had a reat teret  kowlede  eeral ad  the cece  partclar. der h patroae, work o lterary, leal, htorcal, a well a cetc cotet were copled. Soe o thee text were oral work, t  ay cae, they coted o tralato o rac cetc work to Catla.  addto, we hold ay that,  oe cae, they are ot ere tralato, ce we ca d oe pece o orato added y the tralator, a  the cae wth the two chapter o the cotrcto o ʿl  hala’ veral tret that were wrtte y oe o loo’ collaorator, Ra Ça (hāq  Sd), ater the rac oral wa lot. hee loe tralato repreet oe o the rt exaple o Spah cetc laae.  addto, oe o thee work were tralated later to at. lke what happe wth ot o the lterary ad htorcal   See Ela Calvo ad Roer , “he veral late Revted,”  New Perspectives on the History of Islamic Science, ed. Mzaar qal (odo: hate lh, 1), 11–. Reprted ro Suhayl  (): 11–1.   O the lteral o the loe collaorator, ee Joé M. Mllà Vallcroa, “El lteralo de lo tradctore de la Corte de loo el Sao,”  Estudios sobre Historia de la Ciencia Española (Madrd: Coejo Speror de vetacoe Cetíca, 1), –.   O loo’ le, ee H. Salvador Martíez, Alfonso X the Learned: A Biography (ede: Brll, 1); too Balletero, Alfonso X el Sabio (Barceloa: Salvat, 1; repr., Barceloa: El lr, 1); Jlo Saó, “loo X the We,”  Medieval Science, Technology, and Medicine: An Encyclopedia, ed. hoa Glck et al. (ew ork: Rotlede, ), –; Jlo Saó, “loo X,”  B.E.A., –1; Roert . Br, Emperor of Culture: Alfonso X the Learned of Castile and His Thirteenth-Century Renaissance (hladelpha, PA: verty o eylvaa re, 1).

ʿ Aī Ibn Kf ’ s Tis n  Lmin Unis

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work prodced der loo’ patroae, whch are aoyo,  the cae o the cetc work, we have the ae o the athor ad tralator  alot all cae. t  ot clear who, ede the k, choe the work to e tralated, eve thoh there  o dot aot h volveet ad h kee teret  thee atter. Moreover, wrtte cetc work ply that he had a he lrary  the rac laae at h dpoal, aot whch we have lttle orato. he prodcto o th cetc corp tarted arod 1 ad cocded, ro 1 tl arod 1, wth the coplato o the loe tale. We kow that a prora o atroocal oervato lat approxately te year wa lached  order to coplete th work. Sce thee oervato relted  the coplato o the tale, we ca dedce that they were aed, to oe extet, o drect oervato. h, thee tale wold e the tr pot at whch at atrooy ceae to e aed o copy earler odel ad tart to develop oral work, althoh ther orce are, dotedly, rac. The Translation and Elaboration of Arabic Scientic Texts: The Alfonsine Collaborators he k’ collaorator played a proet role  prodc thee cetc work. here were Chrta, Jew, ad Ml ao the. he latter clde Berardo the raa, a Ml covert who collaorated wth Do raha o the revo o zarqel’ treate o the azafea  Bro  1. Sce he  called a “ater,” we ca dedce that he wa a edcated a. other proet Ml collaorator wa Mḥaad al-Rqt al-Mr, who poeed ecyclopedc kowlede ad who taht  Mrca at a chool poored y the oarch, althoh h volveet  the atroocal work  ot doceted. 8  O the loe tale, ee Joé Chaá ad Berard R. Goldte, The Alfonsine Tables of Toledo (Dordrecht: Sprer, ), 1–1; Eael olle, Les tables alphonsines avec les canons de Jean de Saxe (ar: C..R.S., 1); Eael olle, “he loe ale ad loo X o Catlle,” Journal for the History of Astronomy 1 (1): –11; Joh D. orth, “Jt Whoe Were the loe ale?”  From Baghdad to Barcelona: Studies in the Islamic Exact Sciences in Honour of Prof. Juan Vernet, ed. Joep Callera ad Jlo Saó,  vol. (Barceloa: ttto “Mllá Vallcroa” de Htora de la Ceca Árae, 1), 1:–. 9  or the Ml collaorator, ee Jlo Saó, “Do colaoradore cetíco lae de loo X,” Llull  (11): 11–. or the Jewh collaorator, ee ora Roth, “Jewh Collaorator  loo’ Scetc Work”  Br, ed., Emperor of Culture, –1; Davd

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here were varo Chrta cotrtor o who oly oe, Garc érez, ee to have ee copetet a a atrooer. We ca alo d the ae o tala collaorator lke Joh o Creoa or Joh o Mea. Soe o the were chared wth tralat to at work prevoly tralated to Old Catla, ch a the Tetrabiblos, toley’ atrolocal work, or the Libro Conplido en los Iudizios de las Estrellas, a tralato ro   Rjāl’ al-Kitāb al-Bāriʿ fī Aḥkām al-Nujūm. he preece o thee collaorator  loo’ cort cocde wth the perod  whch he apred to e crowed Holy Roa Eperor. he rop o Jewh collaorator wa certaly the reatet  er. hey collaorated oth o the tralato ad o the creato o oral work. o the, we ca eto a tralator, ehda  Mohe, a well a the already-etoed hāq  Sd, kow a Raça, a atrooer, oerver, ad cotrctor o atroocal tret. hree lare cellaeo collecto were prodced wth the help o thee collaorator. Oe o the cotaed work o ac, cld the ot repreetatve work, the Picatrix, a treate o talac ac whoe athor wa ro teth-cetry al-dal. t wa very poplar  Reaace Erope, where t crclated  a at tralato aed o a prevo Catla vero. he ecod coplato  o atroloy, ad the thrd cot o atroocal work collected der the ttle Libros del saber de astronomía. Several other tralato ca e added to the oe already etoed, oe o the o atrooy, ch a  al-Haytha‘ Fī hayʾat al-ʿalam (On the Physical Conguration of the Universe) ad al-Battā’ al-Zīj al-Ṣābiʾ (The Sabian Astronomical Handbook), other o atroloy, ch a toley’ Tetrabiblos, the Libro Conplido, ad the Libro de las Cruces (Book of the Crosses). here are alo oe oral work: the Alfonsine Tables ad the Libro del Cuadrante sennero (Book on the Sine Quadrant), whch  ot clded ao

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Roao, “e opere cetche d loo X e l’terveto del ere,”  Oriente e Occidente nel Medioevo: Filosoa e Scienze. Convegno Internazionale 9–15 aprile 1969 (Roe: ccadea azoale de ce, 11), –11, reprted  De historia judía hispánica, 1–11 (Barceloa, 11). See, or tace, “Joh o Mea,”  B.E.A., . O hāq  Sd, Raça, ee . zv aera, “ Sd, aac  Sd,”  B.E.A., . ū ʿl al-Ḥaa  al-Ḥaa (–ca. 1). O  al-Haytha, ee . zv aera, “ al‐Haytha,”  B.E.A., –. he tralato o th work to Spah, whch the k aked Do raha to do,  lot.  aoyo at tralato  preerved. h tralato how the teret  phycal atrooy at loo’ cort. ū ʿd llāh Mḥaad  Jār  Sā al-Ḥarrā al-Ṣāʾ (–). O al-Battā, ee Beo Va Dale, “Battā,”  B.E.A., 11–1.

ʿ Aī Ibn Kf ’ s Tis n  Lmin Unis

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the Libros del Saber. lthoh wrtte y cotrtor der h patroae, they were proaly pred y  loo’ ow peroal teret. The Libros del Saber de Astronomía he ot portat atroocal collecto copled der loo  the oe kow a the Libros del saber, whch cot o xtee treate. he rt o thee  the Libro de la ochava espera (Book on the Fixed Stars, lt. “Book o the Ehth Sphere”), aed o the Kitāb Ṣuwar al-kawākib (Book of Constellations) y al-Ṣū. he rea treate decre the cotrcto ad e o deret tret, ch a aaloe calclator, the prpoe o whch  the raphc reolto o prole  phercal atrooy. o the tret decred  the Libros del saber we d the celetal loe, the plae ad phercal atrolae, the azafea, the lámina universal, the tret o ataçir, the equatorium, ad the dal. Oe o the a ojectve o the k  copl all thee ateral  tated clearly  the eeral proloe to the Libros del saber. he athor wated to preet th lear  a clear raework  order to ake t ore accele or the reader. h  the reao why,  ay cae, the work were reorazed ad lltrated  the tralato. h, althoh the cotet  drectly depedet o rac orce,  t trctre ad preetato (or exaple,  t lltrato) we d certa oral eatre that appear  a yteatc way  the loe work. Oe o ther charactertc  the earch or perecto, whch led to cceve rework o ot o the tralato clded  th coped. Soe athor decre t a two “drat tae.” he rt wold have ee ade p o early vero o the ook o the xed tar (1), o the espera redonda or dell alcora (the celetal loe, 1), ad the azafea (dated). he text o th rt tae ha ot rvved. he ecod tae  repreeted y the text  the codex copled  the loe crptor, copoed  1–1. here,  addto to revew pre-ext  

     

O loo’ cetc edeavor, ee alo Evely S. rocter, The Scientic Works of the Court of Alfonso X of Castile: Patron of Literature and Learning (Oxord: Oxord verty re, 11). ū al-Ḥay ʿd al-Raḥā  ʿar (–). O al-Ṣū, ee al tzch, “Ṣū,”  B.E.A., 111. t  edted y Rco y Soa. See Mael Rco y Soa, Libros del saber de astronomía del rey D. Alfonso X de Castilla,  vol. (Madrd: tp. De Eeo ado, 1–1), :1–1. h ter derve ro the rac tasyīr, “atrolocal proreo.”

4



tralato ad creat ew vero o the, oe ew ook were added. Mot o the were copoed ex novo y the Jew Raça, who actally prodced the whle copl the Alfonsine Tables (1–1), a tated  the oreword to thee Tables. The Libro de la lámina universal: The Old Castilian Alfonsine Translation of ʿAlī ibn Khalaf’s Text on His Universal Instrument he Book of the lámina universal  oe o the dated ook, t, ce t  clded  the Libros del aer, whoe coplato wa carred ot toward the ed o loo’ re, we ca ae that t elo to the lat perod o the k’ tralato actvty. t  cotaed  olo v–1r o Codex Vllaal 1 o the rary o the verdad Copltee  Madrd. t  clded jt ater the treate o the atrolae ad  ollowed y the treate o  al-Zarqāl’ Azafea zarqaliyya. he ook cot o two ecto: oe o the  devoted to the cotrcto o the tret ad occpe olo v–r o the acrpt. t  ollowed y the ecod part, o the e o the tret, o olo r–1 r. h  a coo dvo  the treate clded  the Libros del saber, a well a  ther rac oral. he rt o thee two ecto  codered to e a oral drat o oe o the collaorator o the k, Ra Ça, ce the athor o the rac treate o the e o the atrolae had ot wrtte a treate o t cotrcto. he treate o e  attrted to ʿl  hala, decred  the text a a eoeter ad atrooer. he ook o the cotrcto o the lámina universal ha ee prevoly tded  depth, ad thereore  wll oc here o oe eatre o the treate o the e o th veral tret.

8 

9 

See é erádez-Ordóñez, “El taller htororáco aloí: a Estoria de España y la General Estoria e el arco de la ora proovda por loo el Sao,”  El Scriptorium alfonsí: De los Libros de Astrología a las “Cantigas de Santa María,” ed. Jeú Motoya ad a Rodríez (Madrd: dacó verdad Copltee, 1), . See Ela Calvo, “a laor de dó de la cltra árae por parte de loo X y  cotrcó a la oracó del leaje cetíco: Los Libros del aer de astronomía,”  La Civilización Islámica en Al-Andalus y los aspectos de tolerancia (Caalaca: Cetro de Etdo l-dal y de Dáloo etre Cvlzacoe, ), –; ad Calvo ad , “he veral late.”

ʿ Aī Ibn Kf ’ s Tis n  Lmin Unis

5

Structure and Contents of the Treatise on the Use of Ibn Khalaf’s Lámina Universal as Presented in the Old Castilian Translation he calclato that ca e perored wth th lámina universal are decred  oe ecto o the treate, whch  dvded to ve part. he rt part cot o twelve chapter. he rt o the decre the kowlede eceary or hadl the plate:

• • • • •

Caledrcal: day ad oth o the Chrta ad rac caledar rthetcal: er, how to add, tract, ltply, ad dvde, ad how to d the qare root troocal-atrolocal: zodacal , lar ao, tar ad plaet terpolato:  order to ota the coordate o a pot located etwee two erda or etwee two parallel he ecto o the plate where t  ore dclt to et a ood relt ro that procedre: o the polar ecto ad the cetre o the plate the projecto ecoe ore dclt to hadle ecae the pace etwee le  arrower (re .1).

he ecod chapter decre the deret part that ake p the tret ad ther repectve ae, whch cocde wth the oe ve  the chapter o the tret’ cotrcto. he ret o chapter ve trcto o a practcal kd, aly how to pt ark o the le eraved o the plate accord to the trcto ve  the ollow chapter. he ecod part cot o xty-three chapter ad  devoted to the calclato related to ay deree o the eclptc.  the rt place, how to locate t o the plate ad, the, how to detere t coordate:

• • • • • •

Eqatoral: declato, rht, ad olqe aceo Related to the eclptc: lotde ad lattde Related to the horzo: alttde ad azth, r apltde Georaphcal calclato: lattde ad co-lattde ekeep: dayte ad octral arc, eqal ad eqal hor trolocal calclato: the or carde o ay horocope, the dvo o the twelve hoe accord to toley ad Here

0 

See Calvo ad , “The Universal Plate,” 1–.

6



Figu . Front of the Lámina Universal.  Villaamil 156. Library of the Universidad Complutense, Madrid, fol. 84 v.

he thrd part cot o ty-eht chapter devoted to calclato related to the . hey ca e dertood a the applcato o the eeral rle decred  the prevo part or ay deree o the eclptc, to the cocrete cae o the deree o the , ad are, thereore, qte repettve. he ew ovelte are related peccally to the : hadow, calclato ad covero, erda alttde o the  ad related calclato, oltce ad eqoxe, ad oervato ad deterato o the or cardal pot. he reddacy o thee chapter, a well a the extece o oe take lar to thoe od  other treate clded  the Libros del saber, lead oe to coder the polty that all or part o th part  oral to the loe crcle ad ot a ere tralato. he orth part cot o xty-or chapter, devoted aly to calclato related to the tar. he calclato dealt wth there are the ollow:

ʿ Aī Ibn Kf ’ s Tis n  Lmin Unis

()

7

Georaphcal: Derece o lotde ad lattde etwee two place he or cardal pot ad the azth ro oe place wth repect to aother () ekeep: Calclato o the or ad eve twlht () trolocal: atvte ad projecto o ray

• • • •

he lat chapter  devoted to kow whether a plaet  drect or retrorade. ally, the th part  devoted alot exclvely to the oo. t cot o twelve chapter devoted to the ollow calclato:

• • • • • •

ar lotde ad lattde ar dtace to the ode ar r ad ett he deree wth whch the oo re or et he eqal hor elaped  cto o the lar alttde he hor o cojcto ad oppoto Some Features of the Back of the Lámina Universal (Figure 3.2)

h part o the tret  called “az de la yaco del Sol” (de o the S’ eqato). t  dvded y the two perpedclar daeter to or eqal part: the qadrat; the le ad the er cocde wth the dpoto o the ac eleet o the ack o a atrolae. The Zodiacal Calendar he zodacal caledar  a et o two crcle that allow oe to d the eqvalece etwee the day o the oth ad the deree o the zodacal : (1) he crcle o the zodacal  ad ther dvo  a cocetrc crcle dvded to º. hee dvo are roped  ecto o º correpod to each . he ae o the   wrtte elow. () he crcle o the oth ad the day  a eccetrc crcle dvded to  part correpod to the day o the Roa caledar. Below t, there  the er o the day that correpod to every Roa oth.





Figu .2 Back of the Lámina Universal. Ms. Villaamil 156. Library of the Universidad Complutense. Madrid, fol. 85 v.

Whe oe copare the vale ve  the text o the treate ad the oe od  the draw that accopae the text  the acrpt, oe dcrepace etwee the ca e oted (ale .1). hee cotece etwee the text ad the draw are poly de to the act that the athor o the draw wa deret ro the athor o the tralato. The Shadow Square he hadow qare  alo od o the ack o the tret. t allow oe to covert ale eared  deree to trooetrc t expreed a dt (a Catla ter?)  ch a way that º eqal twelve dt, whch  the ax vale. t  copoed o two de: the covere hadow or ale



ʿ Aī Ibn Kf ’ s Tis n  Lmin Unis Tb .

Comparison of the the Values Given in the Text of the Treatise and the Ones Found in the Drawing that Accompanies the Text in the Manuscript

1st day of the month

Text

Degree of the sign

Drawing

Jaary erary March prl May Je Jly t Septeer Octoer oveer Deceer

9° ° 9° 9° 8° 8° ° ° ° ° ° °

Caprcor qar ce re ar Ge Cacer eo Vro ra Scorpo Sattar

° ° 9° 0° 0° ° ° ° ° ° ° °

etwee  ad º ad the exteded hadow or ale etwee  ad º. he vale correpod to the ale o alttde ve or each o the twelve dt are how  ale .. Some Features of the Rete he rete o the lámina universal  dvded to two halve y a horzotal daeter called andamio (a lteral tralato ro the rac mamarr), .e., erda. Oe hal how a hal et o ark correpod to the erda ad parallel o declato o eqatoral coordate, ad the other hal how oe tar poter or tar ro the orther ad other hephere (re .).  Chapter 1.1, the treate ve a lt o tar to e eraved o the rete (ale .).

 

he text add “et la otra etrella qe o peta e la red” (ad other tar that are eraved o the rete).

2 Tb .2

 Values Corresponding to the Angle of Altitude Given for Each of the Twelve Digits

Digit

Solar altitude

  3     8 9 0  

;0° 9;30° () 8;° ;3° ;33° 30;8° 30;3° 3;° 39;9° ;30° °

Figu . Rete of the Lámina Universal. Ms. Villaamil 156. Library of the Universidad Complutense. Madrid, fol. 86 v.

ʿ Aī Ibn Kf ’ s Tis n  Lmin Unis Tb .

2

A List of Stars to Be Engraved on the Rete of the Lámina Universal

Old Castilian

Arabic name

Modern star name

Bytre Cayete lahaor leyça layot Oro de Ge e de Ge lrraech Cor de eo Boca del eç Merdoal Caeça Dalol rrd

al-nasr al-wāqiʿ al-shiʿrā al-ʿabūr al-ghumayṣāʾ al-ʿayyūq mankib al-jawzāʾ rijl al-jawzāʾ al-simak al-rāmiḥ qalb al-asad fam al-ḥūt rāʾs al-ghūl al-ridf

Vea (α ra) Sr (α Ca Major) rocyo (α Ca Mor) Capella (α ra) Betelee (α Oro) Rel (β Oro) rctr (α Boot) Rel (α eo) oalhat (α c atr) lol (β ere) Dee (α C)

Some Parameters Provided in the Treatise on the Lámina Universal Mot o the paraeter ed  th treate are doceted  other atroocal treate copled  al-dal. h  the cae or the vale adopted or the olqty o the eclptc, ;º (chapter .). h  clearly a roded vale, coveet or ak calclato wth the tret. Mor ad eve twlht are calclated  the parallel to the horzo o vale 1º toether wth the nadir o the deree o the S (chapter .). he olqty o the lar ort o the eclptc: º (chapter .)  a toleac vale. ally, ao the calclato decred  the text, a aece ca e detected, ce there  o chapter devoted to deter the azth o the qibla. h  a calclato ally od  th kd o treate  rac  

3 

O the olqty o the eclptc  al-da, ee, or tace, the treate o the veral atrolae plate deved y  Bāṣo  Ela Calvo, Abū ʿAlī al-Ḥusayn ibn Bāṣo: Risālat al-ṣafīḥa al-jāmiʿa li-jamīʿ al-ʿurūḍ (Tratado sobre la lámina general para todas las latitudes): Edición crítica, traducción y estudio (Madrd: Coejo Speror de vetacoe Cetíca, 1), , 1, ad 1. h  eqvalet to the e o the vale -1º or the actal deree o the . h  a paraeter ally od  dal treate o tret. See, or tace, Raó Martí ad Mercè Vladrch, “E toro a lo tratado de o del atrolao hata el lo III e al-dal, la Marca Hpáca y Catlla,”  Nuevos estudios sobre astronomía española en el siglo de Alfonso X (Barceloa: Coejo Speror de vetacoe Cetíca, 1), – at .

22



orce. h aece ca alo e od  loe tralato o rac atroocal text, ch a the Treatise on the Spherical Astrolabe, aed o l al-Saḥ’ treate o the plapherc atrolae, whch that alo ot th chapter, althoh the oral rac treate y  al-Saḥ clde th calclato  chapter , ,  ad 11. Technical Vocabulary he lteral that we d  the tralato o the treate o the lámina universal  exteded to the other text  the Libros.  th ee, th treate  a ood exaple o th pheoeo. We d word that are tracrpto o rac word, wth or wthot the artcle, lke axataba, ataçir, alhogera, madahara, zont. here are oe techcal word that are lteral tralato ro the rac oral lke empontizo, andamio, mudamiento, opposito, piértega.  ale . oe o thee techcal ter, preet  the Catla text, toether wth the Elh ad Spah tralato, are ve.  oe tace, the lkely rac orce or the Catla ter  ve. Tb .4

Technical Terms in the Alfonsine Castilian Translation of ʿAlī ibn Khalaf’s treatise on the Lámina Universal

Old Castilian

Arabic

English translation

Modern Spanish translation

alhoera, caeço achra deloretaeto achra del poeto adao [aarrat] archo del da/de la oche ataçr

 

hujra saʿat al-mashriq

l r apltde

lo apltd ortva

saʿat al-maghrib

ett apltde

apltd occída

mamarr eqatoral erda erdao ecatoral qaws al-nahār/al-layl dral/octral arc arco dro/octro tasyīr

atrolocal proreo

proreó atrolóca

See Mercè Vladrch, El “Kitāb al-ʿamal bi-l-asṭurlāb” (Llibre de l’ús de l’astrolabi) d’Ibn al-Samḥ (Barceloa: vertat de Barceloa, 1), –, 11–1, ad 11.

2

ʿ Aī Ibn Kf ’ s Tis n  Lmin Unis Tb .4

Technical Terms in the Alfonsine Castilian Translation (cot.)

Old Castilian

Arabic

English translation

Modern Spanish translation

axataa

shaṭaba

cerco del edodía

dāʾirat wasat al-samāʾ cerco de la altra/ de dawāʾir al-sumūt lo zote cerco de la ladeza dawāʾir al-mayl cerco de la lora dawāʾir al-ṭūl cclare crclaro/crclar coedo de eptetró et edodía deotrador epotzo [alqatarath] etacoe

madār

murī muqanṭar

ht devce/ ple erda crcle

círclo erdao

azthal crcle

círclo aztale

lattde crcle lotde crcle qary dvo (day, deree) eqatoral parallel local erda crcle

círclo de lattd círclo de lotd dvoe qara paralelo ecatoral erdao del lar

dex alcatar

ídce alcatar

tato o the plaet ederezaeto istiqāma (kawkab the tato  (plaeta edereçada) mustaqīm) whch a plaet  drect  t core az de la yacó wajh iʿtidāl al-shams de o the zodacal del ol caledar (o the ack o the plate) ladeza ʿard lattde Eat Wet le la del edo çelo – de coedo de orete et occdete de coedo de Eat Wet le orete et occdete lora ṭūl lotde/dtace – al yador dell da – ila muʿādil al-nahār – to the eqator (declato)

píla

etacoe de lo plaeta (cado  plaeta e drecto e  cro) cara del caledaro zodacal (e el doro de la láa) lattd líea Ete-Oete

líea Ete-Oete lotd/dtaca – al ecador (declacó

24 Tb .4

 Technical Terms in the Alfonsine Castilian Translation (cot.)

Old Castilian

Arabic

English translation

Modern Spanish translation

ayor altra del yador del día

al- irtifāʿ al-kullī li-muʿādil al-nahār

ayor declaco

al-mayl al-kullī

erdao ayor daeto yeral/ ereal oppoto pertea

manāra inqilāb

poeto replectoe rectcar retrataeto (plaeta retrorada) oeto ora epadda ora retorada yador del día yalaeto zodacho zot, zote zot de la caeza

naẓir

ghurūb kusūr raṣada rujūʿ (kawkab rājiʿ) ṭulūʿ al-ẓill al-mabsūṭ al-ẓill al-mankūs muʿādil al-nahār iʿtidāl minṭaqat al-burūj samt samt al-raʾs

erda alttde o the eqator (co-lattde) ax declato: olqty o the eclptc pre erda wter/er oltce adr eqatoral coordate o the rete ett racto oerve retroadato retrorade plaet r exteded hadow revered hadow eqator eqox zodac azth zeth

altra erdaa del ecador (colattd) declacó áxa: olcdad de la eclíptca prer erdao oltco de vero/ de verao adr coordeada ecatorale de la red ocao raccoe (de hora) oervar retroradacó plaeta retrórado orto ora extea ora covera ecador eqocco zodíaco azt cet

 

From the Celestial Globe to the Astrolabe: Transferring Celestial Motion onto the Plane of the Astrolabe Flora Vafea

act  aae a raat, A-Azhar vert, Car, pt [email protected]

Abstract he ceeta e  a ear atrca tret that ve a reatc vew  the heave a the tar a ca ate the ceeta t, t ha e avatae ch a cte  ctrct, traprtat a  carr t eareet. he atrae  a evt  the ceeta e; t repreet the ceeta phere prjecte t the pae, reta the ceeta rat. t prve accrate eareet a hep  v a reat varet  atrca pre. he a  th paper  t hw hw var prcee have ee traerre r the ceeta e t the atrae, eter the r  each part  the atrae.

Keywords atrae – ceeta e – te – e – aphaer – tereraphc prject

Introduction eave a tar,  a , a the ceeta t have ee a the wer that hat ha eperece ce t ear te. he cce  the ea ctate pecc arctra wrk at the apprprate te. e (ear eveth cetr ) preerve trace  th kwee  h pe Days and Works (Ἔργα και ἡμέραι)  e ‒  the pe, he reer t the pt  Arctr, eae, r, r a ae  the k   av a a Water eae, Hesiod’s Works and Days:  Translation and ommentary for the Social Sciences (Berkee, : vert  Cara re, 1); a e, Works and © koninklijke brill nv, leiden, �9 | doi:0.63/9789004387867_007





that t e take t cerat  rer t pre the ve, t harvet a ww the wheat, t harvet the rape, t ph the earth, eve t ha p the hp r the ea at the crrect te. he pt  the ecaa tar  the ht k were e  the acet pta ce the thr e  r eter the te. ce the tar pae a prtat re  evera e, ther reatve pt ha t e recre r the tra  th kwee. h, rp  ear tar were epcte  the r  cteat, accr t the erta  each cvzat. he t reatc epct  the tar a the cteat  ther reatve pt  that  a phere. e  the t acet ecrpt  the reatve pt  tar a cteat,  a qatatve t t qattatve ecrpt,  preerve  Arat’ pe Phaenomena, ae  the h treate    C (rth cetr ). pparch (ec cetr )  h ommentary on the Phaenomena of Eudoxus and ratus crtcze the th r the errr appear  ther Phaenomena;4 the crrect pt  the tar ca e epree   er,  he e atrca tret t eare ther crate. pparch’ tar catae ce the ae a pt r each tar a wa the prcpa rce r te’ catae. Wth th, the ceeta e, a reatc e  the ceeta phere, c e ctrcte (re .1). e (rt cetr ),  h Introduction to Phaenomena, ecre the ceeta e  a ta a “καταστηριζομένη σφαίρα” (ect .), whe Days,  The Homeric Hymns and Homerica wth a h raat  h . veWhte (Care, M, arvar vert re; : Wa eea, 11). 2  arha Caett, ncient Egyptian Science,  v. (haepha, P: Aerca hphca cet, 1), :‒.   Arat, rati Phaenomena, e. . art (reze: a va taa trce, 1); a Aar cha, ratus: Phaenomena, traate, wth a trct a te (Batre, MD: he h pk vert re, 1).   pparch, Hipparchi in rati et Eudoxi Phaenomena ommentariorum Libri Tres, e. ar at (epz: eer, 1).   erar . er, Ptolemy’s lmagest (rcet, NJ: rcet vert re, 1), 1. 6  erae Ajac, Géminos, Introduction aux Phénomènes (ar: e Bee ettre, 1); a ae va a . eart Berre, Geminos’s Introduction to the Phenomena:  Translation and Study of a Hellenistic Survey of stronomy (rcet, NJ: rcet vert re, ) a ar at, Gemini: Elementa stronomiae (epz: eer, 1);  chapter ve “he crce  the phere” are ecre.   at,  Gemini: Elementa stronomiae, , e the ter “καταστεριζομέναις” r MS raet Vat. 1, et the ter “καταστηριζομέναις” c r r

Fom  si Gob o  sob

7

FIGURE . elestial globe on a stand (Inv. no. 98115) from the useum of the History of Science in Oxford. ousy o  Musum o  Hisoy o Sin in Oxod.

the ta  cae “σφαιροθήκη” (ect .). hee ter are ectere  eeva Arac treate a dhāt al-kursī a kursī, repectve. he ceeta e  a ta, accr t the ear ecrpt  e, cta the w eeet (re .):

MSS (Ve , Vatca 1, Vatca 1 a ar ) a the ter “κατηστερισμέναις” a editionum consensus. Ajac,  Géminos, Introduction aux Phénomènes, accept the ter “καταστηριζομέναις”, whe va a Berre  Geminos’s Introduction to the Phenomena, 1, traate the ter  qet a “re wth tar”, whch crrep t the ter “κατηστερισμέναις”. he ter “καταστηριζομένη”  ee preet partcpe pave  the ver “καταστηρίζω”, whch  pave r ea, “t e prppe p”, a ete a e prppe  a ta. he ter “καταστεριζομένη” a “κατηστερισμένη” are repectve the ee preet partcpe pave a the ee perect partcpe pave  the ver “καταστερίζω”, ea “t re wth tar”. ce the ta “σφαιροθήκη”  ete, the ter “καταστηριζομένη”  preerae.





FIGURE . The circles drawn on the Kugel Globe according to Geminus. ousy o NIOLS ND LEXIS Kug.

1. ve parae crce are raw  the e (ect .1, .1‒1, .‒.): . . . v. v.

he arctc, ae the reatet  the crce  perpeta appart; the er trpc; the eqatr; the wter trpc; the atarctc, r the reatet  the crce  perpeta cctat, ae the t  vt  the k thrht the ear.

8  Arctc a atarctc crce are cere a the reatet crce  perpeta appart a cctat, repectve, r erver tate t the rth  the terretra eqatr. er a wter trpc are a cere r erver tate t the rth  the terretra eqatr.  the w we ha awa cer the erver’ cat t e rth , r  the terretra eqatr, ae we pree φ≥°.



Fom  si Gob o  sob

he pt  the arctc a atarctc crce epe  the atte  the cat (1.1). he tace etwee thee crce eare  teth  the era crce a eree are preete  ae .1. he tace  ° etwee the arctc crce a the rth pe crrep t the atte  he (ar r the tace etwee the atarctc crce a the th pe). e ha pra ve a wrke  he. TLE .

Distances between the Poles and the Parallel ircles on the elestial Globe, according to Geminus (Sections 5.46 and 16.10‒12)

Distance

r rth pe t arctc crce r arctc crce t er trpc r eqatr t er trpc r eqatr t wter trpc r wter trpc t atarctc crce r th pe t atarctc crce

. . . .

Sixtieths of a circle

Degrees

6     6

6  2 2  6

he tw cre—thrh the ceeta pe a the eqcta a trpca pt—are epcte  the e, v the ecptc t r eqa qarter (.‒). he tar are epcte  the ceeta e (.1‒1). he hrz  t epcte  the e, ecae t t t ve; the pt  the hrz  ee  the ta: “ Ὑπὸ μέντοι γε τῆς σφαιροθήκης ἡ τοῦ ὁρίζοντος θέσις κατανοεῖται” (.‒). he era, ae the crce thrh the ceeta pe a the zeth  a cat,  a tae r th cat a t epcte  the e (.‒). ce the v  the era t teth wa e r raw the ve parae crce  the e (.‒), t c e pe that the era wa a r rr the e.

9  .. ck, “e”,   Dictionary of Scientic Biography, e. Chare Ct pe et a.,  v. (etrt, MI: Chare crer’ , ), :–.

3 .



he reat aactc crce  t epcte  the ajrt  the e, ecae t wth vare (.).

te, tak t cerat the prece  the eqe, e ecptc crate r h tar catae,  that the atte  the tar w rea ctat, whe ther te w var r r a the tar.  k III.  h lmagest, he ecre the ctrct  a ceeta e (re .), where the  crce raw  t are the ecptc (ve t °), a reat crce thrh the pe  the ecptc a the aactc crce.0 he eqatr  t epcte  the e,  rer t t ee the eqcta pt  the ecptc. A rtatae r  te ar the e thrh the pe  the ecptc; ha  t—r e pe t the ther— ve t 1°; th repreet the tta cre a the pe  the eqatr are arke  t  a tace  ε=;1 eree r the pe  the ecptc. A ar r, ht arer a repreet the era,  te t the prev e  the tw pe  the eqatr. r  pte  the e,  the reat crce raw thrh the pe  the ecptc, accr t t ecptc atte. he pt  terect  the ecptc wth the ecrce thrh the pe  the ecptc a r  cere a the e  the raat  the ecptc, r pt the ret  the tar. he te  the e wth the tw r  pace  a ta (βάσις), whe pper hrzta r ee the hrz. he rth ceeta pe ca e eevate accr t the atte  the pace. h phere ca e ajte  rtat the tta r,  that t pae thrh the crret pt  the tce a ca etera e cta. A the treate  the ceeta e wrtte  the rt e D we have the w: 1.

he parta preerve treate “ the ctrct  the Aratea phere” (Περὶ κατασκευῆς Ἀρατείας σφαίρας) wrtte  et (eveth cetr)  reek, where the ctrct  a ceeta e 

 

Ca teae, Opera quae extant omnia, e. .. eer (epz: eer, 1), III., v. 1.: 1‒1; a er, Ptolemy’s lmagest, ‒.

Fom  si Gob o  sob

3

FIGURE .3 The globe described in .3 chapter of Ptolemy’s lmagest. Based on the design of the precession globe by Hadravová and Hadrava.

ecre. he  crce t e raw  the e are the w: arctc, er trpc, eqatr, wter trpc, atarctc, zac. he tace  the eqatr r each e  the trpc  ° a the tace  each e  the arctc a atarctc crce  1° r the rth a th pe, repectve. h tace crrep t a atte φ=1° (Ctatpe). he e  rre  tw eqa r (ect ve): . he hrz whch  repreete  a r  par “ἡ ἐπὶ τοῖς κίοσιν ἴτυς, ἣ δὴ καὶ ὁρίζοντος τάξιν ποιεῖται”; t  t ete  the r  raate. . he era that pprt the e “ἕτερος δὲ ἴσος μὲν τῇ βάσει καὶ φέρων τὴν σφαῖραν κρίκος, μεσημβρινοῦ δὲ λεγόμενος τάξιν ἐπέχειν” (“ather r eqa t the ae a carr the e, whch  a that t repreet the era”). he tw r ect each ther at rht ae. he ha-r ave the hrz  ve t 1 eree.

 

2 

Aea aravvá a etr arava: “phaera ctava, t a vea  hvezach” [th a cece  tar]: I, Katalogy hvězd a přemyslovský nebeský glóbus [Catae  tar a the re Ceeta e] (rae: Arteact/Acaea, 1), . et, De sphaerae rateae constructione, e. . aa, ommentariorum in ratum reliquiae (Ber: Wea, 1).

3 . . . .



A-Battāī (th cetr)  chapter   h Kitāb al-zīj ce a ecrpt  the ctrct  a ceeta e, t wtht a ta. A treate cpe  Qṭā  ūqā (ca. ‒1)  Arac that cta  chapter  the ecrpt a e  the e.4 he “Bk  the phere a t e”, wrtte  Ḥaah a-Ḥā  the th cetr, cta a ecrpt  the ceeta e a 1 chapter  t e. he treate “ the e  the ceeta e”  a-Ṣūī, wrtte etwee  a , cta 1 chapter arrae  three k.

 w ke a t et the Arac treate Dhāt al-kursī, attrte t te, whch wa cpe etwee the eeveth a the rt ha  the teeth cetr. h treate ecre the ceeta e wth a ta a cta  chapter  t e; t  a a ar  the treate  Qṭā  ūqā wth e ehaceet. he ceeta e c e e r actc prpe; t c a hep  v certa atrca pre. r v pre, the e ha t e pte accr t the pt  the ceeta phere. h ea:  

 

  6 

 

A-Battāī, l-Battānī sive lbatenii, Opus stronomicum, e. Car A a,  v. (a: caz e eae ervatr  Brera  a, 1‒1). he tet   Arac (:1‒1) wth a at traat (1:1‒1) ae  a he. A etae ecrpt  the tret  h, wth trctve re,  preete  e avae-th, Islamicate elestial Globes: Their History, onstruction, and Use (Waht D: tha ttt, 1), 1‒1. W. . Wrre, “Qta  qa  the e  the Ceeta e”, Isis  (1): ‒. h artce cta a h traat  chapter 1‒1 a  the tte  the ret  the chapter. A at traat (thrteeth cetr)  th treate  preete  char rch a é artíez ázqez, “Qta e ca: e phera ”, Suhayl  (): ‒. A cpar etwee the treate  Qṭā  ūqā a the Ae reate “r e a aç e epera”  preete   aó, “Qtā  ūqā a A   the Ceeta e”, Suhayl  (): ‒. he treate  Qṭā  ūqā  te a the rce  the treate Dhāt al-kursī,  ra Vaea, “he treate Dhāt al-kursī attrte t te”  Ptolemy’s Science of the Stars in the iddle ges (rthc wth the prject teae Ara et at). char rch a a tzch: “Ḥaah a-Ḥā’ Bk  the phere a t e”  Zeitschrift für Geschichte der rabisch-Islamischen Wissenschaften,  (1), –. MS ta, pkap ara, Ahet III, , 1 . 1‒, a .. ee, “A-Ṣūī  the Ceeta e”  Zeitschrift für Geschichte der rabisch-Islamischen Wissenschaften  (1), ‒.  the appe  th artce, ee preet the tte  the 1 chapter  h traat a a hrt ar  the ctet r t  the chapter. ee ra Vaea, The Treatise Dhāt al-kursī ttributed to Ptolemy.

Fom  si Gob o  sob

. . .

33

he eevat  the rth pe  the e t e eqa t the atte φ he pt  the eqatr r  the ceeta phere t e the ae  the e  e cae, the era r t e ae t the ca era.

he ceeta e ve a reatc vew  the tar a the ra t, t ha e ajr avatae, ch a the cte: . . .

 ctrct a perect phere  ak eareet  the phere  traprt a phere,  partcar whe t  k a  a ta.

e harp  cceve the ea  “” the phere a epct the tar a the ceeta t  a pae. A “flattee” phere c ve the pre ete ave. Bt the trat r the phere t the pae h ete reta the ceeta rat, the crce  the ceeta phere a the crcar t  the heave. he t t the ave pre  preerve  the wrk  te Planisphaerium r “ Ἅπλωσις ἐπιφανείας σφαίρας”. te e wth et that “t  pe a e  a atter that we ctrct  a flat race the crce whch e  the  phere, a  t were prea t” a cte wth the ecrpt  what ater wa cae tereraphc prject r the th ceeta pe t the pae  the eqatr. te,  h Planisphaerium, ecre the ctrct  the eqatr, the trpc a the ecptc a crce, whe the hrar crce are epcte a traht e (ect e). e prcee wth the ctrct  the hrz, tak a a eape the cate  Rhodes (φ=°) a cacat the ra  the hrz a the tace  t ceter r the ceter  the eqatr (ect eve). 8 

9 

Chrtpher Aatak, “he Arac Ver  te’ aphaer” (h ., Yae vert, ew ave, T, 1); a atha  a . . Berre, “he Arac ver  te’ aphere r atte the race  the phere: et, raat, Cetar”, SIMS  (): –1. Aatak, “he Arac Ver  te’ Planisphaerium”, . he Arac traa-

ّ ‫ن‬ ‫ّ ن‬ ‫ن‬ ‫ة أ ن‬ ‫ث‬  ‫م‬  ‫ ن‬    ‫ ن‬‫ ن‬ ‫ة‬ ‫ه‬‫ ن‬‫ ن‬‫ة‬‫ ة‬ ‫ و‬،‫ ن‬   ‫ه‬‫ ن‬‫أ‬ ‫ة‬  ‫أ‬ ّ ‫ن‬ ‫ ة‬   ‫ن‬ ‫ة ة ة‬      ‫هة‬  ‫هة ن‬    ‫ ة‬  ‫د و ة‬ ‫س‬ ‫ط‬‫س‬‫ة‬‫ ن‬‫ة‬ ‫د‬‫ ن‬‫ة‬.   ‫ ن‬    ‫ ن‬   ‫ة‬ ‫ح‬ t  the apparet t reek tet :  

( a Berre, “he Arac Ver  te’ Planisphere”, ).

3



e awa ve pr t hw the crt  the flat re t what appear  the  phere;  there are pr r ect  the reat crce  the phere  ther prject t the pae: 1. he ecptc ect the eqatr (ect e). . he reat crce thrh the ceeta pe terect the ecptc  aetrca ppte pt  the phere (ect tw). [A the crce thrh the ceeta pe are prjecte a traht e]. . he hrz ect the eqatr a terect the ecptc  aetrca ppte pt  the phere (ect three). . he crce thrh the pe  the ecptc, whch terect the ecptc  aetrca ppte pt  the phere, ect the eqatr (ect tee). te cacate the ze  the crce parae t the eqatr a hw reat etwee ther ra. e a cacate the r te  the zaca  r the rht phere (sphaera recta), ae r the terretra eqatr (ect eht a e), a r the qe phere that crrep t the cate  he (ect tweve a thrtee). At the e, the ctrct  the crce parae t the ecptc (ect tee t tee) a the pt  the tar  eqatra r ecptc crate are ecre (ect twet). he ctrct  the crce parae t the hrz, the cae acatar,  t ce, t t  ar t the ctrct  the crce parae t the ecptc. We tce that wherever the atte  the cat  reqete, t  take a φ=°, whch  the atte  he, t the atte  Aeara (φ=1°) where te wa v.0 h  tr evece that the trat r the phere t the pae wa ccte  he. C th evece wth the rect tete  e that pparch wa the vetr  the prject  a phere t a pae a he ha pace tee tar  the

2 

he cat  reqete r cacat: () the ra  the hrz a the tace  t ceter r the ceter  the eqatr (ect ); () the erece etwee the et (r the hrtet) ate a the eqcta ate,  eree a eqcta hr (ect 11); a () the r te  the zaca   the qe phere (ect 1‒1). te et that he e the atte  he, a he ha e t  the  phere ( a Berre, “he Arac Ver  te’ aphere”, ect , p. ) a a he ha e t  the lmagest ( a Berre, “he Arac Ver  te’ aphere”, ect 1, p. ).

Fom  si Gob o  sob

35

tret, a e rect e  ever ekht, we a cce that the per wh tate the trat r the phere t the pae wa pparch. he t  the crce parae t the ecptc (ect tee t etee) a the reat crce thrh the pe  the ecptc (ect tee) t e ew ea tate  te, ce thee crce are the reerece crce r the ecptc crate he preet r the e tar  the lmagest. t  t cet t have a the crce a the tar  a pae; the ceeta t, a ee  the ceeta e, h e retae  the pae. tat a ceeta e ch a the e ecre  e, we erve that the ve crce (the eqatr a the parae crce) rea  ther pt r the rtat. he crce  the hrz a the era, a the pe  the eqatr a the  the hrz (zeth—ar) rea ve. he tar, the , the ecptc, the tta a eqcta cre, 2 

22 

2 

“Σφαιρικῆς ἐπιφανείας ἐξάπλωσιν, ταυτότητα λόγων ἐν ἑτερότητι τῶν σχημάτων τηροῦσαν, ᾐνίξατο μὲν Ἵππαρχος ὁ παμπάλαιος, καὶ ἐπέθετό γε πρῶτος τῷ σκέμματι”, “οἱ ἑκκαίδεκα ἀστέρες…, οὓς μόνους Ἵππαρχος μετατιθεὶς ἐγκατέταξε τῷ ὀργάνῳ” (“pparch, the acet, ha ark ce the   a pherca race, preerv the prprt  the erece  the appearace, a he wa the rt t ctrte t the t  the pre”, “the tee tar … whch are the  [tar] pparch trape a pace  the tret”). ect   Synesius, Synesii yrenensis opuscula: d Paeonium de dono astrolabii, e. . erzah (e: raphca, 1), 1‒1. .. a, “e raté r ’atrae pa e évère akt”, Journal siatique, ére e, 1 (1): ‒11, ‒. ekht reer e te t the hpher wh ha ctrcte the atrae, ak cear that th hpher  t te ( chapter XXI); he a et that te wa  the atrae (chapter II).  ae hp, “a Aear, ce hp, e  atra eqe ctrcte e”, e. erch ae, Rheinisches useum für Philologie  (1): 1‒11 at 1, t  ete that te pace the e  the eqa hr ew the hrz  the atrae; the ae tet appear  ae hp, De usu astrolabii eiusque constructione, Über die nwendung des strolabs und seine nfertigung, e. Are tückeerer (Ber, üche, Bt: e rter, 1), –. hee tete, ce wth the act that te ha wrtte the Planisphaerium, hw that the hpher wh ha ctrcte the atrae c t e ater te a that the atrae wa area preet  te’ te.  a Berre et that there  a cear v  ject atter that aw  t eparate the treate t tw part: he rt part  ccere wth the eqatr a the crce reate t t, the ecptc a the hrz, a ce a cptata treatet  r-te pheea. he ec part  ccere wth crce reate t the ecptc a aree peca tpc  the practca peetat  the paphere ( a Berre, “he Arac Ver  te’ aphere”, 1‒).

3



a the pe  the ecptc ct chae ther pt r a cpete rtat  the e. h thee crce a pt t e raw  tw eparate pate. e  the h e tae; th  cae τύμπανον, pate r c (re .). he ther h rtate  the c pt, the ceter  the t  the heave: the rth ceeta pe; the vae pate  cae ἀράχνη, per r rete (re ., rht).  the w,  e the h ter spider tea  the at ter rete;

‫ ة‬ ‫ن‬ the reek ter ἀράχνη a the Arac “ ‫ن‬ ” ea “per”, t “et” (rete  at). Ata, the hape  the  reat crce thrh the pe  the ecptc that ve the ecptc t tweve zaca  reee a per, whe thee crce are prjecte thrh a tereraphc prject r e  the ceeta pe t the pae  the ceeta eqatr (re .). t  prae that the ae ἀράχνη (per) wa ve t th part  the atrae, ecae the  crce awa raw  the ceeta e were traerre t th trae part  the tret, where a the ecptc a the e tar are epcte. Ather pre  the che trat r the  e t the pae  that the th ceeta pe a a crce ar t cat e epcte  the pae. h, the atarctc crce, the reatet  the awa ve crce, c e the t, the ter crce  the repreetat;  a cae, the ret  the heave  ever ve r the pace  ervat: he rt ver  the papherc atrae  rea t e ctrcte! Accr t e (a et ater  the th cetr), the e wa ctrcte r a certa atte (° r e, 1° r et),4 2 

et, De sphaerae rateae constructione, 1‒, ect , e ‒: “(δεῖ δὲ) … ἑκάτερον δὲ τῶν ἄων (λέγω δὴ τὸν τε ἀρκτικὸν καὶ τὸν ἀνταρκτικόν) ἀπέχειν τοῦ καθ’ ἑαυτὸν πόλου τῆς σφαίρας μοίρας μαʹ” (“ach e  the ther [ ea the arctc a atarctc (crce)] t have a tace  rt-e eree r the cet t t pe  the e.”); a e,  erae Ajac, Géminos, Introduction aux Phénomènes, ect .‒.: “οἱ δὲ τροπικοὶ κύκλοι ἀπὸ τῶν ἀρκτικῶν οὐ τὴν αὐτὴν ἔχουσι διάστασιν κατὰ πάντας τοὺς ὁρίζοντας, ἀ’ οἱ μὲν ἔλασσον, οἱ δὲ πλέον διεστήκασιν. Ὁμοίως δὲ οὐδ’ οἱ ἀρκτικοὶ ἀπὸ τῶν πόλων τὴν ἴσην ἀπόστασιν ἔχουσι κατὰ πᾶν ἔγκλιμα, ἀ’ οἱ μὲν ἐλάσσονα, οἱ δὲ πλείονα. Καταγράφονται μέντοι γε πᾶσαι αἱ σφαῖραι πρὸς τὸν ἐν τῇ Ἑάδι ὁρίζοντα.” (“he trpc crce have t the ae tace r the arctc e  a  the hrz, t e have eer a e have reater tace. ar, the arctc crce have t the ae tace r the pe  ever atte, t e [have] eer a e reater. ee, a the e are cre accr t the hrz  reece”); a 1.1‒1.1: “ἀπὸ τοῦ πόλου ὁ ἀρκτικὸς διίσταται μοίρας λϛ … ὁ δὲ ἀρκτικὸς ἀπὸ τοῦ θερινοῦ τροπικοῦ διίσταται μοίρας λ”—“Πρὸς γὰρ τοῦτο τὸ ἓν κλίμα καὶ αἱ κρικωταὶ σφαῖραι κατασκευάζονται

Fom  si Gob o  sob

37

FIGURE . The stereographic projection ( from a celestial pole onto the plane of the celestial equator) of the six great circles through the poles of the ecliptic which divide the ecliptic into 12 zodiacal signs.

ce the arctc a atarctc crce were raw  the e. h, the atrae, ether etca r reatve t “the tret  the hr”, a te ca t  the Planisphaerium (ect rtee), wa ee r a qe atte. ecrpt  th ta r  the atrae are preerve  a etter  e t a (rth cetr D); there are a cattere

καὶ αἱ στερεαί.” (“he arctc [crce] ha a tace  thrt- eree r the pe … the arctc [crce] ha a tace  thrt eree r the er trpc. Bth the arar phere a the  [e] are ctrcte accr t th e atte.”). 2 

‫آ‬

‫ ة‬    ‫ا ة‬  ”, ee:  a Berre, “he Arac he ter  preerve  Arac a “ Ver  te’ aphere” p. , e . te a reer t ervat “δι’ ἀστρολάβων ὡροσκοπείων” (thrh tret eter the te  the tar)  etra—Apteeatca: III., e 1‒1; ee: laudii Ptolemaei opera quae exstant omnia, v. .1, e. W. üer, pt . Ber a . B (tttart-epz: eer, 1), 1‒1.

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

reerece  the treate  ever ekht  the atrae wrtte  rac (eveth cetr D). We cat etere whe eact th trat wa rke. te,  the ecrpt  the prece ceeta e  the lmagest, et that the pe  the e ca e pace accr t the atte  the pace. he prece ceeta e wa t the a cae; the a e wa a  e, wth the eqatr a t parae crce raw  t, eqppe wth a era a a hrzta r. he evt  th e  a e, where the pe  the eqatr ca e ajte accr t the atte  the pace  ervat, whe the arctc a atarctc crce are t raw  t. h tpe  e ca e e at a pace  arth. Wh ca th t e e wth a atrae? r the atrae, we ee t ctrct evera pate, each e r eret atte. he atarctc crce cat e the ter crce  the pate. he ecat  th crce epe  the atte φ  the cat; t  -(°-φ)=φ-°, where φ ≥ °.  the aeter  the pate rea ctat, the the aeter  the eqatr a t parae crce var  each pate; therere, we cat e the ae per ave thee pate.  we keep the aeter  the eqatr ctat, the the aeter  the pate vare wth the atte, th the per w e t are r e pate a t a r ther. A t  t retrct the pate t the trpc  Caprcr. h wa the ae per ca e e ave the pate  a atte. hee pate ca e kept  a receptace, δοχεῖον r ater. 26 

2 

28  29 

ee .. a, “évère akt: raté r ’atrae pa”.  the trct a chapter  a XXI  ekht’ treate, there  a “he” ecrpt  a atrae wth ve ze / crce a hav a  crce the “atarctc”, whch crrep t a atte φ=°. h prve evece r the ta r  the atrae, ee r a qe atte (φ=°), pra  pparch. “τὸν δὲ μεσημβρινὸν ὀρθὸν προσαρμόσομεν τῷ κατὰ τὴν βάσιν ὁρίζοντι διχοτομούμενον μὲν ὑπὸ τῆς φαινομένης ἐπιφανείας αὐτοῦ, δυνάμενον δὲ περιάγεσθαι περὶ τὸ ἴδιον ἐπίπεδον, ὅπως ἐξαίρειν ἑκάστοτε δυνώμεθα τὸν βόρειον πόλον ἀπὸ τοῦ ὁρίζοντος διὰ τῆς τοῦ μεσημβρινοῦ διαιρέσεως ταῖς οἰκείαις τῶν ὑποκειμένων κλιμάτων περιφερείαις” (“he we  the era r  pt perpecar t the hrz ee  the ta [ the e],  ch a wa that t  ecte  the ve race  the atter, t ca e ve r  t w pae: th   rer that we a, r a partcar appcat, rae the rth pe r the hrz  the apprprate arc r the atte  qet,  the raat  the era [t pace the r crrect]”), Ca teae, Opera quae extant omnia, III., v. 1.:1.‒1, a er, Ptolemy’s lmagest, . here et e eape  ceeta e whe era r ha he where the pe  the e ca e te. he ter “δοχεῖον” appear  ae hp, De usu astrolabii, 1; a ae hp, Über die nwendung des strolabs und seine nfertigung, .

Fom  si Gob o  sob

3

A atrae  the atter r  ecre  eta  ae hp (th cetr D).0 e a et that there are tret wtht a receptace, ct   e pate.  the ack e  the atrae, each  the pper tw qarat  the crce (r  e  the)  ve t °; the atte  a ceeta  ca e eare (re .) wth a pter pvtae at the ceter  the ater  the raat  the qarat.  chapter .  h treate On the Use of the elestial Globe, a-Ṣūī ecre the ctrct  a ccave etera qarat (re .) r ear the atte  the   the haw  a p- a et that the atte  the tar cat e rect eare  ervat  the e (ce the tar cat  haw). h qarat wa crprate  the ack  the atrae. r ear the atte  a ceeta  wth the atrae (re .), the ceeta  t e tarete thrh the tw ht  the pter (aae); whe the ceeta   ve thrh th ht, the e  the pter prve the atte. h eth r ear the atte  pe a accrate a repace the ar a e accrate eth  ear the atte wth a  te  the ceeta e, a t  preerve  the treate Dhāt alkursī (chapter e), a the treate  Qṭā  ūqā (chapter t-three) a a-Ṣūī (chapter I. a I.)4 On the Use of the elestial Globe. he eera ea r ear the atte  the  wth a e  t ta a  

    2   

ae hp, De usu astrolabii, 1‒1; ae hp, Über die nwendung des strolabs und seine nfertigung, –. ae hp, De usu astrolabii, 1‒1. ae hp, De usu astrolabii, 1. ee chapter : “ the eth  ta the atte  the   the e” ( the Cetar),  Vaea, “he treate Dhāt al-kursī attrte t te”. W.. Wrre,  Qusta Ibn Luqa on the Use of the elestial Globe, , ve a the tte “ the vpart  the eevat  the   the e at a te  wh” r chapter t-three,

‫ث‬ whe the tte accr t the MS Car, ār a-kt,    “

‫ن أ ن‬ ‫ن‬‫ ة‬  ‫د‬‫ ن‬ ‫ة‬ 

‫ة ن أ‬ ‫ن‬ ‫ة‬ ‫أ‬    ‫ة‬ ” (“ take the atte  the   the e at a te ‫ ة‬‫ث‬ ‫ ة‬‫ و‬‫ة‬  ‫ة‬ 

 

 wh”). he tte  the at traat  “ accepce  att  pera qcqe tepre et qacqe hra er”. rch a artíez ázqez, “Qta e ca: e phera ”, . A ar  the eth preete  chapter . a .  preete  .. ee, l-Ṣūfī on the elestial Globe, ‒.





FIGURE .5 easuring the altitude with the astrolabe.

the r  a p  the eree  the , perpecar t the race  the e (re .). he rth pe  the e  pace accr t the atte  the cat a the era r  ae t the ca era. he we rtate the e t reach the pt where the  cat  haw  the e; th happe whe the rect  the   the ae a that  the ra  the . We keep the e e a we t a qarat (re .) ve t °  the e,  ch a wa that the tp crrep t °   the hrz, the tp crrep t ° at the zeth a the qarat pae thrh the pt  the . he cat  the qarat that reache the pt  the  prve the atte  the . he r eree  the eqatr ee the pt  the ceeta phere at that et. he ccave qarat c eare the atte  a tar  the ceeta e that crrep t t atte  the k, prve that the e ha ee pte accr t the ceeta phere.  the pate  the atrae, the atte  eare  the crce parae t the hrz. he are raw ever e, tw, three, r  eree, epe  the ze  the atrae. hee crce, cae the acatar, are ctrcte  the pate  each atte (re .),  a ar wa t that whch te

Fom  si Gob o  sob



FIGURE . easuring the altitude with a globe and an external quadrant.

FIGURE .7 The quadrant for measuring the altitude on a globe, from the S of al-Ṣūfī.

ecre r the crce parae t the ecptc. he eat-wet e that crrep t the hrz  the rht phere, ae t the atte  the terretra eqatr,  raw  each pate. he ceeta eqatr wa awa epcte  the ceeta e (ecept r the prece ceeta e). Accr t the ecrpt  the treate Dhāt al-kursī a the  Qṭā  ūqā a a-Ṣūī, the eqatr  ve  

Dhāt al-kursī: MS Car, ār a-kt, īqāt Ṭaʻat 1, Arac, trct; Qṭā  ūqā: Wrre, “Qta  qa  the e  the Ceeta e”, chapter 1, ; a-Ṣūī, MS ta, pkap ara, Ahet III, ,1 chapter .1‒ (the ceeta eqatr  t





FIGURE . Plate of latitude 30°, according to the description of Joannes Philoponus.

t  eree a the raat  epcte  t, tart r the pt  the vera eq γ. he raat  the eqatr  ecear r  the rht a qe ace  the , the tar a eera a pt  the e: whe a pt  the e re, ae cre the eat hrz r the rtat  the e, the eree  the eqatr that re tae wth t  the ace  th pt. Whe the pe are  the hrz (φ=°), the eqatr  perpecar t the hrz, th we have the rht ace  th pt. Whe the pe are ce  repect t the hrz, the eqatr  qe t the hrz, th we ta the qe ace  th pt; the qe ace epe  the atte  the cat. he r eree  the eqatr etere the pt  the e  cect wth the te r a ve atte. h, t  ver prtat t traer the raat  the eqatr  the atrae. he pre w  that the eqatr  raw  the tae pate  the atrae, whe the pt γ crrep t the vera eq, whch  the e  the raat,  rtat.  the ceeta phere (re ., et) we tce that whe the vera eqcta pt γ re, the pt σ´ crrep t the wter tce a the pt Π crrep t the rth pe  the ecptc reach the era ete  the ar  chapter .1‒  .. ee, l-Ṣūfī on the elestial Globe).

Fom  si Gob o  sob

3

FIGURE . When the point γ corresponding to vernal equinox rises, the point σ΄ of the winter solstice and the pole Π of the ecliptic reach the meridian ring. The Kugel globe (left) is courtesy of Nicolas and lexis Kugel.

r, that , the tta cre σ´ΠΡσΠ´Ρ´ cce wth the era. he tta cre, accr t e,  raw  the e. ce th crce pae thrh the pe, t prject  a traht e  the atrae, a ecae t rtate wth the ra t, t  epcte  the per  the atrae. h e ha ee che a a e r the ace, a a prtr at the pt σ΄  ee (re ., rht). h e  the per  cae “τὸ τῆς ἀράχνης μοιρογνωμόνιον”  reek, pe a murī  Arac.  keep the atrae ctet wth the ceeta e, at the et  r  the pt γ  the vera eq, the e t pt t ° (re .1, tp et pae); at the et  r  the pt σ  the er tce  the rht phere, the e t pt t ° (re .1, tp rht pae); at the et  r  the pt γ΄  the ata eq, the e t pt t 1° (re .1, tt et pae); a at the et  r  the wter tce σ΄  the rht phere, the e t pt t ° (re .1, tt rht pae). hee er are wrtte  the 6 

 

8 

Ρ, Ρ´ are repectve the rth a th pe  the eqatr, Π, Π´ are repectve the rth a th pe  the ecptc, a σ, σ´ are repectve the pt crrep t the er a wter tce. Ajac, Géminos, Introduction aux Phénomènes, .‒.: “Διὰ τῶν πόλων δὲ εἰσι κύκλοι οἱ ὑπὸ τινων κόλουροι προσαγορευόμενοι, … Γράφονται δὲ οὗτοι οἱ κύκλοι διὰ τῶν τροπικῶν καὶ ἰσημερινῶν σημείων καὶ εἰς δ μέρη ἴσα διαιροῦσι τὸν διὰ μέσων τῶν ζῳδίων κύκλον.” raat r va-Berre, Geminos’s Introduction to the Phenomena, 1: “[a] thrh the pe are the crce that e ca the cre … hee crce are raw thrh the trpc a eqcta pt a ve t  eqa part the crce thrh the e  the .” ae hp, De usu astrolabii, 11; a ae hp, Über die nwendung des strolabs und seine nfertigung, .



FIGURE .



From top left: The point γ corresponding to vernal equinox rises and the index of the spider points to 0°; top right: the point σ of the summer solstice rises in the right sphere and the index of the spider points to 90°; bottom left: the point γ΄ corresponding to autumnal equinox rises and the index of the spider points to 180°; bottom right: the point σ΄ of the winter solstice rises in the right sphere and the index of the spider points to 270°.

tae part  the atrae,  the r  the ater, whch  raate r 1‒°.  the pate r the var atte th the hrz  th atte, a a arc, a the hrz  the rht phere, a the eat-wet traht e, are raw. h, whe we pace a tar r eree  the ecptc  the eat hrz, we ta t qe ace, a whe we pace t  the eat e we ta t rht ace, a cat  the e. A cpete rtat  the per repreet the ra t  the ceeta phere.  th wa, the ceeta t ha ee traerre t the pae. he ecrpt  the ceeta e c r reek rce  t et a raat  the hrz. ar, the ecrpt  the atrae r the ae rce  t et azth e. he azth e are the prject  the reat crce thrh the zeth a ar a etere the rect  the hrz. he rect  the hrz were trce ater  the Ara. he treate On the Use of the elestial Globe

Fom  si Gob o  sob

5

 Qṭā  ūqā a Dhāt al-kursī et the r cara pt  the hrz  the e, the r a ett r er a wter a the v  the hrz r t °. A-Ṣūī ecre the raat  the hrz r ° t °  each e  the qarat, tart r the eat a the wet pt (r a ett at the eqe) twar the rth a the th.40 he raat  the hrz  e r eter the rtve apte  the tar a the eree  the ecptc, a the azth  the qibla.4 he azth  the atrae appear  the treate  ʿAī  ʿĪā (fl.  D)  the atrae, where  chapter 1, the azth  the   etere4 a re etae  the treate  a-hwārzī (ehth t th cetr D)  the atrae.4 Azth e are t raw  the pate  the preerve atrae c r the th a teth cetre. he atrae, cta a the eeet  the ceeta e prjecte  the pae  the rt e, ha t pet  ree pace.  th pace ata eeet appear  the atrae, ch a: .

he e  the eqa hr raw  the pate ew the hrz (re .). w the pt  the  r a tar  the k, we ca rea rect the te  eqa hr  the atrae.

9 

Dhāt al-kursī: MS Car, ār a-kt, īqāt Ṭaʻat 1, Arac, trct; Qṭā  ūqā: Wrre, “Qta  qa  the e  the Ceeta e”, chapter 1, . ee a the trct  treate  a the cetar  t  Vaea, The Treatise Dhāt al-kursī ttributed to Ptolemy. A-Ṣūī, MS ta, pkap ara, Ahet III, ,1 chapter . (the ecrpt  the hrz  t ete  the ar  chapter .  .. ee, l-Ṣūfī on the elestial Globe). Dhāt al-kursī, chapter 1: rtve apte  the tar a the eree  the ecptc; chapter : the qibla. Qṭā  ūqā, chapter , , 1: rtve apte  the tar a the eree  the ecptc; chapter : the qibla. A-Ṣūī, chapter .1‒1 azth  the , tar a paet, a eree  the ecptc; chapter II.‒: rtve apte  the eree  the ecptc a the tar; r a ar  the prcere  a-Ṣūī ee .. ee, l-Ṣūfī on the elestial Globe, ‒, ‒. ‫أ‬ ‫ة‬ ee ʿAī  ʿā, “’atrae et a aère e ’e ervr” “‫ا ن‬‫ر‬ � ”, e. ‫ص‬ ‫ا‬ ‫ل ن‬‫ع‬  ‫ ن‬‫ك‬ . Chekh, l-ashriq 1 (11): ‒. e rak, “e Verwe e Atra ach a-Chwārzī”, Ahae zr echchte er atrwechate  er ez, et III (rae: 1), 1‒; a raç Charette a etra ch, “A-hwārzī a ractca Atr  thCetr Baha. he aret tat Crp  et  Arac  the Atrae a ther rtae tret”, CAM  (): 11–1.

 

 

2   





FIGURE .

. . v.

The quadrant of the sine on the astrolabe.

he haw qare a haw arc  the ack e (re .): Whe the pter, r aae, eare the atte  a ceeta , we ca ta rect the taet r the ctaet  the ae  atte.44 he qarat  e  the ack e (re .11): kw the ae, we a ta rect the e  the ae  the aae, whe t ee, etwee the ceter a e  the tp  ve t  r 1 part. he e  the eqa hr (re .)  the ack e: hee e aw  t  t the te  eqa hr, whe ear the atte  the  wth the aae/pter. here are tw eret tpe  thee e: r a atte r r a ve atte; the e  the a a ater  praer (r a ve atte) ca e epcte  the ae qarat.

he prcere we r v atrca pre wth the ceeta e a the atrae are ar. A a eape, we cpare the prcere r eter the te r ate wth the e a the atrae  eqa a eqa hr:  

r re eta  the wa the taet a ctaet  a ae ca e tae  the haw qare r the haw arc, ee ra Vaea, “e traté ’a-Ṣūī r ’atrae” (h ., vert ar  – e ert, ), ‒.

Fom  si Gob o  sob

Celestial globe

7

Astrolabe

. We pace the rth pe  the e We e the pate r atte φ  at a eevat eqa t the atte the atrae. φ. 2. We etere the pt  the   the ecptc r the crret a. We pace a a p-  We ark the pt  the   th pt, perpecar t the the ecptc  the per. race  the e. . ear the atte  the  We et a ra pa thrh the We retate the era  the e t the ca era a the tw ht  the pter a we rea the cat  the tp  the we rtate the e t reach the pt where the   the pter  the qarat  atte  the ack e  the atrae. eree  the  cat  haw. We eare the atte  the  wth a raate qarat. . he pt  the e We rtate the per  the rt crrep t the pt  the e  rer t pace the eree ceeta phere at th et.  the   the acatar accr t t atte, eat r wet  the era epe  whether the eareet  ere r ater . he rt e  the atrae  repreet the pt  the ceeta phere at th et. . We erve a reta the eree We rea the cat d  the d  the eqatr that cre the e  the per. eat hrz (the r eree  the eqatr). 6. eter the te  eqa hr We rtate the e  the ppte We rtate the per  the atrae ee  the zaca ,  that  the ppte ee  the zaca the eree  the  ce t the ,  that the eree  the  eat hrz; we erve a reta ce t the eat hrz; we rea the eree d2  the eqatr that the cat d2  the e. cre the eat hrz.





(ct.) Celestial globe

Astrolabe

he te te  eqa hr ce the re  d2  d 1  , if d1  d2  15 te    360  d2  d1 , if d1  d2  15 .

( hr crrep t a rtat  °  the ceeta phere). eter the te  eqa hr he te tu  eqa hr ce We pace the eree  the   the acatar accr t the re  t atte, eat r wet  the d2  d 1  era epe  whether , if d1  d2  n the eareet  ere r ater tu   d d    360 ; the pt  the eree 2 1  , if d1  d2  n aetrca ppte t the eree  the , a the e  the where n  the er  the eree eqa hr, ve rect the  revt crrep t e te  eqa hr ce re. eqa hr

Conclusions he ctrct  the papherc atrae preppe the tereraphc prject  the e t the pae  t eqatr;  th wa, a the ct  the e ca e traerre t the atrae. Athh the ceeta e  tae r actc prpe, t  re ct t ctrct, traprt a ake eareet wth. he repreetat  the heave  the atrae  re atract, t tae r re accrate eareet.  eeva te, the atrae ecae a ppar tret erche wth a appcat, whch c t  repace the ceeta e  v atrca pre, t a er ater a re accrate ret a rae the rae  atrca pre that c e ve.

 

Knowledge in Motion: An Early European Astrolabe and Its Possible Medieval Itinerary Petra G. Schmidl

xzzstr “rmtv r,” rrt vrsty, rrt m , rmy [email protected]

Abstract s rt ssss t p  t  r, t rr rts,  ssqt trvs   s  t ry rp str (Itrt Istrmt Cst  #11)  prsrv  xr,  t sm  t stry  S. Atr t t srt rr srpts, t vstts t v v y t str r ts st  t,  ssts  pss trry  ts strmt. I t Appx   srpt  t str s prv.

Keywords strs – str t – rt  st strmts – Itrt Istrmt Cst mr #11 – sm  t stry  S (xr)

Introduction  sm  t stry  S  xr s t m   ry rp str (Itrt Istrmt Cst  #11). At s  t, t strmt ts prvs rmt tt s s t spt t ts p  t  r, ts rr rts  ts ssqt trvs.  psst t ts  stry t   mt  t  As.   r   srpt  t str s “Appx: Dsrpt  IIC #11,” Knowledge in Motion s s t tt  vm   zr Iq (.), Studies in the Making of Islamic Science (rm: Ast, 1). © koninklijke brill nv, leiden, �9 | doi:0.63/9789004387867_008

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

Earlier Descriptions r try t rstrt  pss mv trry  ts str, t s pprprt t prst  t sss rst t v srpts  t. I t 1s, rt tr stts  s Astrolabes of the World tt  #11 s  “ry r str … .  1–1 … prs y . vs … t t ss s, rs, 1 r 111.” vsy,  s ts sttmt  rmt prv y s vs, s r,  sssm    st strmts s t sttts t ss  t sm  t stry  S  xr. vs’s r t try, mst pry rtt y m  y tr prs t str  rs, rprts “r”  “. 1‒1.” Itrsty, vs s, ss tr rmt, tt “t rm  t str ptrs  t rt s Ism,”  p  rmt rppr  Dv ’s pt rt t  #11 (s )  sts  ts rt,  tr rts tt “t rt s   ‘t’ typ.” vs’s  tr’s s r st  t  ts str r rm  tr srpts. ss vs  tr,  vr  Sps r   rr t,  t Dr  S r  s s. I tr Computerized Checklist of Astrolabes, mp  t ry 1s, ty st t  r t  “sp-rs” r,  v  t r  try rr, my “. 1.”   srpts  ts spts.  rr ts  t mp  t xr sm  t stry  S mt  “rt t: . 1”     rt . tr, The Astrolabes of the World,  vs. (xr: xr vrsty rss, 1), , . 11, try  t ss s t s t prv y sstt rmt  ts t strmt t t sxtt try (pt y prv y Stp Jst, sm  t stry  S, s t ss t, v  t ttp://.ms.x../p-tt/tms/ms-1-rspsv/mpp/m .pp?r=&m=ys) (ss  J 1).   A  y prv y Stp Jst r t r.   “Spr . 11,” v  t ttp://.ms.x../spr/x.tm?ss11/ rt (ss  J 1). 5  t y prv y Stp Jst   s  (“vs’ r,” v  t ttp://.ms.x../p-tt/tms/ms-1-rspsv/m-m.pp? r=, ss  J 1).   “vs’ r.” 7  tr, Astrolabes, , . 11.   Dr  S r, Sr . r, J A. rs, A Computerized Checklist of Astrolabes ( v, T:  vrsty rss, 1), 1  pssm.

Know n Moon

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“rt p: Sp, rp.”  mpy srpt prv y Ir  vs t sm t    “sp-rs” r. I t t  tts s  t rsr m y Dv   s tm  rrt  t 1s, t “Sps” r  t str s  y  qst mr; t t s mss. y,  pt t  r s   t pts   #11  Dv ’s  The Ciphers of the Monks srs ts strmt vry rly s “ mpst str t  rt tr m rm r spr y  Ism , r r It mtr,  rtr Sp  r pts (#11).”  vs rtr st  ts r r y t. Localisation  sm xtt, t rmt v y ts srpts    y v  sr  t t str ts. Cr vs’s  tr’s rmt   r  r, tr m v r pts 1  , r rs s mt  t, s tt ty   #11 t r. y t tr tt rs, t trs t tt tr rs mt t tt  ts ty. s r  s  y t t tt t A-ss, 1   t r rs, r   s mpty rt rm tr rsptv -ss, s rvs r smr t  tr pts (rt   t ppx:  C). s  t rt s  1  1 s  s    , t smpst xpt— tr rpmt  t pts—s t  qst. Aty,  pts t prpry. r s  vs v  rmv  r yr  rvs r vs rs  sp, sz, r  txtr r t rss  t pts. tr vstt spprts ts srvt. y t rr, p  rs   #11 r   sty rt y. rr, t s mr ps tt  t  t str  

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“r ts  #11,” v  t ttp://.ms.x../ts/sr/ spyrr/?m=spymx&m=t&r= (ss r 1, 1). “xr rrtv  #11,” v  t ttp://.ms.x../t/v/  (ss  J 1). “rrt t:   tts, prt ,” v  t ttp:// .v.r/strmt-t-C.tm#prt (ss  J 1). Dv A. , The Ciphers of the Monks. A Forgotten Number-Notation of the Middle Ages, ts  (Stttrt: rz Str, 1), . J Dvs, t Ds, t (Ips, S), y prv m t t rsts  s mtr vstt  rt  xr  Jy 1 y “x-ry

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mprs y-rv pts s ppst ss r y rv t t s r  t st-st  rt-st s s  s t rs r t qtr  t trps  Cr  Cprr. , ts pts r mpt r  sp tt   s stp  t str  p r r. rm  prt pt  v, t pts m r t sm ty r sprls   s str. As s v, rpmt s  sr. s pt 1   spy sty rt rvs, t pprs v tt ty r m y rt s. W mpr t srpts s mpr y t sm mt  ttrs v, rt sts  t zmt rvs (vry °  pt 1  vry °  pt )  rt ys  rt t mrs  t rs (mr rs  pt 1  -Ar mrs  pt ) pt t t s t r rtr t  (rt   t ppx:  D   A). rr,   t t pts r rs   tr t t tr. vrtss, ty mst v  vs’s  tr’s m v r sst ts str t r. I ty  rz tt pt  s mst pry rv  t sm  s t rt ( A), ts my v v strt tr

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lrs () s mmr, prt qpmt,” “Iv- ( ymps Istrmts) Ap   yzr” (J Dvs, Metallurgy of Medieval Scientic Instruments (MoMSI). rt rps, ps, y prv y y x, sm  t stry  S, xr). I s prmry s,  rts: “st mpts r tts t mm Z  S. t  mr  sty rt ys.  t   s s t t (st) mtr  m s  pr  rss.  pts (  tt) v  r  Z vs rm . 1% t . 1%,  t vry    .  rt v rt Z vs rt t  (xp) t s t ry rm  rt sr t t tr mpts.  r  rs r mst pry mr t t  s y t  r (t t  str y r t sts).” I  prvt vrst ( Sptmr 1)  sps: “r s  t r t t mtr (t qt  Z  rtvy mm-t- )  t rst  t mr mpts. Ays rm rtr rp ry v ts ‘rty’ ( , >.%) v rs ts rm str rs r ‘r’ ( re dditios mde y me to restore the text. S F hs o te of otets. The isted hedigs re oeted from eh hpter.

5

Aī Al-Dīn Al-Aī

‫ن‬   ‫ض‬  ‫ ف‬ 

‫ء‬   ‫ط‬    ‫ء‬ ‫ط‬  ‫ ف‬ 

      ‫ ف‬      ‫ر ف‬ 

‫د‬   ‫شر ف‬  

 ‫صر‬ ّ  ‫شر ف‬  

    > <  ‫شر ف‬  

.         ‫شر ف‬  

.  : ّ‫ط‬ ] ‫ط‬ 

Chpter oe is  itrodutio to the mes of prts d ptes of the stroe with rief exptios of wht they re.  the rest of the hpters, the uthor expis how to operte the istrumet for sovig spei proems. The hedigs of hpters two to fourtee impress o us tht they re very simir to those of the hpters i K-Book, setio oe, i terms of their order d wordig. By omprig the texts of -Treatise d K-Book, we reize tht the ore of -Treatise, hpters two to fourtee is  opy from K-Book, setio oe, though he ever metios the soure. To rify hr’s depedee o K-Book,  wi preset the whoe of hpter two of -Treatise with its soure, mey the etire text of K-Book, setio oe, hpter oe: A-Treatise, chapter twoa

K-Book, section one, chapter oneb

[1] The stroe hgs to the right side, d the stroe’s k is mde fig the u, d you tur the idde o the titude degrees uti the u’s ry eters the upper hoe of the idde’s edge d deprts from the ower hoe. o the titude degrees etwee the idde’s edge d the est poit re the u’s titude; wht is etwee the meridi ie d the idde’s edge is the ompemet of the titude.

[1] ou hg the stroe to your right side, with the mter’s k fig the u, d you tur the idde o the titude degrees uti you pe its two sightig ves fig the u so tht the u’s ry eters the upper hoe d psses through the ower hoe. o the titude degrees etwee the idde’s hed d the est-west iec re the u’s titude t tht momet.





(ot.) A-Treatise, chapter two

K-Book, section one, chapter one

[] f the dy is oud (si!), d the u’s ody is ppret, whie its rys re hidde, we hg the stroe fig oe of the eyes, d tur the idde uti the u’s ody is see y this eye through  hoe [of the sightig ves] of the idde. o [the pe] where the idde’s hed hs fe is the titude. ikewise, the titude of  str t ight is tke. t is etter to put  tue etwee the two hoes [of the sightig ves] of the idde i order to prevet the visu rys from spredig. [3] f we woder whether the titude is ester or wester, we tke the titude d eve for  itte whie, d the tke the titude gi. f the seod titude ireses from the rst titude, it [the rst titude] is ester; if it dereses, it is wester. This questio oy ours whe the u or strs re i the viiity of the middy. [] f we wt the utmost titude of the u or  str, we tke its titude, i the oditio tht it is i the viiity of the middy, momet fter momet. o whe we d it egiig to derese, the titude tht is efore it is the utmost titude.

[] f  dy is oud (si!), d the u’s ody is ppret, whie its rys re hidde, we hg the stroe fig oe of the eyes, d tur the idde uti we see y this eye the u’s ody through the two hoes [of the sightig ves] of the idde. o [the pe] where the idde’s hed hs fe is the titude. ikewise, the titude of  str t ight is equy tke.

[3] f we woder whether the titude is ester or wester, we puse for  itte whie fter tkig the titude, d the we tke the titude gi. f the seod titude ireses, the rst titude is ester; if the seod titude dereses, the rst titude is wester. This questio does ot our exept whe the u or  str is i the viiity of the middy. [] f we wt the utmost titude, we oserve the u or  str uti, whe it is i the viiity of the middy, tht is, it is pprohig it, we tke its titude momet fter momet. o whe we see it egiig to derese, the titude djet to it eforehd is the utmost titude.



Aī Al-Dīn Al-Aī

A-Treatise, chapter two

K-Book, section one, chapter one

    ‫ط‬‫أ‬ ّ  []

  ‫ط‬‫أ‬ ّ  []

‫ض‬  ،   ‫ط‬‫أ‬

‫ء‬  ‫ض‬  ،   ّ‫أ‬

‫ض‬     ‫ ف‬

    ‫ ف‬ 

  ّ   ‫ء‬ 

 ‫ء‬ ّ   ّ  

   ،     

‫ض‬     ،  

  ّ   .   

.   ‫ ف‬  

 )!(    ‫إ‬ []

  )!(     []

،   ‫ء‬ ‫ط‬‫أ‬ ّ 

 ّ  ‫ض‬  ،  

   ، ‫ض‬   

.   ‫ض‬    ،

 ‫ء‬  ‫شر‬ ‫ط‬ ‫ض‬  ‫ء‬   ‫شر‬  ّ  .   ‫ض‬  ‫ن‬

،ً   ً    ‫ء‬ ‫ط‬‫أ‬ ّ  ،   

  ‫ك‬  ّ  ‫ض‬  ‫ض‬      ‫ك‬

 ‫ؤ‬  .   ‫ض‬ .  ‫ـ‬  ‫ؤ‬ ‫ء‬      ّ  ‫أ‬ . ‫ـ‬  ‫صر‬    ‫ض‬

.

‫رق‬   ّ   ‫إ‬ []

 ‫رق‬   ّ  ‫ ف‬  []

  .ً    ّ ‫ ً ث‬

    .ً   

ً  ّ    ،  ّ ‫ ًث‬    ّ  ،   ‫رق‬ ّ‫أ‬    

  ‫إ‬ ، ‫رق‬ ّ‫أ‬ 

ّ   ّ‫إ‬ .   ‫إ‬ ،    .  ّ‫أ‬  

ً  ‫ـ‬     ‫ـ‬     ّ ّ . ‫ن‬ 

. ‫ن‬   





(ot.) A-Treatise, chapter two

K-Book, section one, chapter one

  ‫ غ‬ ‫إ‬ []

 ،  ‫ غ‬  []

    ، ‫ـ‬ 

   ّ  ‫ـ‬  

 ،     

    . ‫ظ‬  ‫ظ‬ 

 . ‫ظ‬  ‫ظ‬ ‫ن‬  ً 

 ،    ‫ن‬  

.  ‫ غ‬  ‫ذ‬    ‫ذ‬   ،  ‫ف‬ .  ‫ غ‬

 ] ‫ؤ‬   : ُ‫ئ‬ ]  

 ، ‫ـ‬ :  =  : ِ  =  ] ّ  

]    :  [    : 

= ‫ـ‬ :  =  ،  ]    ،  :

]    : ّ ]    : .  : 

‫ط‬ = ‫ـ‬ ،  ] ‫ط‬‫أ‬ 

،  ]   ‫ـ‬ :  ]    :  :  =  ]    ، ‫ـ‬ :  = 

]  ‫ ف‬  : ‫ى‬ ] ّ    ، ‫ـ‬ ، 

 ]   ‫ـ‬ :  ]   ‫ـ‬ :  ،  ] ‫ض‬   :  ]   ‫ـ‬ : 

»«( ‫د‬ = ‫ـ‬ :  ‫د‬ = 

‫د‬ + ]    : )‫ط‬   =  :   = ‫ـ‬ [    :

] ‫ء‬   :  =  : 

‫رق‬  ‫ـ‬ :   ]   ‫ـ‬ : 

 ]    )‫ط‬ »«‫ـ‬(  : ‫رق‬ ]

:  = ‫ـ‬ ،  ] ّ‫أ‬    :     ‫إ‬  

   + ]  . – ]  ّ‫أ‬ ]    :    

] ‫ـ‬   ، ‫ـ‬ :  =  ، 

 ‫ـ‬ :   ]    : ‫ـ‬



Aī Al-Dīn Al-Aī (ot.) A-Treatise, chapter two

K-Book, section one, chapter one

  ‫ـ‬ ،  :  =  ،  ] 

.  :  ]    :  ]

 S F: foio , ie –foio , ie .  S : foio , ie –foio , ie ; S P: foio , ie –foio , ie ; S G: foio , ies –; S : foio , ie –foio , ie .  Oe of the two etr ies o the pte drw from est to west; o this tehi term see K-Book, itrodutio edited i ppedix C of this pper.

This exmpe iustrtes tht hpter two is  opy of K-Book, setio oe, hpter oe with some moditio. Espeiy, the rst prt of [] (“f  dy is oud” vs. “f the dy is oud”) shows hr’s strog depedee o Kūshyār’s text. First, this setee writte y Kūshyār must e “in kāna yawm ghayman,” ot “in kāna yawm ghaym,” where he fis to mke ghaym ustive owig to kāna. d the expressio of ghaym is odd i this otext euse this term mes “oud”; he shoud use ghāʾim, whih deotes “oudy.” But hr opies this wkwrd setee with this grmmti mistke. O the other hd, hr sometimes modies the soure text.  the st setee of [] (“This questio does ot our exept whe the u or  str is . . .”), he hges its struture from “. . . does ot our . . . exept whe . . .(wa-lā yaqaʿu . . . illā idhā . . .)” to “. . . oy ours whe . . . (innamā yaqaʿu . . . idhā . . .).” Moreover, he puts dditio iformtio i the st prts of [] d [].  eh of hpters two to fourtee, hr utiizes  hpter (or two hpters) of K-Book, setio oe. The foowig is the ist of K-Book, setio oe’s hpters from whih hr opies the text:

• • • • • • 0 

-Treatise, hpter two: K-Book, setio oe, hpter oe; -Treatise, hpter three: K-Book, setio oe, hpter two; -Treatise, hpter four: K-Book, setio oe, hpters six d seve; -Treatise, hpter ve: K-Book, setio oe, hpter ie; -Treatise, hpter six: K-Book, setio oe, hpter fourtee; -Treatise, hpter seve: K-Book, setio oe, hpter ftee; This poit is owed to the oymous referee of this rtie.





• • • • • • •

-Treatise, hpter eight: K-Book, setio oe, hpters sixtee d sevetee; -Treatise, hpter ie: K-Book, setio oe, hpter eightee; -Treatise, hpter te: K-Book, setio oe, hpter te; -Treatise, hpter eeve: K-Book, setio oe, hpter thirtee; -Treatise, hpter tweve: K-Book, setio oe, hpter twety-two; -Treatise, hpter thirtee: K-Book, setio oe, hpter twethy-three; -Treatise, hpter fourtee: K-Book, setio oe, hpter twety-four.

The ove ist shows hr’s skippig K-Book, setio oe, hpters three to ve, eight, eeve, tweve, d ietee to twety-oe. t is remrke tht whie Kūshyār gthers si opertios i setio oe etited “o idispese mtters,” hr further hooses fudmet oes from them. ordig to hr’s im of seetig esseti opertios, the omissio of hpter twety (o how to drw the meridi ie) is resoe, euse Kūshyār does ot use the stroe i it. mog the rest of the deeted hpters, we d tht Kūshyār expis simir proems i hpters two to ve d eight: o opertig for the djustmet of degrees (e.g., the u’s degree) ot ttig the irtio of the stroi pte. is remov of them suggests tht he thiks tht the djustmet is ot esseti. d hpters eeve d tweve  e ssied i oe tegory: o opertig oerig the xed strs; this tegory might oti hpter ietee, where Kūshyār determies the risig of dw d the settig of dusk y usig the poiter of  xed str.  their omissio, we detet his hesittio i keepig sujets o the xed strs s fudmet, though he metios two opertios usig  xed str’s poiter i hpters three d four.  some hpters of -Treatise, hr uses  prt of the soure hpter(s), whie skippig some topis ot reevt (or fudmet) to -Treatise. For exmpe, he omposes hpter four from K-Book, setio oe, hpters six d seve, d omits the st two topis of hpter seve: how to determie the degrees of the equ hours from the titude of  eesti ojet d how to determie the seso hours y usig spei urves egrved o  type of idde; i hpter eight, he utiizes K-Book, setio oe, hpters sixtee d sevetee, d he skips the se of the equtori regio; i hpter ie, he opies the most prt of K-Book, setio oe, hpter eightee, ut he deetes the st topi: o how to determie the rottio of the eesti sphere from the u’s risig uti the trsfer of yers; i hpter te, he skips Kūshyār’s exptio out the ft tht the stroe oy gives the u’s deitio pproximtey; i hpter eeve, he opies the rst prt of K-Book, setio oe, hpter thirtee, ut skips the seod prt, where Kūshyār presets how to kow the terrestri titude from the titude of  xed str; d i hpters



Aī Al-Dīn Al-Aī

thirtee d fourtee, he uses K-Book, setio oe, hpters twety-three d twety-four, respetivey, ut i eh hpter he omits Kūshyār’s exptio of his opertio y usig  digrm. s show ove, hr mde his ow “Tretises o the Opertio of the stroe” y seetig topis from K-Book, setio oe. Moreover, he sometimes iserts extr iformtio ot foud i Kūshyār’s text. -Treatise, hpter tweve otis  iterestig exmpe of his dditio d hevy editori eforts. Of the two hpters o shdows i K-Book, setio oe, mey hpters twety-oe d twety-two, hr skips twety-oe (o kowig the shdow egth from the titude) i his tretise, ut he uses twety-two (o kowig the egiig of the ṣr d its ed) i his hpter tweve. ie he omits the exptio of how to oti the shdow egth from the u’s titude y usig the stroe give i K-Book, setio oe, twety-oe, he expds  prt of Kūshyār’s text of twety-two. The foowig is the whoe of -Treatise, hpter tweve s we s K-Book, setio oe, twety-two: A-Treatise, chapter twelvea

K-Book, section one, chapter twenty-twob

ou put the idde o the [u’s] titude t middy. o the shdow degrees o whih the other edge of the idde hs fe is the digits of the shdow [egth] orrespodig to the [u’s] titude t middy. ou dd tweve digits to them, d put  edge of the idde o these degrees of the shdow. o the titude degrees o whih the other edge of the idde hs fe is the [u’s] titude t the egiig of the time Aṣr. ou dd twety-four digits to the shdow [egth] of the [u’s] titude t middy, d put the idde o tht titude. o the titude degrees o whih the other edge of the idde hs fe is the degrees of the [u’s] titude t the ed of the time.

ou kow the digits of the shdow orrespodig to the [u’s] titude t middy.

ou dd tweve digits to them, d tke its titude. o wht hs resuted is the [u’s] titude t the egiig of the Aṣr.

ou dd twety-four digits to the shdow [egth] of the [u’s] titude t middy, d tke its titude. o wht hs resuted is the [u’s] titude t the ed of the ṣr.

2



(ot.) A-Treatise, chapter twelvea

K-Book, section one, chapter twenty-twob

f the shdow [egth] is [give] i feet, seve d fourtee re [dded] isted of tweve d twety-four, respetivey. ome smi peope mke the egiig of the time Aṣr t the ed of its time we hve desried, d the ed of its time efore the u’s settig. This is  topi sed o the Sharīʿa d the vriety of their dotries. ‫ن‬    ‫ض‬ ‫ض‬

 ‫ض‬ ‫آ‬     ،

.‫ن‬    ّ   

   ّ ‫ظ‬    ّ ‫ظ‬ ‫ء‬ . ‫ن‬

‫ض‬ ،ً  ‫شر‬   

، ّ ‫ظ‬  ‫ء‬‫أ‬ ‫ك‬  ‫ض‬ 

‫ء‬  ‫ض‬ ‫آ‬    

 ّ     

.‫صر‬

‫ن‬    ّ   

 ‫ض‬ ‫ض‬ ،ً  ‫شر‬   ‫آ‬      

 ‫ء‬   ‫ء‬  ‫ض‬

.  

 ،ً  ‫شر‬   

ّ     ، ً  

. ‫صر‬

‫ كد‬‫ن‬    ّ   

    ،   ،ً 

. ‫صر‬ 



Aī Al-Dīn Al-Aī (ot.) A-Treatise, chapter twelvea

K-Book, section one, chapter twenty-twob

  ،ً   ّ ‫ظ‬  

‫أ‬ ‫شر‬  ً  ‫شر‬ ‫أ‬ . ‫شر‬

 ّ     

  ،  ‫ذ‬   ‫صر‬

   .    .  ‫ب‬   ‫شر‬

‫ض‬ ] ‫ض‬   : ‫ض‬ ] ‫ض‬ 

    :  ]    :

 = ‫ـ‬ ،  :  =  ]  

، ‫ـ‬ :  =  ،  ]    :

  : ‫ض‬  ] ‫ض‬   :   ]

‫ـ‬ ،  :  =  ،  ]   

.  : ‫ض‬  ] ‫ض‬

:  = ‫ـ‬ ،  ،  :  ]  

  : ً  ]    :  ]  ‫ـ‬ ،  :  =  ،  :  ]   ]   – ، ‫ـ‬– =  ،  ]ً   

،  ] ‫ كد‬  :  = ‫ـ‬ ،  ،  :  : ‫ں‬‫ر‬  = ‫ـ‬ : ‫شر‬  = 

 = ‫ـ‬ ،  ،  :  ]   

‫أ‬   : ‫شر ] ىب‬    :

 ،  ]     :‫كد‬ ] ‫شر‬

‫ـ‬ :  =  ،  ]   ‫ـ‬ :  =

 + ]   ‫ـ‬ : =  ،  ]  

:   =  ،  ] ‫ب‬  ‫ـ‬ : . – ]  ‫ب‬ . . .    ‫ـ‬

 S F: foio , ie –foio , ie .  S : foio , ie –foio , ie ; S P: foio , ies –; S G: foio , ies –; S : foio , ies –.

4



ere he tries to keep the osistey of Kūshyār’s text i his tretise y ddig iformtio o how to oti the shdow egth from the titude degrees d vice versa; however, he skips the st prt of twety-two, proy euse of its eig ot reevt to his work. other exmpe is foud i -Treatise, hpter ve, i the egiig of whih we so detet hr’s dditio to the text of K-Book, setio oe, hpter ie, s foows: A-Treatise, chapter vea

K-Book, section one, chapter nineb

ou put the sedt degree o the ester horizo. o mog the degrees of the zodi sigs, tht whih hs fe o the ie of the mid-heve, i.e., the upper hf of the meridi ie, is the egiig of the teth pe. Tht whih hs fe o the wester horizo is the egiig of the seveth [pe]. Tht whih hs fe o the ie of the rdie of the erth, i.e., the ower hf of the meridi ie, is the egiig of the fourth pe. These re the four rdies.

he the sedt degree is put o the ester horizo, the degree fig o the ie of the mid-heve is the egiig of the teth pe.

 ، ‫شر‬   ‫ط‬ ‫ء‬ ‫ض‬

‫ء‬   ّ   ‫ء‬  

‫ن‬   ّ  ‫أ‬   . ‫ر‬  ّ 

The degree fig o the wester horizoc is the egiig of the seveth pe. The degree fig o the ie of the rdie of the erth is the egiig of the fourth pe. These four pes re the rdies.

 ، ‫شر‬   ‫ط‬ ‫ء‬    ‫ء‬   ّ   ‫ذ‬ ‫ء‬ . ‫ر‬  ّ

.  ّ    ‫قع‬ ‫ما‬

ّ      ‫ذ‬ ‫ء‬

 ‫أ‬   ّ   

‫أ‬   ّ   ‫ذ‬ ‫ء‬

 ‫ن‬   ّ  ‫أ‬ 

.   ّ

.  

.   ّ 

5

Aī Al-Dīn Al-Aī (ot.) A-Treatise, chapter vea

‫أ‬ ‫أ‬  

 ]     : ‫ض‬ ] ‫ض‬   :  ]    :  ]    : .  :  ]  

K-Book, section one, chapter nineb

. ‫أ‬  ‫أ‬  

 ّ   ‫ـ‬ : ‫ط‬ ]   

= ‫ـ‬ :    =  ،  ] ‫ر‬

 + ]    : ‫ر‬  

 =  ،  ] ّ    ، ‫ـ‬ : 

‫ذ‬ ‫ء‬  – = ‫ـ‬ ،  ]   ‫ـ‬ :

 + ] ‫أ‬  – ]   . . .

 =  ،  ]    ، ‫ـ‬ :  

. – ، ‫ـ‬– =  ،  ] ّ   ، ‫ـ‬ :

 S F: foio , ie –foio , ie .  S : foio , ie –foio , ie ; S P: foio , ie –foio , ie ; S G: foio , ies –; S : foio , ies –.  SS G d  dd the foowig phrse: “i.e., the degree of the west.”

 this prt, he iserts desriptios of the two ies (the ie of the mid-heve d the ie of the rdie of the erth) o the stroi pte, whie Kūshyār uses these tehi terms without exptio. Tht is euse Kūshyār hs redy expied them whe desriig two etr ies of the pte i the itrodutio, s foows:        ‫ذ‬ ّ :  ‫ ف‬ ّ‫ط‬ ، ‫ء‬   ّ    ‫ذ‬  ّ ، ‫ن‬   ّ       ّ   ‫ط‬ ‫ذ‬ ّ . ‫أ‬   ّ ‫آ‬  .  ‫شر‬  ّ    

(The two ies uttig eh other o the ptes: s for tht whih is exteded from the ord d hves the pte, it is the meridi ie; the hf whih is ext to the ord is ed the ie of the midheve, d the other hf is [ed] the 1 

The whoe ri text of the tter hf of K-Book’s itrodutio, where Kūshyār dees stroi prts, is edited i ppedix C of this pper with  Egish trstio.





ie of the rdie of the erth. s for tht whih hves this ie perpediury t the eter of the pte, it is the est-west ie). O the other hd, hr expis these two ies i hpter oe, s foows: . ‫ة‬   ‫ـ‬    ‫ذ‬  ّ   ‫ن‬   ّ

.    ‫ن‬   ّ    ّ  ‫ء‬  ّ

(The meridi ie is the ie tke from the side of the throe to the other side. The ie of the equtor is the ie uttig the meridi ie perpediury.) This quottio shows tht i hpter oe, he does ot itrodue the ie of the mid-heve d the ie of the rdie of the erth, so he eeds to dee them whe metioig them for the rst time. Moreover,  ompriso etwee the two texts o the two etr ies mkes er tht uike hpters two to fourtee, he writes their exptios without usig Kūshyār’s text; i ft, his termioogy “the ie of the equtori regio” is diferet from “the estwest ie” foud i K-Book. Thus, we must sk: hy does he ompose  ew exptio of stroi prts? To euidte his im,  wi ext ompre the itrodutio of stroi prts y hr d tht y Kūshyār.  strikig diferee etwee them is foud i their texts o the horizo ire d the mutrs, s foows: From A-Treatise, chapter one

From K-Book, introduction

The horizo ire is the ire pssig through the two itersetio poits etwee the equtor d the ie of the equtori regio. The mutrs re the ires ove the erth.

The mutr ires re the ires drw o the ptes roud poit C; some of them re ompete ires, wheres others re iompete; etwee them, the umers of their degrees re writte ordig to the stroe’s irtio: if it is  oe-sixth [stroe], every six degrees re [writte]; if it is  oe-third, every three degrees re [writte]; if it is  hf, every two degrees re [writte]; d if it is  ompete [stroe], every degree is [writte].

 

-Treatise, hpter oe is edited i ppedix  of this pper with  Egish trstio.



Aī Al-Dīn Al-Aī

From A-Treatise, chapter one

From K-Book, introduction

The rst of these mutr ires is the ester d wester horizo,a d “est” d “west” re writte o it. The mutrs djet to the ester horizo towrds the meridi ie re the ester mutrs, d the [mutrs] djet to the wester horizo towrds the meridi ie re the wester mutrs. ht is etwee the eter of the pte d the rst mutr o the ie of the rdie of the erth is the terrestri titude of the regio [supposed i] the pte. ‫ط‬   ‫د‬ ‫أ‬ 

‫ ف‬‫ط‬ ‫د‬  ‫ط‬ 

. ‫أ‬   ‫د‬  ‫ط‬

‫ئ‬   ‫ن‬  ، ّ ‫غ‬

. ‫ء‬  ّ ‫ن‬ ّ   ‫ن‬ ّ  ‫ن‬ ، ‫ ص‬‫ط‬ ‫ط‬  ّ ً    : ‫ط‬‫أ‬  

  ‫إ‬ ،  ً   ‫إ‬ ، ّ 

. ‫ء‬ ‫ء‬ ًّ  ‫إ‬ ،   ً 

 ‫شر‬  ‫ط‬   ّ ‫ط‬ .  ‫شر‬  

 ‫ن‬   ّ  ‫شرق‬ ‫أ‬  

  ‫أ‬   ، ‫شر‬ ‫ط‬  .  ‫ط‬  ‫ن‬   ّ

 ّ  ‫ط‬ ّ    

.  ‫د‬   ‫أ‬ 

 SS G d  dd: “d the diretios of est d west.”





he desriig the mutrs, hr oy idites their pe, wheres Kūshyār gives more detied iformtio out them d metios sever types of ptes with diferet irtios.  this prt, hr’s text is shorter th Kūshyār’s just ike i -Treatise hpters two to fourtee, ut hr writes it i his ow words. ht is remrke i his wordig is tht we  detet the eessity for the reders to refer to  stroe. ere he oy deotes the positio of the mutrs with respet to the erth, i.e., the horizot ire; if the reders do ot hve  stroe, his deitio woud ot mke y sese to them. s for the text y Kūshyār, we must ote tht he sets the mutrs roud poit C.  this otext, poit C mes the poit of iety degrees give o the zeith, ut this poit is ot wys mrked y C i every stroe. Tht is euse the pte of eh stroe is desiged idividuy, so oy some stroes hve  pte mrked with C. Kūshyār’s usge of poit C impresses o us tht, whie he refers to sever types of stroe, he supposes i K-Book  pte hvig poit C. Moreover, i his desriptio of the horizo ire, he metios the Est d est mrks; these re so ot wys egrved o every pte, so his referee to them shows tht the pte he is thikig of hs prtiur mrks for Est d est. These three mrks orm tht he omposes the itrodutio to the stroi prts with respet to  spei stroe t his dispos. O the other hd, we d tht “the oum (ʿamūd) of ries d ir,” oe of hr’s prts, is ot metioed i K-Book. hr expis it, s foows: .   ‫ ع‬ّ   ‫ط‬   ‫ط‬ ‫ذ‬  (The oum uttig the rete t the two poits ries d ir is ed the supporter of ries d ir.) This desriptio idites tht it is  prt of the rete etwee the ver equiox poit d the utum equiox poit; however, this prt is ot wys foud i every rete, sie there exist vrious types of rete ordig to their desigs. Thus, hr’s iusio of it orms tht he supposes  spei rete tht hs it, whie Kūshyār’s rete proy does ot oti it. The otets of -Treatise, hpter oe, d K-Book, itrodutio, show tht hr d Kūshyār hve their spei stroes i mid whe itroduig stroi prts: whie Kūshyār’s stroe hs the mrks of C, est, d west, without  supporter of the rete, hr’s stroe does ot hve these 3 

Tht is euse C (Ṣād) is  i jd umers.

Aī Al-Dīn Al-Aī



three mrks, ut hs the supporter. Tht their supposed stroes re diferet  e deteted i oth works fter the itrodutory prt. For exmpe, K-Book, hpter two, gives  exmpe of how to oti the u’s titude with the stroe, s foows: (For exmpe: o  pte for the titude thirty-six degrees, we suppose the [u’s] titude t tht time to e twety-four degrees est, d suppose the u’s degree to e Turus tweve degrees. The we put Turus tweve degrees o the twety-four degrees mutr, so we d Gemii t eightee degrees o the ester horizo. e  it the sedt degree. f this titude is, for exmpe, the titude of qui, we put its poiter o the twety-four degrees mutr. o we d Cprior t twety-two degrees o the ester horizo. e  this the sedt degree). ‫ء‬  ‫ر‬  ‫ كد‬   ‫ لو‬  ‫ ف‬ 

 ، ‫ كد‬‫ط‬    ‫ب‬ ‫د‬  ،   ‫ب‬ ‫ ف‬ . ‫ط‬ ‫ء‬   ‫شر‬    ‫ء‬  ‫ يح‬‫د‬

‫ كد‬‫ط‬  ‫ظ‬  ، ً  ‫ط‬ ‫ر‬      

. ‫ط‬ ‫ء‬   ‫شر‬        ‫د‬ 

‫شر‬  =  : ‫شر‬   =  ] ‫ كد‬  ، ‫ـ‬ ،  :  =  ]  

‫ء‬    :  =  :  = ‫ـ‬ ،  ]    ، ‫ـ‬ :

  = ) ‫ ف‬ » «(  ،  ]   ‫ب‬ ‫ ف‬

+ =  : ‫شر‬  ‫ ف‬  = ‫ـ‬ :    ‫شر‬  ‫ ڡ‬ ّ ‫ـ‬   ‫» ف‬‫ط‬«( ‫ط‬  )  ‫» ف‬«( 

      )»«    ‫ ف‬ » ‫ط‬« ‫ط‬

– =  : ‫شر‬   ّ ‫ َد‬  =  ] ‫ب‬ ‫د‬    ، ‫ـ‬ : 

 = ‫ـ‬ : ‫شر‬  =  ،  ] ‫ كد‬  ، ‫ـ‬ : ‫شر‬  ‫د‬  = ‫ـ‬ ،  : ‫شر‬  =  [ ‫ يح‬  ،  : ‫شر‬  ‫ ڡ‬+ =  : ‫ر‬ 

    6 

S : foio , ie –; S P: foio , ie –foio , ie ; S G: foio , ies –; S : foio , ie –foio , ie . SS G d  dd: “i order tht oth t the divisio of the stroe uti we wi expi how to operte with tht whih does ot t them.” SS G d  dd the foowig phrse: “o the ester side.”





: ‫شر‬  =  ،  [ ‫ كد‬ ‫ـ‬ :  ]   ‫ـ‬ :  ]    ، .  ، ‫ـ‬ ،  : ‫شر‬  =  [    ، ‫ـ‬

ere he uses  pte desiged for the titude of thirty-six degrees, whih orrespods to the pe of his tivity, yy. Thus, i this exmpe he ery refers to his spei stroe. Moreover, the settig out of the exmpe suggests tht the mutrs of his stroe re irted t six degrees, whih mes tht he hs  oe-sixth stroe. s redy show, i -Treatise, hpter two, hr uses K-Book, setio oe, hpter oe; however, he deetes this exmpe. t seems odd euse his tretise is imed to preset fudmet opertios of the stroe, so  spei exmpe ike this wi hep the reders to uderstd the proess of opertio. Thus, his omissio idites tht this exmpe is ot ppie to his stroe desiged for  titude other th thirty-six degrees. The ompriso of their otets iustrtes tht oth of them presuppose the use of their ow stroes throughout the works. uggested y the te of otets of K-Book, however, Kūshyār tries to ompose  tretise tht ppies to  wider otext th his spei stroe.  ft, he metios sever fetures foud i other stroes: i the itrodutio, he metios vrious types of stroe suh s the oe-sixth stroe; i setio oe, hpter seve, he desries  type of idde egrved with urves deotig seso hours, though they re ot iuded i the itrodutio; i setio oe, twety-oe, he itrodues the two types of shdow uit, digits d feet, d he expis how oe kows whih uit is used i his stroe. These exmpes orm his tedey of omposig  omprehesive work, whih ed his work to e oe of the most popur tretises o the opertio of the stroe i the mediev smi word. Uike Kūshyār, hr ever metios other type of stroe; whe opyig K-Book, setio oe, hpter seve, he omits the topi of the spei urves o  type of idde. s for the two uits of shdow, he skips the whoe of K-Book, setio oe, twety-oe, d whe usig the shdow egth for determiig the Aṣr, he supposes digits s the uit without givig y ote o the other uit feet. is seetio of topis from K-Book impresses o us tht he imits the exptio to the stroe t his dispos. The ove ysis shows the reso why hr rewrites  exptio of stroi prts: sie he presupposes  stroe diferet from Kūshyār’s, he 7 

 ft, SS G d  dd the exptio tht Kūshyār hooses tweve degrees for djustig the exmpe to his stroe; see footote  of this pper.

Aī Al-Dīn Al-Aī



ot use Kūshyār’s text, d writes the itrodutio fresh. s regrds the opertios, most of them re reevt to y stroe, so he dupites  prt of Kūshyār’s text with some editori hges for djustig the extrted words to his ow stroe. is editori work iustrtes tht every sige stroe hs  distit desig tht eds  shor write  ew hdook. though the mjor prt of -Treatise is  opy of K-Book, it is origi euse hr writes it for his ow stroe.  the mediev smi word, shors proposed my iovtios o the stroe, d istrumet mkers mde  umer of stroes with ew youts. s  resut, eh stroe hd distitive fetures, so theoretiy every stroe eeded its ow hdook. deed, my smi shors wrote tretises o the opertio of the stroe, d these tretises woud oviousy hve ee useess without referee to  stroe. s the se of hr’s tretise reves, my ri tretises hd their ovety t est gurteed y the uiqueess of the spei stroe tht eh uthor hd t his dispos. Appendix A: Arabic Manuscripts of Kūshyār’s Book of the Astrolabe The ri musripts of K-Book t my dispos re the foowig thirtee musripts (i the order of the dtes of their opyig; the rst etter is the sigum of eh musript): G: Istanbul, Yeni Cami  784, folios 362b–376b (copied around the sixth century ) The opy ws writte i naskh without voiztio. s Kruse otes, the st three foios hve dmge i the ower prt. The opyist did ot eter y orretio. The hpter hedigs, tes, d digrms re i ruri. A: Istanbul, Ayasofya  2671, folios 80b–103a (copied in 621  = 1224/5 ) The opy ws writte i naskh with osio voiztio. The opyist etered  few orretios i the mrgi. The hpter hedigs re i ruri.

8 

9 

Bsed o Kruse’s estimtio; see Mx Kruse, “tmuer shrifte ismisher Mthemtiker,” Quellen und Studien zur Geschichte der Mathematik, Astronomie und Physik: teiug B: tudie  (): – (). ee Kruse, “tmuer shrifte,” .

2



P1: Paris, Bibliothèque nationale de France,  arabe 2487, folios 2a–31b (copied on 24th Shawwāl 679  = 23 February 1281 ) The opy ws ompeted o  hwwā  AH, s the opyist oted i the frot pge (foio ) d the oopho (foio ): Frot Pge: 

      ‫ط‬   ّ �     

 ‫ ف‬   ‫ع‬  

    

  ‫ ف‬    ‫س‬    

(Book of the stroe y the mster, eder, d shor ū ‐Ḥs Kūshyār i ā Bāshhr ‐, my God hve mery upo him, omprisig the oepts, the opertios, d the ext utio. Tht is the resposiiity of the merifu servt, my God hve mery upo him d forgive him. Tht [opy] is y virtue of the opyig i the midde of hwwā of the ri yer ). Coopho:    ‫شر‬    ّ    ‫س‬     (The ompetio y the perso who opied it hppeed o udy  hwwā of the yer ). t ws writte i naskh with osio voiztio. The opyist etered oe orretio i the mrgi of fo. . S: Istanbul, Ayasofya  2672, folios 37b–54b (copied in 684 =1285/6 ) The opy ws writte i naskh without voiztio. The opyist oted it with the exempr s we s with other opy; he etered my orretios i the mrgi (frequety with the mrk “orret ()” or “other opy ()”). 30  31 

e e, Catalogue des manuscrits arabes (Pris: Biiothèque tioe, –),  erroeousy reords the opyig dte s  AH. ee Kruse, “tmuer shrifte,” .

Aī Al-Dīn Al-Aī



P2: Paris, Bibliothèque nationale de France,  arabe 5972, folios 2b–36b (copied in 1641 =1329 ) The opy ws writte i naskh without voiztio (exept  few tanwīns). The opyist oted it with the exempr s we s with other opy; he etered my orretios i the mrgi (frequety with the mrk “orret ()” or “other opy ()”); moreover, he dded  og extrt from other opy o foios –. C: Dublin, Chester Beatty Library  Ar. 5254, folios 163a–186b (copied around the tenth century ) The opy ws writte i naskh with osio voiztio. The opyist oted it with the exempr s we s with other opy; he etered my orretios i the mrgi (sometimes with the mrk “orret ()” or “other opy ()”). Te: Tehran, Tehran University  2092, folios 3b–25b (copied in 1057  = 1647/ 8 ) The opy ws writte i naskh without voiztio. The opyist etered  few orretios i the mrgi (sometimes with the mrk “orret ()”). Se: Istanbul, Selim Aga  730, folios 23b–42a (copied in 1107  = 1695/6 ) The opy ws writte i naskh without voiztio. The opyist did ot opy setio four. e etered  few orretios i the mrgi (sometimes with the mrk “orret ()”). The mes of stroi prts i the itrodutio re i ruri; the hpter umers re i ruri. Ma: Qom, Mashhad Astan Quds  5529, pp. 7–21 (copied around the eleventh century ) The opy ws writte i naskh without voiztio. The opyist opied the text i the frmed spe s we s i the mrgi. e did ot eter y orretios. 3  33 

3  3  36 

ee E. Bohet, Catalogue des manuscrits arabes des nouvelles acquisitions (1884–1924) (Pris: Biiotheque tioe, ), . Bsed o rerry’s estimtio; see rthur . rerry, The Chester Beatty Library: A Handlist of the Arabic Manuscripts (ui: odges, Figgis & Co., ), :. ote tht Fut ezgi, Geschichte des arabischen Schrifttums  vos. (eide: Bri, ), : reords the dte  AH without y referee. ee Mustf eryti, Fehrestwara-ye dastneweshtha-ye Iran,  vos. (Tehr: irry, Museum d oumet Ceter of smi:  AH sor-yer), :. ee Kruse, “tmuer shrifte,” . ee eryti, Fehrestwara-ye, :.

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

M1: Tehran, Malik  2242, folios 26b–44b (copied around the eleventh century ) The opy ws writte i naskh without voiztio. The opyist etered sever orretios i the mrgi (sometimes with the mrk “orret ()”). Y: Princeton, Princeton University Library  (Yehuda collection) 1168, folios 69b– 91b (copied around the twelfth century ) The opy ws writte i naskh without voiztio. The opyist etered my orretios i the mrgi. M2: Tehran, Malik  3455, pp. 320–378 (no date) The opy ws writte i naskh without voiztio. The opyist etered some orretios i the mrgi. Mu: Mumbay, Mulla Firuz  86, folios 2b–33b (no date) The opy ws writte i naskh without voiztio. The opyist etered quite  few orretios i the mrgi (sometimes with the mrk “orret ()”). From togue etries, the foowig ri musripts re so kow s witesses of this ook, though  oud ot exmie them: () () () () ()

  38 

39 

0  1   

Kzimiy, the opy registered i Mhfuz’s togue o.  (opied i  AH) Tehr, Tehr Uiversity S / (opied i the teth etury AH) Tehr,  musript i siri Privte irry (opied i  AH) Qom, Mshhd st Quds S yt / (opied roud the eeveth etury AH) Ciro, ār -Kutu S Fādi mqāt m (opied roud the eeveth etury AH) ee eryti, Fehrestwara-ye, :. Bsed o Mh’s estimtio; see udoph Mh, Catalogue of Arabic Manuscripts (Yehuda Section) in the Garrett Collection in the Princeton University Library (Prieto, NJ: Prieto Uiversity Press, ), . Edwrd ehtsek, Catalogue Raisonné of the Arabic, Hindustani, Persian and Turkish Manuscripts in the Mulla Firuz Library (Bomy: Mgig ommittee of the Mu Firuz irry, ) – reords tht this opy hs o dte; however, ezgi, Geschichte, : otes the dte sixth etury AH. ee ezgi, Geschichte, :–; osefed d hsoğu, Mathematicians, ; eryti, Fehrestwara-ye, :. ee ezgi, Geschichte, :. ee ezgi, Geschichte, :.

Aī Al-Dīn Al-Aī

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() Qom, Mshhd hykh  ydr S / (opied i  AH) () odo, British irry S ADD / (opied roud the seveteeth etury ) () odo, British irry S DL AR / (opied roud the seveteeth etury ) () Prieto, Prieto Uiversity irry S (ehud oetio)  (opied i ) () Ciro, ār -Kutu S miqt / (o dte) () Ciro, zhr S fk  (o dte) () Tehr, Mjis shurā S  (o dte) ie the egiig d edig of the text do ot iude its tite, this work hs ot  deitive tite. s fr s  kow, oe of the musripts gives the tite exept S P, where the opyist dds the ove-metioed frot pge otiig the tite “Book of the stroe.” Thus,  use it s the tite. s for the textu retioship etwee these musripts, there re two fmiies ordig to the otets of setio oe, hpters ftee to sevetee: Fmiy α: SS G, , P, , C, e, M, d Mu; Fmiy β: SS P, Te, M, M, d .  hve redy puished the whoe ri text of this work y usig SS P, P, C d .  this editio,  preseted the texts of oth fmiies; however, the ft tht Fmiy α otis the odest four musripts orms tht Fmiy α represets the ery stge of the trsmissio of K-Book, wheres musripts i Fmiy β re feted y ter moditio. ee, i this pper  estish the text y usig the four odest musripts from Fmiy α: SS G, , P, d . he some musripts hve  diferet redig,  reord it t the ottom of the text. Throughout this pper,  use the foowig ottio for deotig vrit redigs (so give i ote ): ] : + 3     

eprtes redig i the text from the vrit eprtes vrit d musript sig dded i

This is  moder opy of ār -Kutu S Fādi mqāt ; see Mh, Catalogue, . The ri text edited y me with  pese trstio is iuded i Mohmmd Bgheri ed., Risālah-yi Usṭurlāb-I Kūshyār Gīlānī (Tehr: Mirs-e Mktoo, ).  m pig to edit this work sed o these four musripts with  Egish trstio.





– ()

Missig from My ommets

  ‫ـ‬    

S  S P S G S  ‫ط‬ (rossed out i) ‫ ف‬‫ط‬  (ove the ie i)  (mrgi)

The vrit redigs show the proximity of S  to S P gist SS G d . ere we must remrk tht setio four, hpters te to eeve re missig i SS G, , C, d M; this orms the oseess of S G d S . ie the tes of otets of SS G d M fter the itrodutio idite setio four “i te hpters,” whie those of SS  d C metio setio four “i tweve hpters,” the origi of setio four oviousy hd tweve hpters just ike i SS , P, d so o. Therefore,  wi give priority to the redigs from the group of SS  d P. Appendix B: Arabic Manuscripts of Abharī’s Treatise on Knowing the Astrolabe The foowig two ri musripts of this tretise re kow to me: F: Pris, Biiothèque tioe S re , foios – (opied i  AH = / ). C: stu, Cruh S , foio  (o dte). The odex BF S  is  majmū‘ (oetio) of  tretises o stroomi istrumets. tem  is  opy of hr’s Treatise. The egiig of the opy (foio ) gives the tite “Tretise o Kowig the stroe”: Begiig:

6  7  8 

S G: foio , ie ; S M: p. , ie . S : foio , ie ; S C: foio , ie . The detied iformtio out this odex, see e e, Catalogue, –.

Aī Al-Dīn Al-Aī

   ّ � 

 ‫د‬    ‫ط‬  ‫ة ف‬ 

ً  ‫شر‬   ‫ض‬ ّ � ّ 

( the me of God the Merifu d Compssiote. This is  tretise o kowig the stroe y our mster d eder thr ‐ -hr, God iumite him y restig him, whih is i fourtee hpters.) t ws ompeted i  AH i rede, mey Krm i Turkey, s reorded i the oopho (foio ). Coopho: ‫ك‬ ّ �      ‫ ف‬      ‫ف‬  (The tretise is y the hep of God the Kig d oor i the ijr d Propheti yer  i rede, the proteted ity.) t ws writte i naskh with osio voiztio. The opyist did ot eter y orretios. other hd etered oe orretio i the mrgi of foio . Ca: Istanbul, Carullah  1468, folio 1b (no date) s Kruse otes, this opy hs oy  prt of hpter oe. The rest of this odex (foios –) is  extrtio from oymous zījs opied y other two hds. Begiig:   ّ � 

 ‫ض‬ ّ� ّ  ‫د‬    ‫ط‬  ‫ ف‬ 

 ‫شر‬ 

( the me of God the Merifu d Compssiote. This is  tretise o kowig the stroe y our mster d eder thr ‐ -hr, God iumite him y restig him, whih is i fourtee hpters.)

9 

Kruse, “Stambuler Hanschriften,”  ommets tht foio  is y  moder hd.





s oe  see from the egiig, the opy is very simir to S F. By omprig SS F d C,  ot d y sigit vrit etwee them.  so foud  opy of  reessio of this work, desried eow. Mi: Tehran, Millī  arabī 1171, pp. 273–282 (copied around the tenth century ) The mjor prt of this odex (pp. –) is  opy of hr’s Utmost Attainment in Comprehending the Orbs, his rgest stroomi work. The st prt of it (pp. –) is  tretise o the opertio of the stroe.  ompriso etwee this opy d S F reves tht this is  reessio of the text trsmitted i S F. heres S F hs fourtee hpters,  redtor divides some hpters, so tht this versio hs sixtee hpters. From togue etries, there exist t est three musripts of this reesio, though  hve hd o opportuity of exmiig them: () Ciro, ār -Kutu S Tymur riyd / () Qom, Mshhd st Quds S yt / (opied roud the eeveth etury AH) () Qom, Mr‘sh S / (o dte)  this rtie,  estish the text y usig S F, the oy musript otiig the etire umer of hpters. he  emed  redig,  ote the origi t the ottom of the text, where  deote S F s “” with the sme ottio deed i ppedix oe of this pper; i the text, words i < > re dditios mde y me to restore the text. Appendix C: Kūshyār’s introduction to Astrolabic Parts: Text and Translation s redy desried, Kūshyār’s itrodutio osists of two prts: o the purpose of usig the stroe, d o stroi prts d ptes. To ompre 0  1 

 

Bsed o the estimtio y eryti, Fehrestwara-ye, :. O the importe of this work i the history of smi stroomy,  gve  pper “Summary of the Almagest: other stroomi Trditio i the ys of ṣr  Ṭūs d its igie i the istory of ovig Proems Coerig the iur Motios,” SAW emir “Exporig mthemti prties roud  stroomi questio oe: Mthemti pprohes to the iur motios of the u, the trs, d the Moo,” o  Ferury,  i Pris. ee osefed d hsoğu, Mathematicians, ; eryti, Fehrestwara-ye, :.

Aī Al-Dīn Al-Aī



Kūshyār’s exptio of the prts d ptes with -Treatise, hpter oe,  wi preset the text of the seod prt of K-Book’s itrodutio with  Egish trstio. ‫ط‬‫أ‬  ّ     ‫ي‬  ‫ظ‬   ّ‫أ‬

   ،        ّ‫ط‬   .

‫شر‬  ّ ّ ‫آ‬ ،   ّ ّ   ‫ط‬  

. 

ّ         ّ   ‫حج‬

 ّ‫ض‬ ّ‫أ‬  ّ  .   ّ   ‫ت‬ ‫ء‬ ، ً ‫ء‬ .  ّ   ّ ّ  ‫ي‬ ، ّ   . ّ‫أ‬     ‫ض‬

.   ‫ن‬   ّ  ‫ف‬

 ّ .       ‫ء‬‫أ‬   ‫ء‬

. ً ‫ء‬  ً  ‫ن‬   ّ  ‫ي‬  ‫ل ّذ‬ 

. ّ‫أ‬    ‫ء‬‫أ‬   ‫ ف‬ ‫ء‬‫أ‬  ّ‫ظ‬ ‫ء‬

     ‫ذ‬ ّ :  ‫ ف‬ ّ‫ط‬

 ّ    ‫ذ‬  ّ ، ‫ن‬   ّ   

 ّ   ‫ط‬ ‫ذ‬ ّ . ‫أ‬   ّ ‫آ‬  ، ‫ء‬  .  ‫شر‬  ّ        

 ‫ط‬ ، ‫ر‬    :  ‫ ف‬ ‫د‬

.    ‫ظ‬ ،   

، ‫ ص‬‫ط‬ ‫ط‬  ‫ ف‬‫ط‬ ‫د‬  ‫ط‬ 

  ‫ئ‬   ‫ن‬  ، ّ ‫ غ‬‫ن‬ ّ  ‫ن‬

 ‫إ‬ ،   ً   ‫إ‬ ، ّ  ّ  ً    : ‫ط‬‫أ‬

‫ط‬   ّ . ‫ء‬ ‫ء‬ ًّ  ‫إ‬ ،   ً  

‫أ‬   ‫ط‬ .  ‫شر‬    ‫شر‬ 

 ّ   ‫أ‬   ، ‫شر‬ ‫ط‬  ‫ن‬   ّ  ‫شرق‬

3   

S : foio , ie –foio , ie ; S P: foio , ie –foio , ie ; S G: foio , ie –foio , ie ; S : foio , ie –foio , ie . The whoe text of the itrodutio  e foud i Bgheri ed., Risālah-yi, –.

4



 ‫ط‬ ّ      .  ‫ط‬  ‫ن‬ 

.  ‫د‬   ‫أ‬   ّ

 ‫أ‬     ‫ط‬  ‫ز‬  ‫ط‬

.   ‫ي‬ ،    ‫أ‬ ‫ر‬   ‫ي‬

.   ‫أ‬   ّ

. ّ ‫ظ‬ ‫ي‬ ، ّ     

  ‫ء‬ ‫ي‬  ‫ ف‬ّ ‫د‬   ‫ط‬ 

‫ء‬        ّ  ّ  ‫ط‬‫أ‬   ‫م‬

. ‫ط‬ ‫ ف‬ ‫ا‬ ‫ء‬

‫ن‬   ّ   ،  ‫ـ‬   ‫ ف‬ّ ‫ظ‬

. ‫ـ‬ 

. ‫حج‬ ‫ء‬  ّ   ‫ ف‬  ‫ز‬  ‫ء‬‫أ‬ 

‫ط‬      ‫ط‬   

    ّ  ،       .     ّ ‫ي‬

  :  = ‫ـ‬ :  =  :   =  ] ّ   ‫ـ‬ :   ] ّ‫أ‬ 

 ] ّ  – ]    ،  : ‫ط‬ = ‫ـ‬ ،  ] ‫ط‬‫أ‬

] ً ‫ء‬ . ‫ـ‬ : ً   ] ً ‫ء‬ ّ  ‫ـ‬ : ‫حج‬ ‫حُج‬ ] ‫حج‬   : ‫خ‬   :    + ]    ، ‫ـ‬ : ‫ض‬    ‫ي‬ +

‫ـ‬ :  ]  ّ  ‫ـ‬ : ‫ض‬ ‫ض‬ ] ‫ض‬  )»«  (

(  :   + ]    ، ‫ـ‬ :  =  ،  ]  

]   ‫ـ‬ :     ]  ‫ء‬  )»« 

‫ل ّذ‬   ّ ،    : ‫ّذ‬ = ‫ـ‬ ،  ] ‫ل ّذ‬  ‫ـ‬ :  ] ّ ‫ظ‬ ‫ء‬   :  ] ً ‫ء‬   :  ]ً   – ] ‫ي‬ 

‫ ڡ‬ ‫ط‬ ]  ‫ ف‬ ّ‫ط‬  ‫ـ‬ : ‫ظ‬  ‫ظ‬ 

»«( ]   ‫ـ‬ :  ]   ‫ـ‬ :  ‫ ڡ‬ ‫ط‬    :  ]   – ، ‫ـ‬– =  ،  ]   ‫ـ‬ :  )‫ط‬

:  ‫ ڡ‬ ‫د‬  ‫ ف‬ ‫د‬ ]  ‫ ف‬ ‫د‬

: ‫ط‬  ‫ط‬  ] ‫ط‬   – ]   ‫ـ‬

Aī Al-Dīn Al-Aī

4

  : ‫ط‬  =  : ‫ط‬ )‫ط‬ »«( = ‫ـ‬ ،  ] ‫ط‬  ‫ـ‬

: ‫ط‬ ] ‫ط‬‫أ‬   ، ‫ـ‬ : ‫ى‬ =  ،  ] ‫ن‬   : ‫ن‬ ] ‫ن‬

 + ]    : ّ  ]ً    :  ]ً    : ّ ُ ]ً   

  : ‫ط‬ ] ‫ط‬   : ‫ى‬ ]    ، ‫ـ‬ :  ‫ر‬ ]  ّ  – ] ‫ط‬  ‫ن‬   ّ   ‫أ‬   ، ‫شر‬

 ‫ ف‬‫ط‬   »«( ]   )»«  (  : ‫ن‬  + ‫ط‬ ] ‫ز‬  ‫ط‬   ، ‫ـ‬ : ‫د‬ =  ،  ] ‫د‬  )

] ‫ي‬   ‫ـ‬– ] ‫ط‬  ‫ـ‬ : ‫ز‬  ‫ط‬  

:  =  ] ‫أ‬   :   = ‫ـ‬ :  =  :   = 

   :  ]   ‫ـ‬ :  ]    ، ‫ـ‬ :  ‫ته‬ =   )»«  (  :   + ] ّ    ، ‫ـ‬ :  =  ،  ] : ‫ي‬ ] ‫ي‬  ‫ـ‬ : ُ  ‫ط‬   ‫ط‬  ]  ‫ط‬ 

،  ]    : ّ  ] ‫ا‬   ،  : ‫ط‬ = ‫ـ‬ ،  ] ‫ط‬‫أ‬  ‫ـ‬

]  ‫ ف‬ّ ‫ظ‬   :  ُ  ] ّ  – =  ، ‫ـ‬ ، 

‫ـ‬  – ]  ‫ ف‬. ‫ـ‬ :  ‫ ف‬ ‫ط‬  ‫ط‬ ] ‫ء‬‫أ‬   ‫ـ‬ :  ] ‫ـ‬   ، ‫ـ‬ : ‫ـ‬ =  ،  ]

 ‫ـ‬ : ّ ُ ] ّ   ‫ـ‬ ،  ،  :  =  ]   ‫ـ‬ :     ‫ٮ‬  + = ‫ـ‬ :    + ]    : ‫ى‬   + ] ‫حج‬

 = ‫ـ‬ :  =  :  =  :  ]    :  ]    :  =  ،  ]   – =  :  ]     :

. ‫ـ‬ :  =  :

(The mter is the outside pte hvig the hde d the rig for the ord from whih the stroe hgs. O the k, there re two ies uttig eh other t the eter of the pte perpediury: oe of them is drw from the pe of the ord d hves the pte, whih is ed the ord ie; d the other is ed the est-west ie. The rim is the rig set o the iside of this pte, eig divided ito  degrees. The egiig of its divisio is o the ord ie. t is ed the rim euse it emres  the ptes s we s the rete.  

SS G d  dd: “t hs so the hde d the rig for the ord.”

42



The idde is tht whih is o the k of the mter. t hs two poited edges. There re two sightig ves eretig o it, eh of whih hs  sm hoe. The titude degrees re the iety degrees o oe side of the ord; sometimes there re two qudrts o oth sides of the ord, eh of whih is divided ito iety degrees. The shdow degrees re the degrees i the qudrt opposite to the titude degrees o the k of the mter. The two ies uttig eh other o the ptes: s for tht whih is exteded from the ord d hves the pte, it is the meridi ie; the hf [of the ie] ext to the ord is ed the ie of the midheve, d the other hf is [ed] the ie of the rdie of the erth. s for tht whih hves this ie perpediury t the eter of the pte, it is the est-west ie. The three ires o the ptes: the smest is the iruit of the hed of Cer; the midde is the iruit of the heds of ries d ir; d the rgest is the iruit of Cprior. The mutr ires re the ires drw o the ptes roud poit C; some of them re ompete ires, wheres others re iompete; etwee them, the umers of their degrees re writte ordig to the stroe’s irtio: if it is  oe-sixth [stroe], every six degrees re [writte]; if it is  oe-third, every three degrees re [writte]; if it is  hf, every two degrees re [writte]; d if it is  ompete [stroe], every degree is [writte]. The rst of these mutr ires is the ester d wester horizo, d “Est” d “est” re writte o it. The mutrs djet to the ester horizo towrds the meridi ie re the ester mutrs, d the [mutrs] djet to the wester horizo towrds the meridi ie re the wester mutrs. ht is etwee the eter of the pte d the rst mutr o the ie of the rdie of the erth is the terrestri titude of the regio [supposed i] the pte. The ies of seso hours re the ies o oth sides of the rdie of the erth, [eh of whih hs] oe edge [o] the iruit of the hed of Cer d the other [o] the iruit of the hed of Cprior. They re sighty et. The ie of the rdie of the erth is tke with them. The rete is the upper hoowed pte, i whih there re shrpeed poiters. The ire of the zoe of the zodi sigs is the ompete ire o the rete. O it re the mes of the zodi sigs d their degrees d divisios

6  7 

SS G d  dd: “d the diretios of est d west.” The ie of the rdie of the erth is tke s oe of the ies of seso hours.

4

Aī Al-Dīn Al-Aī

ordig to the ostrutio of the stroe: per six degrees or three degrees or two degrees or oe degree, s we metioed i [the setio o] the mutrs. The shrpeed poiters i the rete re the xed strs. O eh of them is the me of  str. The iditor of the degrees is the idex o the hed of Cprior, y whih the degrees of the rim re outed. s for other [prts] suh s the pi, the sm rig, the horse, the hde, the rig for the ord, the sm rh protrudig from the rete’s frot for rottig the rete, the futio of  of them is ovious d the reso why they re eeded is er, ot requirig exptio.) Appendix D: Abharī’s Treatise on Knowing the Astrolabe, Chapter One: Text and Translation The foowig is the text of -Treatise, hpter oe, with  Egish trstio. ّ ً ‫ء‬ ّ           ّ . ‫حج‬  

. ‫ـ‬ ّ ‫أ‬   ‫ي‬   ‫ز‬

.      ‫ط‬‫أ‬  ّ  

. ‫ة‬   ‫ـ‬    ‫ذ‬  ّ   ‫ن‬   ّ .    ‫ن‬   ّ    ّ  ‫ء‬  ّ

.    

.     ‫د‬  ‫ط‬

.   ‫ ف‬  ‫ز‬  

‫ ف‬ ‫ظ‬    ‫ي‬   ‫د‬   ><  .  ‫ط‬‫أ‬ ‫ ف‬

. ‫ر‬  ‫ي‬   ‫د‬  ‫ر‬  

8  9 

 sm hde o the rete. S F: foio , ie –foio , ie .

44



.    ‫ي‬   ‫د‬  ‫ن‬ ّ 

. ‫ء‬  ّ ‫ن‬ ّ   ‫ط‬   ‫د‬ ‫أ‬ 

. ‫أ‬   ‫د‬  ‫ط‬

.   ‫ ع‬ّ   ‫ط‬   ‫ط‬ ‫ذ‬ 

. ‫أ‬    ‫ن‬ ّ    ‫ط‬   ‫ط‬

. ‫ط‬       ‫ ف‬‫ذ‬ .  ّ ‫ط‬  ‫ذ‬

.  ‫ي‬  ‫ي‬   ‫ط‬‫أ‬   ‫ط‬ ‫ض‬

.  ‫ط‬ ‫ط‬‫أ‬   ‫ط‬ ‫د‬    .    ‫ ف‬‫ط‬‫أ‬    ‫ء‬

]    :  ]    :  ]    : ّُ ] ّ   : ّ ] ّ 

.  :  ]    :  ]    : ُ 

(The mter of the ptes is the pte surrouded y  rig divided ito  degrees; this rig is ed the rim. The dditio to it i the upper side is ed the throe. The prt of the rig from whih the stroe hgs is ed the hde. The meridi ie is the ie tke from the side of the throe to the other side. The ie of the equtor is the ie uttig the meridi ie perpediury. The rete is the iised pte. The et of the zodi sigs is the ire o the rete divided ito the zodi sigs. The iditor is dded to the hed of Cprior. The iruit of the hed of Cprior is the ire o whih the hed of Cprior rottes, eig the rgest iruit i the orther stroe’s pte. The iruit of the hed of Cer is the ire o whih the hed of Cer rottes. The equtor ire is the ire o whih the heds of ries d ir rotte. The horizo ire is the ire pssig through the two itersetio poits etwee the equtor [ire] d the ie of the equtor. The mutrs re the ires ove the erth. The oum uttig the rete t the two poits ries d ir is ed the oum of ries d ir. The ies of hours re the ies etwee the equtor d the iruits of the tropis eow the horizo.

Aī Al-Dīn Al-Aī

45

The prt of the rete i the eter of the ptes is ed the pi. Tht i whih there is the pi is ed the sm rig. The idde is the ruer eogig to the stroe’s ody o the k; o it re two sightig ves hvig  hoe. The titude ire is the ire drw o the stroe’s k, whih emres it [i.e., the k]. The titude degrees o the stroe’s k re i the irumferee of the titude ire.)

60  61 

ote tht the pi is  seprte ompoet of the stroe, rther th  prt of the rete. The sm rig is the oe yig etwee the horse d the rete, prevetig the tter from eig dmged.

 

Changing the Angle of Vision: Astrolabe Dials on Astronomical Clocks Günther Oestmann

Institt ür hiosophie, iteratr-, Wissenshats- n ehnikeshihte, ehnishe niersität Berin, traße es . Jni ,  Berin, Germany [email protected]

Abstract From the mie o the orteenth entry nti the ary oern perio, seera monmenta astronomia oks were erete in rope, an on many o them astroabe ias were pae. n a rop o earier oks, “sothern astroabes” (i.e. with stereoraphi projetion rom the orth oe) were empoye, whereas ater exampes show a “northern astroabe” (i.e., a stereoraphi projetion rom the oth oe), whih is ommony se on portabe astroabes. he materia an texta eiene as we as reasons or this hane sha be examine. oreoer, the qestion o transmission o speia ariants o stereoraphi projetion rom ast to West wi be issse.

Keywords Astronomia oks – astroabes – astroabe ias – stereoraphi projetion

Introduction he arth’s axis points towars the oe tar, an the stars irate one eery twenty-or hors in an antiokwise iretion (Fire .). Aorin to the pattern o the “eestia ia,” this sho oiay be the ase on ok ias aso. Bt the hans o oks an wathes moe “bakwars,” bease the sense o rotation has been aopte rom the astroabe, whih preee the mehania ok as a eie or time measrin.   enri ihe, “orqoi es horoes tornent-ees à ’eners?” Journal suisse d’horlogérie  (): –; ierie Wetze, “Astroabim, hr n hrzeier-inn,” Chronométrophilia  (): –. © koninklijke brill nv, leiden, �9 | doi:0.63/9789004387867_05

    

URE 12.1



Sense of rotation of the celestial sphere for a terrestrial viewer (Henri Michel, “Pourquoi les horloges tournent-elles à l’envers?,” 127).

otatin star maps show the eestia sphere rom the interior aorin to or natra impression (Fire .). Bt in ase o the astroabe the oation o the iewer is otsie the osmos, an he ooks own rom the northern eestia poe to the pane o the eestia eqator (Fire .): in his ine o ision the eestia sphere rotates okwise, an the positions o stars appear mirror-inerte (aorin to anient pratie eestia obes ispay this “otsie perspetie” aso, i.e., ratie representations o the onsteations are epite in orsa iew). In portabe astroabes the tropi o Capriorn say oinies with the oter irmerene o the tympanm, an the entre o projetion o the eestia sphere is oate in the sothern eestia poe (aso enominate as “northern astroabe”). oweer, the orth oe an aso onstitte the entre o projetion, so that the tropi o Caner is on the otsie (“sothern astroabe”) (Fire .). I the astroabist’s traitiona iew rom otsie o the eestia sphere is abanone in aor o a terrestria ane o ision, the iretion o rotation remains okwise. he “sothern astroabe” (northern projetion) with its onex horizon ine an be on on astronomia ias o eary monmenta oks erete nti the mi-teenth entry.

  y Dekker, Illustrating the Phaenomena: Celestial Cartography in Antiquity and the Middle Ages (xor: xor niersity ress, ), –.



URE 12.2

O

Rotating star-map of the nineteenth century (Modern reproduction, © Md Vg, Nud  H).

he ok in the athera o n (Fire .) is one o those eary exampes, aeey atin to  (athoh there is no arhia onrmation o this).3 hen oow Doberan () (Fire .), trasn (), Berne, übek

  heoor Wåhin, Horologium mirabile Lundense: Det Astronomiska Uret i Lunds Domkyrka (n: C. W. K. Geerp, ), –. 4  Gsta hamann, Frierih Brns an Fritz irsh, Die Marienkirche (= Die Bau- und Kunstdenkmäler der Freien und Hansestadt Lübeck, .2) (übek: öhrin, ), pp. –.

    

URE 12.



Stereographic projection from the south pole–“Northern Astrolabe” (Henri Michel, Traité de l’astrolabe [Paris: Librairie Alain Brieux, 1976], 17).

(both ), Chartres (), rae (), Wismar (a. ), an Bores (–) (Fire .). he astronomia ok o iinen (, estroye in ) ery ikey ha an astroabe ia with northern projetion, too. his an be one rom a ertiate reitin the okmaker Cas Gtsh with the onstrtion o an astronomia ia whih showe the orse an seasona heiht o the n: We, the heri, ayor an Coni onrm pbiy, that master Cas Gtsh rom ottwei […] has mae a aenar isk an a sphere [an astroabe] or or Cathera in iinen [...], on whih the n rises an

  Aophe eoq, “otie historiqe et arhéooiqe sr es horoes e ’éise otre-Dame e Chartres,” Mémoires de la société archéologique d’Eure et Loir  (): –.   Zeněk orský an mane roházka, “ražký oroj,” Acta historiae rerum naturalium nec non technicarum  (): –. 7  anre hkowski, “Die astronomishe hr in Wismars arienkirhe,” Wismarer Beiträge: Schriftenreihe des Archivs der Hansestadt Wismar, H.  (): –. 8  mmane oe, Un constructeur d’instruments astronomiques au  siècle: Jean Fusoris (= Bibliothèque de l’École des Hautes Études, e section, Fasc. 308) (aris: ibrairie onoré Champion, ), –.

1

O

URE 12.

Stereographic projection from the north pole— “Southern Astrolabe” (Michel, Traité de l’astrolabe, 16).

URE 12.5

Astrolabe dial of the astronomical clock in Lund Cathedral in its condition before 1916 (Wåhlin, Horologium mirabile Lundense, 45).

    

URE 12.6

11

Tympanum of the astrolabe dial of Doberan, 1390. Drawing by Hans Wåhlin, 1923; (Wåhlin, Horologium mirabile Lundense, 80).

sets an moes hih an ow aorin to the time o the year, an the oon rises an sets an rises an sets an is waxin an wanin […]. 9  “Wir er hthaiss, er Brermaister n er ratt emainih er tatt ze iinen knen meniihem mit isem brie n erehen oenih, az er erber man maister Cas Gtsh on otwi, zöer is bries ns in nserm münster ze iinen ain per eornot n emahot hat, ie aso wiset n bettet, az hie nah an isem brie eshriben stat: Dez ersten ain rae, az es jars ainost mb at, n ist az kaenarim aran n ie zwö manot emaot mit en eberen, az enn ze ma ewonhait ist ze tn; n siht man ie eni zwshent wihennehten n asnaht a jar, n sitzt ain menny aor, az zaiet  ae ta rh as jar, n inet man ae irtae in em jar. b em ra ist ie sper eornot, aran ist bezaihent t, wasser n ertrih n nne n man n ie zwö zaihen, n at ie snne  n ze naen n hohet n niret nah em, az es in em iare ist; er man at oh  n ze naen n hohet n niert in ie em shin az i, az

12

URE 12.

O

Astrolabe dial of Bourges, 1423. ( Jules-Louis Barreau, Description de la cathédrale, des vitraux de Bourges et des autres monuments de la ville [Châteauroux: A. Majesté, 1885], n.p.).

horty beore (in ) the maistrates o ottwei ha sent a reqest to the oniors o trasbor to show the aenar isk o the astronomia ok

ie snne ains jars tt, n ait z n nimpt ab an em shin n wirt nwe in er stn, az man iset, az er an em hime nwe si; n stan beie, nne n man, taeihen in irem stae n zaihen, az man iset, az si an em hime stanin; n siht man in er snnen ae stnen ez tas n er naht, n sint arob ie haien ri kn n ri kneht, ie an mb z ainer tr ss n z er anren tr wier in; wisent nser rowen n kerent sih mb en ir n nient ir, n kert sih az kini mb en inen, n shwept ain ene ob inen mit ainem sternen, n stan zwein ene  em ehs n basent, so ie kn weent an; n ist ain positi aran, az sint, ie wi si ant. Dis ornn n is werk hat er obenant maister Cas mit hotzwerk wo eziert. n is aes z ainem waren n stätem rkn so haben wir nser tatt Insie oenih ehenkt an isen brie, er ze

    

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in trasbor Cathera to Gtsh. ene it an be assme that the rst ok o trasbor Cathera (whih ha been erete in –) sere as a moe or the ok in iinen. he astronomia ok in Frankrt Cathera, ompete in –, was arey rebit in  by Johann hnitzer rom aena in Asatia. It is ikey that he aso aopte the rst trasbor ok as a moe. n an enrain o  showin the interior o the athera the astronomia ok is isibe in the bakron, bt ony a tripartite strtre (aenar pate, astronomia ia, an atomata) an be iserne rom the epition (Fire .). he ok was emoishe in , an no other pitoria reors or esriptions are extant. Bt there are at east two exeptions. he astronomia ok onstrte by ihar Wainor (–) in the monastery o t. Abans ha an astroabe with sothern projetion. It an be one that Wainor oowe the anient traition o the anaphori ok whih aso ha sothern projetions (this is proe by arhaeooia nins).3 he “Astrarim” o Gioanni

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 

iinen eben ist an em nehsten rita nah em maye ta, o man zat nah Cristy ebrt ierzehenhnert Jare n arnah in em ersten Jare” (iinen-hwenninen, niipa Arhie, MS  a). “nser wiier ienst steor. Besnern ieben rün, as ir in werm münster ze traszbr han az jar rae ist ns eseit, az az ze mä ain hübsh t werke si, n az wir oh ze mä ern hettent in nser tatt otwi. n  az so habent wir z ûh eshikt Casen Gtshen, zöer es bries, asseb werk ze beshowen n arinne rat ze shen, as ns az oh emahet were. Darmb wer ten rntshat bitten wir mit ernst n lissentih, az ir shaen weent een em Cstos oer shaner oer en wenne z notrti sie, az man en eenennten Casens Gtshen az eenant wer werk ayenih beshowen asse n az Im arinne beraten n ehoen were, n az Im we arz eben werint az er ns assebe werk oh obrinen me. Daz weent wir in aen sahen aezijt wietih mb h eienen. Geben am mitwohen noh sant Geonen [?] ta Anno ni. M..LXXXX.V. on ns em at ze otwi” (Arhies e a ie et Commnaté rbaine e trasbor, ér. , , r. ). rnst . Bassermann-Joran, “Die einstie onmentahr im Dome z Frankrt am ain,” Die Uhrmacherwoche: Handelszeitung für den Uhren- und Bijouteriewaren-Markt  (): ; Ior A. Jenzen, “Die onmentahr im Frankrter Dom,” in: Uhrzeiten: Die Geschichte der Uhr und ihres Gebrauches, e. Ior A. Jenzen (arbr: Jonas, ), –. John Dai orth, “onastiism an the First ehania Coks,” in The Study of Time : Proceedings of the Second Conference of the International Society for the Study of Time, e. Jis homas Fraser an athanie awrene (Berin: priner, ), ; John Dai orth, Richard of Wallingford (xor: Carenon ress, ), :–; :. n anaphori oks o ate Antiqity see . axe-Wery, “ote sr es objets antiqes éoertes à Gonreort (ese) et à Gran (oses),” Mémoires de la Société Nationale

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URE 12.

O

The astronomical clock in the northern transept of Frankfurt Cathedral. Detail of an engraving in the “Crowning Diary” of Emperor Matthias, 1612 (Carl Wolf, Der Kaiserdom in Frankfurt am Main: Eine baugeschichtliche Darstellung, [Frankfurt a. M.: Jügel, 1892], 22).

    

15

e’Doni (–) bit in – aso ha an astroabe ia with sothern projetion ommony se on portabe astroabes (Fire .). he sothern projetion has been appie on astroabe ias o monmenta oks rom the eary sixteenth entry onwars: Winterthr (), ünster (–), aint-mer (–) (Fire .), m (), omo (–), trasbor  (–) (Fire .), Asbr (), an yon (). he hane rom northern to sothern projetion was reonize rst by heoor Wåhin (–), the arhitet o the Cathera o n, an in , when the Czeh siene historian Zeněk orský (–) presente a typooy o astronomia ias. his hane was the rest o the rowin

4 

    7 

8  9  0 

 

des Antiquaires de France  (): –; tto Bennor, rnst Weiss, an Abert ehm, “Zr azbrer Bronzesheibe mit ternbiern,” Jahreshefte des Österreichischen Archäologischen Instituts in Wien  (): –; are oron, “r n objet en bronze éoert à Gran en orraine en ,” Bulletin d’ANCAHA  (): –; Anthony John rner, “he Anaphori Cok in the iht o eent esearh,” in Sic itur ad astra: Studien zur Geschichte der Mathematik und Naturwissenschaften. Festschrift für den Arabisten Paul Kunitzsch zum 70. Geburtstag, e. enso Fokerts an ihar orh (Wiesbaen: tto arrassowitz, ), –. Giovanni Dondi dall’Orologio: Tractatus Astrarii, Biblioteca Capitolare di Padova, Cod. D. 39, e. Antonio Barzon, nrio orpro et a. (atian City: Bibiotea Apostoia atiana, ), os. v, v o the asimie. Ao henk, Die Uhrmacherfamilie Liechti von Winterthur und ihre Werke (Winterthr: hönenberer, ), –. ee the postsript to this essay. Günther estmann, “Die astronomishe hr am athas z mütz–omo,” in Mittelalterliche astronomische Großuhren: Internationales Symposium in Rostock 25. bis 28. Oktober 2012, e. anre hkowski, ta Jahnke an Woan Fehber (eipzi: Akaemishe erasanstat, ), –. rnst . Bassermann-Joran, “Die erorene onmentahr im Dome z Asbr,” Die Uhrmacherkunst  (): . François Braniar an Chares orat, L’horloge astronomique de la Cathédrale Saint-Jean de Lyon (aint-Étienne: Dmas, ). heoor Wåhin, “Astroabe Coks an ome hohts earin the Ae an Deeopment o the Astroabe,” in obert heoore Gnther, The Astrolabes of the World: Based upon the Series of Instruments in the Lewis Evans Collection in the Old Ashmolean Museum at Oxford, with Notes on Astrolabes in the Collections of the British Museum, Science Museum, Sir J. Findlay, Mr. S. V. Hofman, the Mensing Collection, and in other Private Collections (onon: he oan ress, ), ‒. Zeněk orský, “Astronomy an the Art o Cokmakin in the Forteenth, Fiteenth an ixteenth Centries,” Vistas in Astronomy  (): –.

16

O

URE 12.

Astrolabe dial of Giovanni de’Dondi’s “Astrarium,” 1348–1364 (Granville Hugh Baillie, H. Alan Lloyd and F. A. B. Ward, The Planetarium of Giovanni de Dondi [London: The Antiquarian Horological Society, 1974], 60).

proieration o portabe astroabes, in whih the sothern projetion was aways se. here is ony one notabe exeption: a portabe ropean astroabe with northern projetion, whih oriinate in the thirteenth-entry Frane. his instrment has a rete eqippe with a ear train or representin the moements o sn an moon, bt the enrains on the tympanm an on the bak hae been et nnishe. In a probabiity this instrment was erie rom the ia o an astronomia ok.  

onon iene sem in. no. –; haron Gibbs, Janie A. enerson an Derek e oa rie, A Computerized Checklist of Astrolabes (ew aen, T: Department o istory an iene an eiine, Yae niersity, ), # ; Gnther, The Astrolabes of

    

URE 12.1

1

The astronomical clock of Saint-Omer, 1555–1558 (historical postcard in possession of the author).

o sm p, three ariants o projetion o the eestia sphere are to be istinishe: the World, ; John Dai orth, “ps qarnam rotarm mirabiim,” Physis: Rivista Internazionale di Storia della Scienza  (): –; Johann üin, “Astroabim mit äerwerk as em . Jahrhnert,”  Neue Uhrmacherzeitung: Schmuck und Uhren  (): –.

1

URE 12.11

• •

O

Astrolabe dial of the astronomical clock of Strasbourg Cathedral, 1571–1574. © Mu d  f d Sug; P Mu d Sug.

ype  has the entre o projetion an position o the obserer in the oth oe. he appearane o the sky is terrestria (insie the eestia sphere), the oter imit o the projetion is the tropi o Capriorn, the sense o rotation onterokwise. It represents the “norma” iew o the obserer on the earth an is se or rotatin star maps. ype  has the entre o projetion an position o the obserer in the orth oe. he appearane o the sky is aso terrestria (insie the eestia sphere), the oter imit o the projetion is the tropi o Caner, an the sense o rotation okwise. his ariant is on on astroabe ias o eary monmenta oks.

    

•

1

ype  has the entre o projetion in the oth oe, bt the obserer is in the orth oe. he appearane o the sky is mirror-inerte (externa to the eestia sphere), the oter imit o the projetion is the tropi o Capriorn, an the sense o rotation aso okwise. Contrary to type , star positions between the tropi o Capriorn an the orth oe an be shown. It is enontere in the ast majority o portabe astroabes an ate monmenta astronomia oks (i.e. rom the eary sixteenth entry onwars).

In a three ariants there is no ierene in the aray an the ease o reain, bt one may woner why okmakers eiate rom the ommon astroabe when onstrtin astroabe ias an empoye the nsa projetion rom the northern eestia poe? eproin the n’s motion in the zoia was o oremost importane when esinin an astronomia ia, an this projetion enabe the ispay o the anna orse o the n in a most natra way, bease here the aiy ar aboe the onex shape horizon ine is oner in smmer than in winter an ths orrespons to rea onitions. I the projetion enter is oate in the oth oe, the n rns throh a short aiy ar aboe the onae shape horizon ine in smmer, an the winter ar is ery on. Bt notwithstanin this aantae the oer representation was isare in the sixteenth entry with the proieration o the ommon panispheri astroabe. Is the northern projetion a spei ropean eeopment oiniin with the onstrtion o the rst mehania oks in the thirteenth to orteenth entry? It is we known that knowee abot stereoraphi projetion an astroabe onstrtion mainy sprea rom sim pain to rope, an so the northern projetion may be a transer rom Arabi-Isami tre aso.3 A-Farhānī (a. –ater ), a-ijzī (seon ha o the tenth entry) an a-Bīrūnī (–) worke on new projetion types an orms o the astroabe. he onstrtion o the sothern astroabe was esribe by a-Farhānī, bt the projetion probaby areay existe beore his time. he mathematiian an astronomer a-ijzī eat exhastiey with the theory  

4 

Aorin to Wåhin, “Astroabe Coks,”  an , the sothern projetion is oer, an he postate that the hane to northern projetion ommony se on portabe astroabes miht be e to ipparhs, bt this is a ery speatie assmption an rather nikey. ḥamma ibn Kathīr a-Farhānī, On the Astrolabe, e. an tr. ihar orh (Wiesbaen: teiner, ), –, –; Jose Frank, “Zr Geshihte es Astroabs,” Sitzungsberichte der physikalisch-medizinischen Sozietät Erlangen – (–): .

2

O

o the astroabe an ompose a treatise on mixe orms o the northern an sothern astroabe with a wie ariety o shapes o the rete. he text howeer, is not extant. meros onstrtions o “mixe astroabes” were aopte by the poymath a-Bīrūnī, who wrote a “Comprehensie reatment o the ossibe ethos o the rotion o the Astroabe,” where he treate the “northern” an “sothern” astroabe as we as many hybri orms.3 e aso mentione these in his “Instrtions to the ements o the Art o Astrooy” ompose in  E/H .3 It may be assme that the onstrtion o those ariants was ony reare as an inteeta haene an exerise o mathematia theory. Bt it was not merey a “oqetterie éometriqe,” as enri ihe one thoht.3 hoh the tiity o sh instrments was imite an they were ery it to hane ompare to the orinary astroabe, we hae oasiona exampes  

  7  8 

9 

0 

   

Fat ezin, Geschichte des arabischen Schrifttums,  os. (eien: Bri (os. ‒); Frankrt am ain: Institt ür Geshihte er Arabish-Isamishen Wissenshaten an er Johann Woan Goethe-niersität (os. ‒), ‒), :– an :–; ax Krase, “tamber anshriten isamisher athematiker,” Quellen und Studien zur Geschichte der Mathematik, Astronomie und Physik, Abt. B, o.  (): ‒, at –. Kitāb fī Qawānīn mizājāt al-asṭurlāb al-shimālī maʿ al-janūbī, as qote by a-Bīrūnī (ezin, Geschichte des arabischen Schrifttums, :). ezin, Geschichte, –. Istīʿāb al-wujūh al-mumkina fī ṣanʿat al-asṭurlāb; or a German transation o the introtion see ihar Wieemann, “ineitnen z arabishen astronomishen Werken,” Das Weltall  (): –; aso einrih ter an ihar Wieemann, “Über a Bīrūnī n seine hriten,” Sitzungsberichte der phys.-med. Sozietät in Erlangen – (–): . Maqāla fī tashīl al-tasṭīḥ al-asṭurlābi wa-l-ʿamal bi-murrakabātihī min al-shimālī wa-ljanūbī (n an easiy omprehensibe aont o the projetion o the astroabe an the se o the ompon astroabe mae o the northern an sothern astroabe); ezin, Geschichte des arabischen Schrifttums, :–. ihar Wieemann, “Beiträe zr Geshihte er atrwissenshaten, I: Aemeine Betrahtnen on a Bīrūnī in einem Werk über ie Astroabien,” Sitzungsberichte der phys.-med. Sozietät in Erlangen – (–): –; ter an Wieemann, “Über a Bīrūnī,” ; François Charette, Mathematical Instrumentation in Fourteenth-Century Egypt and Syria: The Illustrated Treatise of Najm al-Dīn al-Mīṣrī (eien: Bri, ), –. Aorin to a qote o the teaher an patron o a-Bīrūnī, Abū aṣr anṣūr b. ʿAī b. ʿIraq, the astronomer Ḥabash (iin in Baha . ) ha written a ie or the onstrtion o the northern an sothern astroabe (Ṣanʿat al-asṭurlāb al-shimālī wa-ljanūbī; ezin, Geschichte des arabischen Schrifttums, :). The Book of Instrtion in the Elements of the Art of Astrology, e. an tr. obert amsay Wriht (onon: za & Co., ), . ihe, Traité de l’Astrolabe, .

    

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o their onstrtion.33 Bt the mansripts on astroabe onstrtion by aFarhānī, a-Bīrūnī, an a-ijzī i not reah rope, as ar as is known.3 oweer, there is eiene or the transmission o speia astroabe types, namey the “sothern” astroabe. he Jewish shoar Abraham ben eir ibn zra (–/–) ie in pain nti , an on his sbseqent restess Wanderleben he traee to Itay, Frane, an nan. e wrote three treatises on the astroabe in ebrew ( an ) an one in atin (). In his ebrew treatises Ibn zra is mh onerne with the hanin o a “sothern” astroabe in a northern atite3 an esribes the ierent ayot o tympana o “northern” an “sothern” astroabes.3 A atin treatise on the astroabe (De forma astrolabii), extant in two opies o the mi-twet entry (onon, British ibrary: MS Cotton esp. A  , os – an MS Arne , os r–) has been attribte to Ibn zra by José . iás airosa (–).3 his was at rst qestione,3 bt reent researh tens to onrm the athorship o Ibn zra.3 Contrary to iás airosa (who assme onon as pae o omposition), now oen,

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  7  8  9 

Charette (n. ), –; Aain Briex, “otes sr n astroabe nor-s,” XIVth International Congress of the History of Science, Tokyo and Kyoto, Japan, 19–27 August, 1974,  os. (okyo: iene Coni o Japan, ), :–; Anthony John rner, Astrolabes, AstrolabeRelated Instruments (he ime sem, Cataoe o Coetion, o. I, art ) (okor: he ime sem, ), –. Dominiqe J. Boiot, “’ere ’a-Berni: ssai bibioraphiqe,” Mélanges de l’Institut Dominicain d’Études orientales du Caire  (): –; Franis J. Carmoy, Arabic Astronomical and Astrological Sciences in Latin Translation: A Critical Bibliography (Berkeey–os Anees, : niersity o Caiornia ress, ), –. Josena oríez Arribas, “eiea Jews an eiea Astroabes: Where, Why, ow, an What For?” in Time, Astronomy, and Calendars in the Jewish Tradition, e. aha tern an Chares Brnett (eien: Bri, ), –. oríez Arribas, “eiea Jews”, . José . iás airosa, “n neo tratao e astroabio, e . Abraham Ibn czra,” Al-Andalus: Revista de las escuelas de estudios árabes de Madrid y Granada  (): –. aphae ey, “he Athorship o a atin reatise on the Astroabe,” Speculum  (): –. homo ea, Abraham Ibn Ezra and the Rise of Medieval Hebrew Science (eien: Bri, ), –; enate mithis: “iene in ormany an nan ner the Aneins: he Creation o Abraham Ibn zra’s atin Works on Astronomy an Astrooy,” in Hebrew to Latin, Latin to Hebrew: The Mirroring of two Cultures in the Age of Humanism, Colloquium held at the Warburg Institute, London, October 18–19, 2004, e. Giio Bsi (Berin–orino: ino Arano itore, ), , , –.

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O

erona, or antoa are onsiere. he text oows Ibn zra’s ebrew treatises on the astroabe ery osey, an in it “riht” an “et” astroabes are mentione: the arest ire o the atter, whih is more reqent, is the tropi o Capriorn, the smaest ire the tropi o Caner an vice versa. In both ariants the eestia eqator is in the mie, i.e., between the tropis. his sore onrms that knowee o ariations o the stereoraphi projetion an speia astroabe onstrtions mst hae reahe rope rom Isami areas (probaby pain) in the tweth entry, ths proiin essentia knowee or the onstrtion o astroabe ok ias. Acknowledgement his artie is a reise an enare orm o a paper ien at the XXXth ienti Instrment ymposim o the ienti Instrment Commission, art, . Postscript he astronomia ok o ünster Cathera represents an exeptiona ase. It was onstrte . – by Frieris, monk o the Cisterian monastery e near Bremen3 an amae rin the setarian oernment 40 

4  4 

4 

ea, Abraham Ibn Ezra, ; homo ea an Ga Freentha: “Abraham Ibn zra’s hoary Writins: A Chronooia istin,” Aleph: Historical Studies in Science & Judaism  (): –. ea, Abraham Ibn Ezra, ; oríez Arribas, “eiea Jews,” –. “Genera astroabiorm o snt: extrm et sinistrm. mers sinistrorm maior qam extrorm est. Dpiiter ea isernims. rimo qo in sinistris stee xe septentrionaes intra zoiam, astraes extra rantr. In extris e ontrario. eno ero qo in sinistris trim rotarm maxima est Capriorni, minima Canri, in extris e ontrario. qinotiais in trisqe meia sripta est”: iás airosa, “n neo tratao,” . “emporibs sis Freris monahs isteriensis e a ompeit horaoim in eesia monasteriensis In qa qiem horaoio habentr hore eqaes et ineqaes asenens sinm mots meii omnim panetarm reimine eornem in horis et kaenarim m estis mobiibs”; Chronie o the Cisterian abbey ariene; taatsarhi ünster: s. V nr. , o. —see aso Das Chronion Campi s. ariae in er ätesten Gestat (–), e. Frierih Zrbonsen (= ünsterishe Beiträe zr Geshihtsorshn, ) (aerborn: höninh, ), . he ate  ien ater

    

2

o Anabaptists with its ionoasm in /. In  the athematiian an printer Dietrih zwye, Joannes Aqensis (Johannes rom Aahen), inorite riar an minister o ünster Cathera, an the baksmith ikoas Winemaker joine or a rerbishment o the ok. he paintins were arrie ot by er tom in the er an (probaby) his son ermann. In its present state the astroabe ia has a sothern projetion onnete with a rete onstrte rom the interior o the eestia sphere, an thereore its sense o rotation is onterokwise. he tympanm o the astroabe ia showin a map o the wor (iewe rom the interior o the obe) was painte in . A enrohronooia anaysis showe that the trees se or the ok pate with its astroabe ia were t own between  an , an x-ray examinations oerin are areas onte beore ommenin an extensie restoration in / reeae, that in / oriinay a northern projetion with ines or the tempora hors name iteray onterokwise ha been appie. he ia with its onex horizon ine ooke simiar to the ia in Doberan (. ) an was most ikey a opy o the oriina paintin o the ate th entry. erhaps the esire or a proper orientation o the astronomia ok within the hrh biin ae rise to proie or a onterokwise rotationa sense.

44  4  4  47 

(„orooim ops ist artiiosissimm à monaho qoam Cœnobii ensis orinis Cisteriensis Comitats Demenhorstensis Anno  peretm, maeis seribsqe psant, sinari ero oio et rore Baptisterim, reiqiarmqe repositoria omminnt”; ermann Kok, eries episoporm monasteriensim, eornemqe itae a esta in eesia  [ünster: Koerink, ], ) is not onrme by any oriina sore, howeer. n the sores see ax Geisber, Die tat ünster (= Die Ba- n Knstenkmäer on Westaen , part ) (ünster: Ashenor, ), . heoor Wieshebrink, Die astronomische Uhr im Dom zu Münster (ünster: Ashenor, ), . he inestiation was mae by ans ortsteen (Coone Institte o Conseration ienes) an restorer arita hüter (erswinke). For the ia o the astronomia ok o Berne see arks arti, Das Astrolabium am Zeitglockenturm in Bern: Die Neuentdeckung eines Kulturguts von europäischer Bedeutung (Berne: tämpli, ).

 

Astrolabes for the King: The Astrolabe of Petrus Raimundi of Barcelona Azucena Hernández

epartet  Meea Art Htr, ptee Uert  Mar, a Uertara,  Mar, Spa [email protected]

Abstract The atrae  Petr Ra, ae  Barcea  , ccpe a gcat pt  the et  eea Spah atrae th Lat crpt, a t  the  e ge a ate that ha re t the preet a. A  ecrpt a t  the atrae  preete  the ctet  the pprt ge t the aactrg  cetc tret  Kg Peter   Arag. Athgh the atrca a te recg eatre  the atrae are  etae, peca attet  ge t t arttc a ecrate eatre. The reathp etee Petr Ra’ atrae a the aactre  a-Aa, the reg er Iac re th the Iera Pea  the Me Age, are hghghte, a e a the  th atrae prct  ther Erpea hrta g. The re pae  atrae  ece  cere a rt tep are tae tar cerg the ett  Petr Ra.

Keywords ate atrae ‒ Kg Peter   Arag ‒ Lat atrae ‒ Petr Ra

Introduction The teret that ptca a reg per t  atrae  the Me Age, a the artcratc patrage  the h aactre thee acatg arttc a cetc ject, epa the g ct  cerat a the gcat er  the that hae re t the preet a, epte ther a e a the eae  reg ra, the a  hch the © koninklijke brill nv, leiden, �9 | doi:0.63/9789004387867_06

    D  C

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are ae. The e  the atrae  atrer cat ae acct r t prerat  the Me Age; e t a cer the ptca, ca, a techgca apect  the ctre that prce ch tret. The atrae  Petr Ra  a te t the cet  the ec ha  the rteeth cetr  the g  Arag2 er Kg Peter  el Ceremonioso h a a pprter  cece, a atr, atrg, ece, a, ae a, the aactrg  cetc tret. The Astrolabe of Petrus Raimundi of Barcelona The papherc atrae  Petr Ra preete here (Fgre .) ccpe a prtat pt ag the eea Spah atrae th Lat crpt, a t  the  e ge a ate that ha re t the preet a, a ar a e are aare.3 It ear a crpt egrae  the ege  the r that ge the ae  the aer r er, a the ear a the ct  t aactre. The crpt  e care aae e, t t  reeat t hghght  that Petr Ra ete he a a “eer  the He  the Kg  Arag.” The ter “eer  the He  the Kg” appear  the cet t et a h e here the g e a therere e r e ct t ather th the g, ae r h hat he rere a ere pa r the ra crt get.4 1  A cpete t  the rt-e etat atrae ae  the Iera Pea rg the Me Age, th  A-Aa a the Hpac hrta Kg cg the reate ptca, ca a techgca apect  Acea Heráe, Astrolabios en alAndalus y los reinos medievales hispanos (Mar: La Ergáta, ) a Catálogo razonado de los astrolabios de la España medieval (Mar: La Ergáta, ).   The Kg  Arag er Peter  ce the preet reg  Arag, ataa, a Vaeca  the Iera Pea, p the Baearc Ia a the theat  Frace p t Mtpeer.   The atrae  he  the Me  Fe Art  Bt (acce er ). It  ete a #  the Iterata Itret hect Ner etahe  a A. Kg (th t  reprce  th peca e—ee ect t, #,  Kg’ artce— a  a pc aaae e at http://.aag.rg/tret-catage TO.ht). Th atrae #  t ce  ere J. Prce’ chect, ere J. Prce “A Iterata hect  Atrae,” Archives Internationales d’Histoire des Sciences  (): ‒, ‒.   Fr eape, The Vaeca erth e e Baa  ete a “eer  the He  the Kg”  t cet ge  Kg Peter    a  r the paet r a er atrae: “…  trea e arget qe e e e Baa, e caa a, ta e Perpea e  preet e e ctre a p e t er re …” (“… a er atrae

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G .

nndz

Astrolabe of Petrus Raimundi, front and back. oos by  uo wi  ousy o  usum o in s, oson.

Var hpthee eerge r th act: ether Petr Ra a e  the atrae aer prtecte a pa  Kg Peter  r he a a char (e.g., atrer, atrger, phca) h rere the atrae t e ae  a thr per, r h  e r t e ge t the g a a preet. A thee hpthee  e tae t cerat th th paper, pag attet t the re that atr a atrae pae  eea ece. The atrae a area ete  a A. Kg   a  , cg a re ecrpt  the tret, a e  the e eea atrae ae  the Kg  Arag. cat  e  Baa, a eer  h he. He cat the atrae  Perpga  the preet th  Octer at the reqet  the g …”); “… a  aer qe e  e Baa, argeter e Vaeca e caa e er re,  e egt per […] e  etaare ’arget e er re q pea  e qart …” (“… e hae a et th e  Baa, erth  Vaeca, eer  the he  the g. The et  e t […] a e er atrae r the g he eght a e a a qarter a …”). Fr re eta ee At R  Lch, cet per ’Htra e a tra ataaa Mg-ea,  . (Barcea: Ittt ’Et ataa, ‒), :‒. 5  a A. Kg, “Atra e a ataa eea,”  La Ciència en la Historia dels Països Catalans, e. J. Veret a Ra Paré,  . (Vaeca: Ittt ’Et ataa,

    D  C

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The atrae  ae  gt ra, ha a aeter   , a eght   gra, a ere te atte (r ° t °N)  e pate egrae  th ace. It ac ear the a ac a caerca cae a a ata cae th the tet-eght he  the  r atrgca prpe. It ha a ecrate thre th a etrca par  ate te. It rete (Fgre .) ear a cpete eqatra rg that cre the ecptc, a rare eatre  eea atrae. The Mater The   the ater te  t egrae. It  carre a cae graate r ° t ° aee r each ° tera  thc era a e r each ° a the each °. The r  aage, a the part  the cae r º t º a r º t º are g. The gt   the er   the cae  egrae a a rrr age  a regar , r rather, a a rrr age  etter Z. Th er ccr  ce  the r t re te  the ac  the atrae. The gt , , a  are pae  ther taar eea r.

‒), :‒; a A. Kg, “The Earet K Erpea Atrae  the Lght  Other Ear Atrae,” Physis: Rivista internazionale di storia della scienza  (): ‒ at , ; a A. Kg a Krt Maer, “The Meea ataa Atrae  the Scet  Atqare  L,”  From Baghdad to Barcelona. Essays on the History of the Islamic Exact Sciences in Honour of Prof. Juan Vernet, e. Jep aera a J Saó,  . (Barcea: Uera e Barcea “Ittt Má Vacra,” ), :‒ at . 6  F eta  the aeter, thce a eght  each pece  the atrae  Heráe, Catálogo razonado de los astrolabios, –. 7  a A. Kg, “Atrca Itretat  the Meea Iac Wr,”  a A. Kg, In Synchrony with the Heavens: Studies in Astronomical Timekeeping and Instrumentation in Medieval Islamic Civilization,  . V. : The Call of the Muezzin. V. : Instruments of Mass Calculation (Lee: Br, ‒), :. Kg cer that the rt et  the prcere r the ctrct  ar a caerca cae  the ac  a atrae    the Treate  the Atrae  the Aaī atrer Aū a-Ṣat (ca. ); J Saó, Las Ciencias de los Antiguos en al-Andalus,  e. (Aería: Facó I Ta e Et Árae, ), . The preece  the ar a ac caear cae  the ac  a atrae etahe a -ca crrepece etee each ate  the Ja caear a the acta ar gte.   hare Brett, “Ia Nera  the Meterraea Ba  the Teth etr, th Speca Reerece t the ‘Eater Fr,’ ”  From China to Paris: 2000 Years Transmission of Mathematical Ideas, e. Y. -Sap et a. (Stttgart: Steer, ), ‒ at 

8

nndz

G .

Rete of the astrolabe of Petrus Raimundi. oo by  uo wi  ousy o  usum o in s, oson.

The ege  the r carre a eegat Lat crpt  thc crpt that ce the ae a aat  the atrae aer r patr, pace a ate  aactre, a the atte a gte  Barcea. The crpt rea (Fgre .): HO ASTRALABIUM BARHINONE: ANNO PI  PER PETRUM RAIMŨI: E OMO REIS ARAONUM: LATI BARHINONE: : LONI : a ; Rchar Lea, “The Hpac Org  r Preet Nera Fr,” Viator  (): ‒.

    D  C

G .



Details of the inscription engraved in the edge of the rim of the astrolabe with the name of the author, date, place, latitude and longitude. oos by  uo wi  ousy o  usum o in s, oson.

Th a e traate a: Th Atrae  Barcea,  the ear  hrt ,  Petr Ra  the He  the Kg  Arag: at the Latte  Barcea , Lgte . The ct, Barcea, a the ear, , acre th atrae t the r  Arag er Kg Peter  h re Arag, Vaeca, ataa, a Marca r  t h eath  . Wth regar t the gegraphc crate cate  the crpt, the atte °  the ae age t Barcea  the Me Age, ht the gte ° reqre carcat. The preet ae r the gte  Barcea  reat t the reech era  °′E t reech a t etahe re a the pre era t . Var pace, ch a Aeara, Ar, Mecca, Par, a, the aar Ia, Nape r the Are, ere e a a er pt t eare gte  the Me Age. The ae ° r the gte  Barcea pra reer t the ater era, a pre era ete  Andalusī htrca rce. Sch a pt crrep t a pt  the Atatc Ocea, °′W  the t eter pt  the aar Ia.   1 

11 

The egat  Peter  a Kg  Marca t pace eera ear ere,  . Kg, Astrolabis de la Catalunya medieval, . Kg rea “Lgte ”  the crpt rather tha “Lgte ” a egrae, pra e t the pr qat  the phtgraph he re th. eqet, the epaat ge t jt the ae ° r the gte  Barcea   ger appcae. J Saó, Las Ciencias de los Antiguos en al-Andalus, , ‒. The pt  the “ater era” a et at º’ et  the aar Ia  Aarqe  h Tea Tae (ca.  D).Fr re eta at th e, ee Mercé e, “The ‘Mera  the

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nndz

erg that the a Herr  the etert a  the aar archpeag a that the er gte  Rqe e ch, the etert cape th the a Herr,  °′W, e get a gte  °′W r the Andalusī ater era. Barcea  hae ha a gte reate t that pre era  °′E. Athgh the er  the crpt  the atrae  °, t er  tte re tha ° r the cacate ae, a acceptae errr. Th atrae  th a tet t the e  the Andalusī ater era t etah gegraphca gte  the Iera Pea rg the rteeth cetr. The Back The ac ear r atte cae e r ° t ° r eer ° a e r each egree. Each qarat  ere r the eat a et pt t the th a rth pt. The t cae  the pper qarat are aee r each ° a the gt   er  a   egrae a a rrr age  a etter Z a  the ater. The t cae  the er qarat are aee r each ° a the rrr age  gt  appear a  the er . The a ac a caerca cae, -ccetrc th each ther, are the et e t ccr. The ac cae  e r each ° a e r each egree a aee r each °. The ae  the ac g are egrae a : ARIES TAURUS EMINI ANER LEO UIRO LIBRA SORPI9 SAITARI9 AṖORN9 AQUARI9 PISES The egraer ha repace the eg  “-”  r  the g  a character that  e the cpher “” hch  qte c th the repertre Water’  the Tae  egraphca rate  a-Aa a Nrth Arca,” Journal for the History of Arabic Science  (): ‒; Mercè e “Tae  egraphca rate a the Se  the Meterraea Accrg t the Atrer  aAa,”  Al-Andalus. The Scientic Legacy, e. Rrg térre (raaa: Prect Sr e Ece, ), ‒; E.S a M.H. Kee, Geographical Coordinates of Localities from Islamic Sources (Frart a Ma: Ittt ür echchte er ArachIache Wechate a er J.W. ethe-Uertät, ), . Kee ce the ae  the gte r Barcea reate t ther era t t t the ater era.

    D  C

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 eea areat. The tte t er the “P”  aprcr cate a a areat, ae “.” 2 The caerca cae  e r each e a a e r each a a the aee r each te a (–– r the th th  a a –– r Ferar). The ae  the th are egrae a : IANUARIUS FEBRUARI9 MARIUS APRILIS MAYYUS IUNIUS IULIUS AUUSTUS SEPTEMBER OTOBER NOUEMBER EEMBER I thee th ae, the repaceet  the eg  “-”  a “” ha  ee ae  Ferar. The ae MAYYUS  a rthgraphca arat  the Lat ae MAIUS.3 The era eq  et at  March.4 A ata cae ha ee ce g the caear. It carre the tet-eght a  the  aee th the er e t teteght. Sce the ar a are e re r atrgca jgeet, e ght cer that the atrae’ rt er practce atrg. The rt a crrep t the tet-th egree  Are. A e hrar qarat ha ee cate  the pper cetra pace, ht the er part eatre a e ha qare th cae e t tee gt a aee r each three.

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a A. Kg, “Rertg Htr thrgh Itret: The Secret  a Meea Atrae r Pcar,”  Making Instruments Count: Essays on Historical Scientic Instruments Presented to Gerard L’Estrange Turner, e. R..W. Aer, J.A. Beett, a W.F. Ra (Farha: Ahgate Varr, ), ‒. rg the Me Age the ae  the g ere rtte  ar a, cg er areat. The areat  aprcr th a t er the “p”  attete  ar Erpea eea atrae ch a the Frech atrae #, # a the tch atrae #, ag ther. Fr the areat  “-” ee Ara ape, Dizionario di Abbreviature Latine ed Italiani (Ma: Urc Hep, ), . a A. Kg, “The Atrae epcte  the Itara  the t  Arche Feerc  Ur,”  Astrolabes from Medieval Europe (Farha: Ahgate Varr, ), :. The arat MAYUS r Ma    the caerca cae eatre  the ac  atrae # preere  the Me  Stra ea Scea, Frece. Kg, Astrolabis de la Catalunya medieval, . The era eq  t atrae he ate a pace  aactre  attrte  Kg t the rteeth cetr a the Kg  Arag  et at  March (atrae # preere at the Scet  Atqare  L) a , March (atrae # preere at the Nata Marte Me, reech).

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nndz

The Rete The rete  a  eg. It tcte eatre  a cpete eqatra rg that cre the crce  the ecptc at the t eqe, Are a Lra (ee Fgre .). The ter a eqatra rg  the atrae’ rete th carr cae graate r ° t ° aee r each te-egree tera,  thc era, a e r each t egree. The ter rg  aage a the part  the cae r º t º  g. The er  the cae cce th the er egree  aprcr  the ter rg a th the er egree  Are  the eqatra rg. The tar-pter are faehape, the eqcta ar ha a ge cter-chage te the ecptc, a the thc crpt are a care eecte   crpt. Each ac g  the ecptc  e t three aee te-egree tera a e r each t egree. The ae  the ac g are egrae a : ARIES , TAURUS , EMIN , ANE , LEO , UIRO , LIB RA , SORPI9 , SAITARI9 , APRIORN9 , AQARI9 , PIS ES. The egraer ha a repace the eg  “-”  r g  a “”. The rece pace aaae  the cae  the ecptc ret  the hrteg  the ae e a acer t EMIN a ANE. The ae LIBRA a PISES are pt  the e th a pace etee the t part t a r r the jg  the ecptc a the eqatra rg. The g Aqar ha ee egrae “Aqar” hch  e  the ar eea areat r that ae. The rete eatre tet-t tar pter, th the tar ae cre  thc crpt. Tae . ete each  the tar. 15 

16 

17 

Kg, Astrolabis de la Catalunya medieval, . The cae  the ter rg eare   the a ee  Atqt ht the cae  the eqatra rg eare t  the preet taar a. Kg, Rewriting History through Instruments, . The areat  Aqar a “Aqar” r “Acar”  attete  ar Erpea eea atrae ch a the Spah atrae #, # a # a the Frech atrae #. “Acar”  the ter e  Ra L  h Treate  Atr () he he trce the Zac g: ee Jr aà, th La Baa, “Ra L. Tractat ’Atra (eg e M. A. . e Brth Me),”  Textos y estudios sobre Astronomía española en el siglo XIII, e. Ja Veret (Barcea: Uera Atóa e Barcea, ), ‒ at . Kg, Astrolabis de la Catalunya medieval, . Kg pre the ae  tee  the tet-t tar tht etcat; Brhar Stat, Untersuchungen von

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    D  C  . Identication of the Stars in the Rete of the Petrus Raimundi Astrolabe No.

Star-name in

Current star-name Arab star-name

Identication

pha Bate Kat Acherar Aeara Rge Sr Prc Aphar Reg eah r Agra Spca Arctr eea he Aa Aphecca Vega Atar ee  Mrach apea

β et ζ et α Er α Ta β Or α Ma α M α Ha α Le γ r δ r α Vr α B β Le α UMa η UMa α rB α Lr α Aq ε e β A α Ar

the rete

1    5 6 7   1 11 1 1 1 15 16 17 1 1  1 

ENEBAYTO PANTAAYTA ALETENAR ALEBARAN RIIL ALHABOR ALOME ALFARAR OR LEO ORUUS ALORAB AZIMEH ALRAMEH BMENA URSA ALAY ALPHA UEA ATAYR ELFIN MIRA YOU

dhanab al-qayṭūs baṭn al-qayṭūs ākhir al-nahr al-dabarān al-rijl al-ʿabūr al-ghumayṣā al-fard qalb al-asad janāḥ al-ghurāb al-yaman al-ghurāb al-simāk (al- aʿzal) al-rāmiḥ dhanab al-asad ẓahr al-dubb al-akbar al-qā’id banat al-naʿsh nayyir al-fakka al-wāqiʿ al-ṭāʾir dhanab al-dulfīn al-miʾzar al-ʿayyūq

There are a ctrct ar egrae  the reere  the rete, ae a the cae e a e t ae t  the pt  the e  the three rg (Fgre .).

mathematisch-astronomischen Darstellungen auf mittelalterlichen Astrolabien islamischer und europäischer Herkunft (Ba: G, ), ‒ a ‒; Pa Ktch, Arabische Sternnamen in Europa (Weae: Ott Harrat, ), ‒.

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nndz

G .

Reverse of the rete of astrolabe of Petrus Raimundi with workshop construction marks. oo by  uo wi  ousy o  usum o in s, oson.

The Plates The atrae ha e pate egrae  th e. The a ear atte crce r eer e egree, ath crce r each te egree, a the e  the tee eqa hr. Nether the crce r the e are aee. The crpt  the pate rea a h  Tae .. The th pate eatre the teregraphc prject r atte °, the eqatr,  the e here the crpt EQUINOIUM ta, hch  qte a (Fgre .). The ther e ere atte °N hch crrep t the t  the hate r  the eea rce. The at t pate ere t eat r erat, t  r teachg. The ret  the atte ere  the atrae are qte c  the Spah eea atrae. The r “Vaeca” appear re cratche e the e-egrae ae “ ” a  hae ee ae  a ater er  the atrae (er e g  Vaeca)  rer t eect the pate r h ct re ea (Fgre .). A cratch th the r “Par” appear e the ae “ ”  the crrepg pate.

    D  C

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 . The Inscriptions on the Plates Plate No.

Inscription

1a 1 a  a  a  5a 5

   6   Vaeca    1    5   Par EQUINO IUM  66

G .

Detail of the plate for latitude 0° with the engraved word EQUINOC CIUM. oo by  uo wi  ousy o  usum o in s, oson.

The pe cte tee t e ere  the r pate are ge  Tae .. 1 

a A. Kg, Wr Map r Fg the rect a tace t Mecca. Iat a Trat  Iac Scece (Lee: Br, ), . It  rth tg that atte

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nndz

G .

Detail of the word VALECIA scratched in the plate for latitude 39 of the astrolabe of Petrus Raimundi. oo by  uo wi  ousy o  usum o in s, oson.

 . Possible Cities Served by the Astrolabe Plate No.

City

Plate No.

City

1a 1 a 

º = ar 6º = Agecra º = Vaeca º = Te

a  a 

1º = Barcea r Zaraga º = ra r Perpga 5º = Te º = Par

The Remaining Elements of the Astrolabe The aae  cter-chage; t ha  cae a each  the pae ha e pe he. The rt rer  etca  hape t ha  the aae. The per te  rga a ecpae a rearae thre e t the r at r pt  ctact. It preet a par  etrca °, °, °, °, a ° crrep t the cetra a  e  the ee gegraphca cate  Atqt a the ere c ce  eea atrae.

    D  C



ate te he hape  aae ater  th paper. The hae  tre-hape a tte th a crcar rg. The p ee t e rga ht the ege  a er at. Brass Analysis Report A  et  tet e  each pece  the atrae g the X-ra frecece (X) eth cr that a t eeet are ae  eea ra. The ater, the rete, a a the pate are gt t t ha ee pe t aae the ra er the gt. The a r the ater, the r, the rete, the thre, a t  the pate (the r atte °/° a °/°)  er ar, th ar % cpper, % c a e tha % t, ea, a er. The ther three pate (the r atte °/°, °/° a °/eq) hae a ght hgher percetage  c, th ar % cpper, % c, a e tha % t, ea, a er. The ata pece (aae, rer, p, hre, hae, a rg) hae e eret cpt th percetage  c r .% t .%.2 Decorative Dimension of the Astrolabe of Petrus Raimundi Meea atrae ccetrate ther raeta eeet  the rete a the thre. I Iac a-Aa a  the hrta g  the Iera Pea, the ecrat are erate a reea a preerece r atert. A area te, the rete  the atrae  Petr Ra  tcte  eg e t the preece  the cpete eqatra rg hch eh etere the hape a cat  the ecrate eeet, ae a  crce  the ertca a a t ecrce  the hrta a. The are a pace e the pper ha  the eqatra rg. The preece  crcar rae a raeta eeet  the rete  qte c  the atrae r a-Aa, hch ere the rce  1 

 

The X aa  each part  the atrae a ae   Octer   Mchee errc  the Scetc Reearch Laratr  the Me  Fe Art, Bt, , . M gratte t Aga H a Reecca Te r ag the aa reprt aaae t e. F eta  the ret  X aa  Acea Heráe, Astrolabios en la España Medieval: de al-Andalus a los reinos cristianos, (Mar: Uera ptee e Mar, ), –.

8

nndz

G .

Detail of decorative circles in Andalusí astrolabes #116 (top left), #2527 (top right), #129 (bottom left) and #136 (bottom-right). oos by  uo wi  ousy o  sbibliok lin nd  usum o  isoy o in, xod.

prat r the eea atrae th Lat, eracar, a/r Here crpt aactre  the hrta g  the Iera Pea. A eape  ch e  the crcar rae t  rth etg atrae # (Ber Staatte), # (Me  the Htr  Scece, Or), # (Spah Ra Acae  Htr), a eght  the rtee Andalusī Aha atrae that Mḥaa  Fattūḥ a-Khaāʾrī ae  See etee AH (‒ C) a  (‒ C), a  hch eatre a crce etee the ceeta eqatr rae e the ecptc a the ter r  the rete (Fgre .). The teret  crce a ecrate eeet e r a-Aa t the hrta g  the Iera Pea a the a crce e the ceeta eqatr rae  preet  atrae #, #, a #, a ge t cere  a Kg t e Hpac r  the rteeth r teeth cetr.2 Partcar reeat th regar t the e  crcar 1 

Fr atrae #, ee Mhae Aae, a A. Kg a Petra Sch, “Fr a Heae Arac Pe t a Egatc Jae-Arac Atrae,” Suhayl  (): ‒ at  a . Fr atrae #, ee a A. Kg, “A Atrae r Meea Spa th Icrpt  Here, Arac a Lat,”  In Synchrony with the Heavens, ch. , at :, a Sphe Maar, “Fcha e atra,”  Los mundos del Islam en la colección del Museo Aga Khan. Catálogo de exposición (Barcea: Facó a aa, ), . Fr atrae # ee Kg a Maer, The Medieval Catalan Astrolabe, .

    D  C

G .8



Retes of the astrolabe of Petrus Raimundi (left, photo by the author with the courtesy of the Museum of Fine Arts, Boston) and of Mamluk astrolabe #4164, Cairo Museum of Islamic Art nr. 15368 (right, photo courtesy of Alain Brieux, Paris).

rae  atrae # (reech Marte Me), hch eatre t ecrce, e peg ar a the ther par,  the eqcta ar etee the ecptc a the ter r. Th eatre, tgether th the fae-hape tar pter  th atrae, ete t a the cet e, th eea Spah prct, t the Petr Ra atrae r the ecrate pt  e. Wth regar t the t ecrce  Petr Ra’ rete, the th pe ar a are a  the t eget  the eqcta ar e th the eqatra a the ecptc rg. Ag the te  pre char, the  atrae that er a ar eatre  # (ar Me  Iac Art, r. ), a ge a ate Ma atrae eae  a Kg  22 (Fgre .). Whether r t the arte etee the Ma atrae a the e r Barcea are a ret  rect reathp etee ther repecte aactrer  er t. I a cae, the terear re pae  the Nar g  raaa h t e eretate.23

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a A. Kg, “Se Atrca Itret r Meea Sra,”  In Synchrony with the Heavens, ch. , at :‒. Fr reathp etee atrer r the Ma taate a the r the a-Aa Nar g, ee Ea a, “I Bā’ Atrae  the Maghr a Eat,”  From Baghdad to Barcelona, :‒ at .

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nndz

A  the tar pter  the rete  Petr Ra’ atrae are faehape. Fae-hape tar pter  t ce r the Andalusī atrae trat t ecae ppar  hrta Erpe  the rteeth a teeth cetre.24 Or atrae ha a thre th a rearae eg  cre eae reeg te etrca pace a ag t the r th a eegat hta-hape e. Thee e ee t care h a rae the crpt egrae  the ege  the r. The rt a ac  the thre are etca  hape t the rt ear re egrae e. The eg a e reate t the Andalusī Aḥa  Ḥa  Bāṣ atrae thre2 t th a ata pt  phtcat, eg r I Bāṣ’ geetrca patter t a re atratc te  eae a hta hape (Fgre .). The crcat th the r  Arag  the  treate  the papherc atrae rtte  eracar ata, the Libro del Astrolabio Llano (e  the tee part  the Libro del Saber de Astrología  Kg A X  ate), epa the a reathp etee the thre epcte  the acrpt a the e  the Barcea atrae, pra a I Bāṣ’

G .

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Throne of the astrolabe of Petrus Raimundi compared with the one of the andalusí astrolabe #132 of Aḥmad ibn Ḥusayn ibn Bāṣo. oos by  uo wi  ousy o  usum o in s, oson, nd  nis oyl dmy o isoy.

The e- Frech atrae aer Jea Fr (ca. ‒) e fae-hape tar pter  the rete  h atrae, a ther ge a ate pece a ce thee eegat tar pter. I partcar atrae # (Spah Ra Acae  Htr) a # (Me  Iac Art, ha, Qatar).

    D  C

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thre.2 The Petr Ra thre eg a hae fece tre atrae ch a the -cae “Ur atrae” pra ae  .2 Hag ecre a aae the atrca a raeta e  the Petr Ra atrae, t  te t apprach the ctet that hep t erta h th ject a ae. Historical and Social Context of this Astrolabe: King Peter V of Aragon and the Astrolabe Workshops Patronized by Him The eepet  cece a gcat  the Kg  Arag rg the rteeth cetr. A he at  g pprte cetc reearch, cg t  t practca e: the ctrct  cetc tret. Ag thee, Jae  (‒), Aphe  (‒), Peter  el Ceremonioso (‒), Jh  (‒), a Mart  (‒) ere the greatet prter  tret-ag.2 Ata, the recre t  the actte  ther g that ha a ecc pact, cg the ctrct  atrae a ther atrca tret. Thee cet, hch hae re  arge er, are a eceet rce r the ca a ptca ctet  hch a atrae ch a that  Petr Ra ght hae ee ctrcte. The rtte rce et three a cetre  prct  atrae  the ec ha  the rteeth cetr  the Kg  Arag: Marca, Barcea, a Perpga, th Marca eg the t prtat. The thre pprte the rhp a here the aactrer, th Jeh a hrta, th hr. epte the g er  cete atrae aer a gth, the ae  Petr Ra ha t et ee .

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Kg, Astrolabis de la Catalunya medieval, . Kg te the reathp etee the thre  Petr Ra’ atrae a that  the atrae epcte  the Lr e Atra La, part  A   ate’ Libro del Saber de Astrología, a ete th reathp t ther eeet  the rete. Fr eta  th atrae # hch a te   a he crret cat rea , ee Kg, The Astrolabe Depicted in the Intarsia, ‒. Mge Batr Mé, “La ctra cataa-Aragea rat a atía e Barcea ‒: rret acta e a etgacó,” in  Congreso de Historia de la Corona de Aragon, e. J. Zrta,  . (Barcea: Uera e Barcea, ), :‒.

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nndz

Who was Petrus Raimundi? A a ere, reearch ha t et ee a cear ret  the ett  Petr Ra, the per he ae  egrae  the ege  the r  the atrae.2 Neerthee, a per th the ae ae, Petrus Raimundi, magister in artibus et bacallarius in medicina ha ee   the arche a the athr  a teretg acrpt  , Tractatus primus Rosae Philosophiae (The Frt Treate  the Re  Phph’), hch ha re  a cp ae   (Fgre .).3 The acrpt  ept  the Bteca a  aptar  See. The Tractatus  a t  the reathp etee the cece  the tar a ece, a t athr, h ecare he t e a phca, etrate thrght the  ege  th atr (paet, , tar, cet, etc.) a ece (the ha , eae, etc.), t cpe er ce e  the Me Age.3 The  a ecate    

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I at t tha r At Mpet r rag  attet t Pere Ra a r a h pprt. Jep Perara  Epet, “N atr  tet cataa atc: Pere e Pgra, Fgatge, e Aar, Pere Ra,” Arxiu de textos catalans  (): ‒. Icpt: “Tractat pr Rae Phphae, act et cpat per agtr Petr Ra, agtr  art et acaar  eca, qe cpat  a Trep.” Epct: “pt et cpat t er te q Ra Phphae apeatr, a agtr Petr Ra, agtr  art et acaar  eca  c e Trep, a  ,  e e jaar. Et pree crptra t crpta per a e Jac Hera, tet Baagar et ta  e epter a a Nattate  .” See are Áare Márqe, “E terar e aqce e r e a e Hera ó,” Historia, Instituciones, Documentos  ():  at , . Tractat pr Rae Phphae a e  the   regtere   the prate rar  Fera  (‒), the ec   hrtpher  (‒). I preet e qtat r the acrpt See, Bteca aptar  a, M -- a eape: “Hc tractatr e qaa cteate, qe t  et , ccet a  ° CCC° XXX’’, ccet e ccte Mart c Satr….” (. r); “Hc tetr qt  t tret crp tr. Hc tetr qe apect haet ee a crp ha, et qt t geera eer.” (. ); “Hc tetr q a qatr  part et cctat etr et t, rate paetar et gr. Et pr, e paet, pt e g …” (. );. “apt cta,  q tractatr e tea cata,  tetr qe et atera tee cate, et qe caa ece, et  geerat p, et qt t tee cate, et c ag cee e geerat, et reg, qa eptetra. Et a atetetr pra rte prcp, et ag prcp qa ar. Et e gcate p. Ut, e ctate tear, qare pe ctat” (. r). A thee reerece h that th  t a techca atrca r atrgca tet; t  rather a cgca r phphca

    D  C

G .0

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First folio of Tractatus primus Rosae Philosophiae by Petrus Raimundi. oo ousy o  iblio Ciul nd Colombin o vill, CC s --.

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nndz

t Ara e Ma, Bhp  Urge, h a pra a pprter  Ra’ eca career a partcar  the prct  th . The  a rtte  Trep, a a age eght-e  r Lea, ataa, the ct here the rt ert  Arag a e    Kg Jae .32 erg that Peter  re h g r  t , the , ate , a rtte rg h reg. It  er e that a a atre egh t e a phca a t rte th  c hae a ee the aer  a atrae ate , t t  pe that the t ere reate, perhap ather a  r graather a gra. The Spah trat  atag the ae hrta ae  a a r geerat t geerat, a the eece that the practce  ece a pae r ather t , ge  e gr t prpe that Petr Ra, the a he ae  egrae  the atrae, a hae ee a phca,  r gra  Petr Ra, the athr  the Tractatus primus Rosae Philosophiae a that th a hae gt ther egree  ece r the St eerae  Lea.33 Frther reearch  gg t cr r reject th hpthe. Who Qualies to Sign an Astrolabe? The Authorship Debate The cet cr that phca a ctr ha atrae. The ha a ar at  ege  atr, geetr, a atheatc, a the pt that the theee ege the atrae the ce h t e e. The cratahp  the tret reqre pecc  a  ra-th  hae ee ae t aactre the atrae part, t the rt theretca phae c hae ee ertae  a magister in artibus et medicina, the tte he  Petr Ra. It h

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e prg the geera eccpec ege eee r eea ece. The rter e t ae a reerece t atrae. The St eerae  Lea a e  Lea (Lera)  Kg Jae   Arag (‒) a the te  ece t pace there rg the reg  Kg Peter . The t age ete  th acrpt, Trep, here Petr Ra rte h , a Baager (“tet Baagar”), the rthpace  the tet h ae the cp, are cate  the prce  Lea. Atr, e  the ee era art a ece ere taght  the St eerae  Lea. Fr eta ee J Arraaaga, “Le Uertat,”  La Ciència en la Historia dels Països Catalans :‒; a Eía Serra Rá, Una Universidad medieval. El Estudio General de Lérida (Mar: Lrería eera Vctra Sáre, ), ‒ a J.J. Bqeta (e.), Llibre de les Constitucions i Estatuts de l’Estudi General de Lleida (Prcp e rar; Lea: Uertat e Lea, ).

    D  C

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e te that a etca tte a he  the Frech atrae aer, Jea Fr (‒).34 The prce  ag a atrae e at eat three et  :

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S r the teregraphca prject  eret crce, phere, a pt a r the graat  the eret cae that the atrae pa. Metarg  t cat r haer the ra t crcar heet-eta pate a t ae the rete a thre th ther raeta eeet. Egrag  t ra the e t the ra pece, eepg ther crrect pt t the a etet  rer t ere the accrac  the tret, a e a rtg the ae a er prper.

 a ge per hae eje a thee  tgether  the Me Age? Perhap, t pra t, r the  are t ere a  hae ee acqre at ar ttt, each th pecc egree regate  the apprprate g. A rth perat h e ae t the area ete tr a th  the patr: the g, a crter, a preate, r a char h acta rere the aactre  the atrae a pa r t. The qet the are: he ae ag the r pepe p e  the atrae prct h g t,  a?3 Th qet ha area ee ae  a art htra he tg the e eea artr that happe t hae ee  

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Kg Jh   Arag recee   a atrae ae  Jea Fr a the cet hch recr the eet reer t h a “ect tr Jha Fr  art et eca agtr, R  Lch,” Documents :. Mt  the htrgraph  atrae  each atrae t a ge per, the atrae aer,  the atrae  ge, r a a per  t  ge. A ge gatre e t ea a ge ha a e  the he prce r the theretca ccept  the ject t the a ajtet  the eta pece, a th prcpe appe t a   aactre ject, hether pe r cpe, hether cetc, arttc, r th. The   ar  the aactrg  atrae  pprte  char (.e., Rert B. r, “Steeth-etr Metarg Techg e  the Maactre  t era Atrae,” Annals of Science  (): ‒ a B.. Ner, M.R. Nt, B. Stephe, .S. arg  a .B. Stephe, “The Atrae rate  Lahre a Ear Bra Metarg,” Annals of Science  (): ‒). O the ject  eea atrae aactrg prce th reerece t eea cet ee Acea Heráe “e ccept a j  e tra a ató. Maactra e  atra e  taer eea,”  Alando el pincel, dibujando la voz. Prácticas pictóricas góticas, M. Mqe, O. Pére a P. Martíe (e.) (Mar: Etra ptee) –.



nndz

ge. A g eape  h cpe the etahet  athrhp ca e  the “Br Bcet” (Hertage Me, St Peterrg), a agcet cat ra car a th er a cpper ge  r pepe: the patr h rere t, the etarer h chae t, the artt (arta) h ae the a ecrat a a the per h recee t a a preet.3 Whch ae h hae ee ept  t egh pace r a the ae a aaae? Wh pa the t reeat re  the prce? The a at  art pece appe a t the atrae a th  h th atrae ge  Petr Ra  qe ag the  Lat crpt r eea Spa. The ert t et Ra a h re  the aactre are gg. The preece  a atrgca eatre ch a the cae th the tet-eght a  the   a preereta pt  the ac  the atrae, gget that t rt er a partcar terete  atrgca prect. A reearch rect rea acte, t at the et e are cg r attet  the ct  phca  Arag ar  rather tha the etarg g. Fg th apprach , e hpe, e a cearer aer. Acknowledgements Th paper  ecate t a A. Kg. M gratte t r. hare Brett a r. Jea Rríge Arra r ther tat t t th paper. The t  th atrae  hae ee pe tht the hep  the Me  Fe Art  Bt,  partcar  Aga H (cratr), Mchee errc (acate reearch cett), a Maretta aarer (cratr). Th t  part  the Spah R& Prject –-R: “A-Aa,  re hpa  Egpt: arte, per  ccet e e Meterráe eea. La ree e terca   pact e a ctra a,” e  Saa a a Ja ar R Sa. M tha t the r ther pprt a a t err Larece, Herert áe, a Fac a A.. Mrr-L r ther hep.

6 

The crpt  t r a e traate: “Orere  ʿA-a-Raḥā  ʿAaāh a-Rahīī. hae  Mḥaa  ʿA-a-Wāḥ. ecrate  Ḥāj Maʿū  Aḥa, the ecratr [a-aqqāh]  Herat r t er, the eate Ḵhāja R-aī, pre  the erchat, the t trtrth  the M, grace  the pgr a the t actare [the h pace Mecca a Mea], Rahī-a-ī  ʿAīī  Aū-a-Ḥa a- Zajāī, a h gr at.” The hae pre the ate “ the th  Mḥarra  ear  .” eqaet t eceer  C.

 

A New Approach to the Star Data of Early Planispheric Astrolabes Giorgio Strano

Mueo aeo, Pazza de udc 1, 1 orence, Ita [email protected]

Abstract urng the twenteth centur, choar attempted to date ear atronomca ntrument  the centc normaton dcernae n ther degn. In partcuar, the deved “method” to date panpherc atroae  the poton o the verna equnox on the caendar cae or  the preceona eect over the tar coordnate. Such method uua overooked the man proem ehnd the ntrument’ degn and contructon and the vctude n a partcuar oject’ htor. Crtcm o the naveté o the centc approach dd not peruade choar wth an atronomca ackground. he remaned convnced o the upreme expanator power that the preent knowedge ha or decpherng the pat. he crtcm, ntead, duaded choar wth a htorca ackground rom pang attenton to the centc data. he et comortae n anang centc rec on the a o other tpe o evdence, uch a textua ource, conograph, and te. he tar coordnate o ear panpherc atroae, a wtneed n ther tar ponter, can nether e regarded nor treated a the data o preent cence. Even  the do not decre the k at the ver moment o the makng o the ntrument, the ma, neverthee, e condered a non-textua ource that contan precou normaton. he tar coordnate on the atroae rete ma n act connect group o ntrument wth ear tar tae.

Keywords Cataan atroae ‒ eore Chaucer ‒ ata nterpretaton – Engh medeva atroae ‒ Peudo-Meahaa tar tae

© koninklijke brill nv, leiden, �9 | doi:0.63/9789004387867_07

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Introduction Panpherc atroae have acnated oth htoran and centt or centure. he two choar dcpne, however, edom nteract rutu. ather, the evove pecc method or tudng atronomca ntrument. When the two choar group meet, each part preer t own “htorca” or “centc” method o nvetgaton and tre to convnce the other part that thee are the mot reae. In order to provde atance, other peope are occaona nvoved n the tude, ncudng art htoran, phoogt, matera expert, and  modeer. In th artce, I w ocu on two tradtona “centc” method or handng atroae’ data. otwthtandng ther reevant drawack, the tend to reappear rom tme to tme n choar tude. I w ucceve outne an ntermedate approach to the atroae’ tar data. he new approach wa tentatve deveoped durng the comparatve tud o the oma-Koeker atroae (gure 1.1), and ve other ear Engh “Chaucer-tpe” atroae. he new approach tart rom the gatherng o tar data rom the ntrument’ ponter, a an atronomer woud do, ut ue uch data to etah poe reatonhp wth other avaae ource, a a htoran or a phoogt woud do. he premnar reut are encouragng enough to tet the approach on

  oma-Koeker atroae, Mueo aeo: Inttute and Mueum o the tor o Scence, orence, nv. no. 1 (Kng no. 1). or Kng’ numer ee: avd A. Kng, “An Ordered Lt o European Atroae to ca. 1,” n Kng, Astrolabes from Medieval Europe (arnham: Ahgate, 11), X/1–11 (X/). See ao: avd Kng, A Catalogue of Medieval Astronomical Instruments: Provisional Table of Contents (eron Ma ), avaae onne at http://www .davdakng.org/ntrument-cataogue-OC.htm (acceed 1 Apr 1).   “Chaucer” atroae, dated 1, rth Mueum, London, nv. no.  1, –1.1 (unther no. 1, Ward no. , T no. 1); Panwck atroae, Mueum o the tor o Scence, Oxord, nv. no.  (unther no. , T no. ); Atroae, rth Mueum, London, nv. no.  11,1.1 (unther no. , Ward no. , T no. 1); Parne atroae, Smthonan atona Mueum o Amercan tor, Wahngton D (unther no. ); unther atroae, Mueum o the tor o Scence, Oxord, nv. no.  (Kng no. , T no. ). or unther, Ward and T numer ee repectve: oert W.. unther, The Astrolabes of the World,  vo. (Oxord: nvert Pre, 1), : –; ranc A.. Ward, A Catalogue of European Scientic Instruments in the Department of Medieval and Later Antiquities of the British Museum (London: rth Mueum, 11), 11–11; T, avaae onne at http://www.mh.ox.ac.uk/epact/cataogue.php (acceed 1 Apr 1).   See Jm ennett and orgo Strano, “he So-Caed ‘Chaucer Atroae’ rom the Koeker Coecton, Man,” Nuncius: Journal of the Material and Visual History of Science .1 (1): 1‒ (‒).

  D f ly lisi slbs

FGUR .

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The Tomba-Koelliker astrolabe, front (Museo Galileo: Institute and Museum of the History of Science, Florence, inv. no. 3931).

other ntrument a, or exampe, the Cataan atroae wth a Chaucer-tpe rete, preerved at the atona Martme Mueum o reenwch. Dating Early Astrolabes by Astronomical Methods Snce the at centur, proeona and amateur centt ue the hat o datng panpherc atroae atronomca. Among the “centc” method to 4  Cataan atroae, atona Martme Mueum (Card Coecton), reenwch, London, nv. no. AS ( no. 1). or ’ numer ee: Sharon L. , Jance A. enderon, erek John de Soa Prce, A Computerized Checklist of Astrolabes (no ocat: no prnter ndcaton, 1), 1.

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accomph the purpoe, two are arge preerred. he oth re upon the mpct aumpton that atronomer n the pat acted n the ame wa that the do toda and that the awa ued reae, reh gathered data.  oowng th ne o reaonng, the atronomca normaton repreented on an ntrument woud approxmate the rea k at the moment o the ntrument’ creaton. An dcrepanc etween the k and the ntrument woud e due to random error n oervaton and the manuacturng proce. The “First Point of Aries” Method he “nventor” o the mot common method o datng ear atroae  unknown. A the mathematc nvoved  eementar, the denton o the operatona procedure woud have een wthn the at o anone aware o what prompted the regoran reormaton o the caendar. he purpoe o the reormer wa to x the exact date o the verna equnox on 1 March and keep t rom drtng over the coure o centure. owever, t wa not cear how to do th. he work contnued over a perod o more than a centur and nvoved rt-ca mathematcan uch a Johanne egomontanu, coau Coperncu, and Egnazo ant. he mot dcut part o the work wa the new denton o the oar ear cce o  and  da. In the od Juan caendar, aed on a mpe our-ear cce, the average ength o the ear (. da) wa too ong n comparon to the tropca ear, aed on two conecutve trant o the Sun at the verna equnox (. da, preent gure). he reormer outned three rue to determne  a ear woud e exte or not. he ear whoe gure  dve  our are uua exte, a n the Juan caendar. I the gure  ao dve  1, the ear , however, not exte. ut  the gure  ao dve  , the ear return to eng exte. he reutng average ear o . da repreented an exceent approxmaton to the tropca ear. he derence (ca. eventeen econd) w requre a urther correcton on ater another  ear. nt the regoran reorm, the exceve ength o the average Juan ear had an mportant conequence: the date o the verna equnox progreve hted ackward. A a reut,  the end o the xteenth centur, the equnox e on 1 March. he caendar reormer, thereore, had to repoton the equnox to the correct date. In 1, Pope regor X decreed, wth the papa u Inter gravissimas, the uppreon o ten da. In Cathoc countre,  Octoer wa oowed  1 Octoer. Other countre adopted the new caendar evera ear or even a ew centure ater. A an mportant coroar, the equnox da o the new caendar dd not tart at noon, a n the atronomca prax, ut at mdnght. h act expan the ha-da derence etween the regoran and

  D f ly lisi slbs



the Juan count o the da, whch  t ued  atronomer n ong-term cacuaton. he o-caed “rt Pont o Are method” ree upon the average derence o . da etween the Juan and the regoran average ear. eore the reorm, the verna equnox hted ack at the rate o one da ever 1 ear (or 1 ear  reerrng to the preent gure o the tropca ear). A the da and tme o the verna equnox can e ound  examnng the caendar cae on the ack o the atroae, the dpacement o the rt pont o Are repreent a tme ndcator. he derence rom the ten da corrected  the caendar reorm, mutped  the ht rate, woud ndcate the o-caed “age o the ntrument.” In 1, th technque wa avoured  oert unther: “he epoch o contructon [o an atroae]  accurate ndcated  the da o the month o the verna equnox, when the Sun enter the rt pont o Are.” he opnon o uch an authortatve choar, who n 1 competed the rt extenve work on panpherc atroae, wa not mmune rom crtcm. In 1, enr Mche re-examned the method and ponted out two aw n th wa o datng an atroae  the poton o the rt pont o Are. Accordng to Mche: (1) the hour tem o ear atroae  the atronomca one (tme  meaured n equnocta hour rom noon); () the exte cce produce a mean ocaton o the equnox’ date o ±1 hour. ecaue o uch drawack, Mche dagreed wth the outcome aed on the method. ot on wa unther’ opnon “compete wrong,” and “the date o the verna pont doe not aow u to determne the arcaton ear,” ut the appcaton o the method to check a dated atroae demontrated that “ao n th cae, or whch we have at our dpoa a happ comnaton o normaton, the date o the verna pont doe not gve u a modcum o precon on the arcaton ear.” urther crtcm wa oered n 1  Emmanue Poue. hee warnng went ether unheeded or mundertood. On the one hand, n 1, the method wa apped to the undated atroae ncuded n the Computerized Checklist of Astrolabes  erek de Soa Prce and Sharon 5      8  9  0 

oert W.. unther, Early Science in Oxford, 1 vo. (Oxord: Carendon Pre, 1‒1); acme reprnt (London: awon o Pa Ma, 1‒1), : 1. enr Mche, Traité de l’Astrolabe (Par: auther-ar, 1); anatatc reprnt (Par: Lrare Aan reux, 1), 1‒11. enr Mche, Traité, 1. enr Mche, Traité, 1. enr Mche, Traité, 11. Emmanue Poue, “Peut-on dater e atroae médévaux?,” Revue d’Histoire des Sciences et de Leurs Applications  (1): 1‒ (‒).

2



, and rom tme to tme t ha reappeared n tude  choar wth a centc ackground. On the other hand, Mche’ Traité ha een nterpreted a a deence, ntead o a crtcm o the rt pont o Are method. hereore, t  worth notng agan the compete unreat o th technque. h unreat houd e apparent to centt much more than to htoran. In act,  a centt take the troue to examne the method careu, he or he w reaze that there are a numer o actor that make t proematc to ocate the rt pont o Are wthn the caendar cae:

• •

• •

ood know  an ear atroae wa made or a exte or another ear o the Juan cce. Moreover, wa uch a dtncton mportant to an atroae maker? h uncertant ead to an a priori error o aout ±1 hour; here  no guarantee that the tme tem adopted on the ack o the ear atroae  the atronomca one. ependng on the maker, the cutomer, oca tradton, and other actor, an atroae mght ue the aonan (count o hour rom unre), Itaan (count o hour rom unet), cv (count o hour rom mdnght), or an other tem. h uncertant produce an a priori error o aout ±1 hour; Intrument are not exempt rom error. In partcuar, the poton o the verna equnox  determned  the maet dvon o the caendar cae. or a cae dvded  one da, the a priori error amount, at et, to ha a dvon, that  ±1 hour; ood ha et notced the random error o determnng the exact ntant o the equnox. he error etmated  Caudu Ptoem n the Almagest on the at to dtnguh 1/1° on a vertca graduated rng remaned the ame up to the age o egomontanu. Ptoem’ optmtc etmate wa ± hour.

Even dcountng other uncertante—a, or exampe, the act that the maker mght have reed upon od atronomca tae or ntrument—the reut o the datng proce  ver vague. he tota error on the poton o the verna  

    4 

erad L’Etrange urner, “A Crtque o the e o the rt Pont o Are n atng Atroae,” n Sic Itur ad Astra: Studien zur Geschichte der Mathematik und Naturwissenschaften: Festschrift für den Arabisten Paul Kunitzsch zum 70. Geburtstag, ed. Meno okert and chard Lorch (Weaden: Otto arraowtz, ), ‒ (). ugemo ghn, “I grande atroao de Mueo d Stora dea Scenza d renze,” Annali dell’Istituto e Museo di Storia della Scienza di Firenze . (1): ‒ (‒). See urner, “A Crtque,” ‒1. .J. oomer (ed.), Ptolemy’s Almagest (ew ork: Sprnger-erag, 1), 1.

  D f ly lisi slbs

3

equnox wthn the caendar cae  the um o the nge error ted aove, up to ± hour. Once tranormed nto ear, the overa uncertant on an cacuated date coud e up to ± ear. A an exampe, the verna equnox o the oma-Koeker atroae a on March 11. (gure 1.). Accordng to Mche, the contructon date aocated wth the ntrument  the ear 1. he error , however, ± ear, and the atroae coud have een made at an tme etween 11 and 1, an extreme arge nterva. A etter etmate  ea otaned  conderng other eature o the ntrument. The Star Coordinates Method he econd wdepread method o datng ear atroae  aed on meaurng the tar coordnate on the atroae’ rete. he na procedure repreent the evouton o the other three method mentoned  Mche a etter uttute or the rt pont o Are technque. he centc phenomenon condered  no onger the apparent moton o the Sun aong the ecptc, ut rather the preceon o the equnoxe, whch ncreae tar ongtude at the

FGUR .2

5 

The rst point of Aries on the calendar scale of the TombaKoelliker astrolabe, detail.

uo oma, “Poea e cenza dee tee ne Medoevo ngee: un atroao dea ‘radzone Chaucer,’ ” FIMAntiquari: Arte viva: Pubblicazione della Federazione italiana mercanti d’arte  (1): ‒ (), cted the wrong date o 11 March.





contant rate o 1° ever  ear (preent gure). he derence etween the tar coordnate on the atroae and thoe o the preent k  an ndcator o the tme eaped etween the epoch o the ntrument and the preent. Accordng to Mche, the eaet wa o datng  the tar nvove ther ongtude; there , ndeed, drect proportonat etween the preceon dpacement and the tme nterva. In order to ncreae precon, t  preerae to conder on thoe ew tar coe to the ecptc, uch a eguu (α Leon) and Spca (α rgn). her ongtude can e read drect on the atroae ecptc rng and are aected  mnmum random error. I the dtance rom the ecptc  great, the tar ongtude mut e cacuated and the random error ncreae. he unreat o th method  made apparent  a mpe check. he ongtude o eguu, or Cor Leon, n the oma-Koeker atroae  1° Leo. At the epoch  eguu wa at ° ′ Leo. he preceon derence o 1° ′ correpond to a tme nterva o  ear. A a reut, th partcuar Chaucer-tpe atroae—havng the tpca “” rame o the rete—woud have een made n 1. egretta, the date  mpoe n ght o a coupe o post quem ndcator. he rt  the ear 1, when eore Chaucer wa orn. he econd e n the tar ponter or Ahaor, or Sru. he ponter  n the hape o a dog head, whch wear the o-caed “Lver Coar o Ee,” a mo o the oue o the Lancater (gure 1.). he rt documentar evdence o the coar  ound on the gravetone o Sr John Swnord, who ded n 11, and  ured n the Church o St. Andrew, n Spratton, orthamptonhre. he two ndcator ugget that the atroae coud not have een made eore the econd ha o the ourteenth centur. O coure, the tar ponter o eguu mght have een damaged over tme, whch coud expan the erroneou reut. In act,  the cacuaton  repeated or the other utae tar Mche ndcated, Acmek, or Spca, the reut  derent. In th cae the cacuaton gve the ear 1, whch make even e ene! o ome extent Mche acknowedged the pot o otanng gncant dcrepance, and extended the ana to the rght-acenon and  

  8 

Mche, Traité, 1‒1. unther dd not expound an method o datng atroae aed upon ongtude. e on cted the preceon eect on tar ongtude a a tme ndcator. See, or exampe, unther, The Astrolabes of the World, 1: 1. ennett and Strano, “he So-Caed ‘Chaucer Atroae,’ ” . he thrd exampe mentoned  Mche, Traité, 1, coe reca the cae o the omaKoeker atroae. he rench atroae o the Muée de a e Waonne, Lège, nv. no. , reveaed the date 1  ung eguu, 11  ung Spca, and wa neverthee attrutae to the ourteenth centur rom unther’ ttc pont o vew.

  D f ly lisi slbs

FGUR .3



Detail of the Tomba-Koelliker astrolabe pointer for Alhabor (Sirius) displaying the so-called “Collar of Esses”.

the medaton o the tar. he three ntrument on whch he teted the derent tpe o coordnate reveaed the ow reat o ongtude and rght-acenon. On n the cae o tar medaton, “notwthtandng the coarene o the procedure, the reut agree wth each other remarka, and aow one to determne, to wthn a ew ear, the age o thee three atroae.” In 1 the ver act that derent tar mght ndcate derent date npred oand orode to generae the tar coordnate method. A nge tar ponter ma e aected  a conderae random error, makng the datng proce unreae. I, however, the choar crutnze a the tar on the rete, the overa random error o the ponter woud e reduced. rom the tattca pont o vew, the random error o a arge data ampe tend to have a nu average (whch doe not mean that the tattca error o the tem  nu). he new method , thereore, conceptua mpe. It cont o cacuatng the date that et t wth the coordnate o each tar o the rete and then averagng a the date.

9  0   

Mche, Traité, 1‒1 and 1‒1, repectve. Mche, Traité, 1, 1, and n partcuar 1. oand K.E. orode, “A Mathematca Stem or Identng the Star o an Atroae and ndng t Age,” Astrolabica  (1): ‒ ().

6



he practca work  not eementar, even wth the ad o a computer. In order to mnmze the random error n tar poton, orode outned a pecc procedure, whoe prncpa tep can e ummarzed a oow: meaure the poton o the tar o the rete nde a Cartean grd; tranorm the meaurement nto equatora coordnate, rough modernze them, and dent the tar  reerrng to a modern cataogue; tranorm the meaurement nto ecptc coordnate; determne the preceon dpacement o each tar rom the preent; cacuate the date aocated wth the tar; average a the date; and determne the tattca error (tandard devaton). When preentng the reut otaned on a group o thrteen atroae, orode trange added another tep. e dcarded ome o the date cacuated or each ntrument on the gue that, “It  perme to dcard thoe date whch are more than one tandard devaton rom the mean.”  repeatng the cacuaton on the remanng date, he ound that the tattca error wa, n act, remarka reduced. orode dd not menton ether a manua on tattc rom whch he derved uch an addtona tep, or  the data eecton wa h own dea. e dd not reaze that, n the correct procedure, the expermenter  aowed to dcard on the nge datum aected  the arget apparent error eore handng a the other data. Severa ource o urther uncertant ma however occur n the od atroae. A orode ndcated, the reerence crce and pont o the rete ma e vague et; the ecptc rng ma contan dvon aected  random and tematc error; the tar ponter ma e rounded, unt or deormed; the rete te can e warped or deormed; na, an error o ±1° n the tar poton ead to a tme error o ± ear. In an cae, orode wa convnced that h twood method o meaurng Cartean coordnate and averagng a reatve arge numer o data woud get rd o uch error. Ao n the wort cae, the method coud at eat ndcate the ear o the data adopted  the atroae maker. orode woud have een ver urpred  how thorough h method wa crtced. In 1, E ekker argued that, ede howng mtake n     4  5   

orode, “A Mathematca Stem,” ‒. See ao orode, “A Stud o Atroae,” Journal of the British Astronomical Association 1.1 (1): ‒ (). orode, “A Mathematca Stem,” 1 t. . On th proem, ee E ekker, “O Atroae and ate and ead End,” Annals of Science  (1): 1‒1 (1‒1). orode, “A Mathematca Stem,” ; orode, “A Stud,” ‒. orode, “A Mathematca Stem,” ; orode, “A Stud,” .

  D f ly lisi slbs

7

tattc, a centc “method” never ndcate the contructon ear o an atroae or the ear t data were gathered. The Intermediate Approach to Star Data he generou donaton o the oma-Koeker atroae to the Mueo aeo o orence  t at prvate owner, Lug Koeker o Man, urnhed the occaon to perorm a mutaceted tud o th mportant arteact. he temptaton to date the ntrument  the centc method decred aove wa trong. he puzzng and contradctor premnar reut, however, uggeted that t wa et to aandon th tpe o ana. here wa, neverthee, no reaon not to gather and tud tar coordnate or another purpoe than to nd unconvncng and ncontent date o manuacture. Intead o checkng the atroae agant the k (medated  cacuaton to compenate or the preent undertandng o the ceeta phenomena, ke preceon), the new purpoe wa to compare the gathered tar data wth other htorca ource and, n partcuar, wth data rom derent atroae eongng to the ame tradton. In order to acheve uch a goa, t wa ndpenae to ketch a urveng procedure ver derent rom the centc one. Determining Star Coordinates Accordng to the ceerated motto that ever ntrument “peak t own anguage,” the rt ndpenae tep o the new approach to tar data wa, o coure, to peak the ame anguage. Cartean, equatora, or ecptc coordnate had a nu or margna nuence n how ear atroae were made. Meaurng the tar poton on the rete requre one to adopt the ame coordnate tem ued durng the Mdde Age. In addton to eng ntrnc to the atroae rete, th tem  at the a o evera tar tae. he tem ree on two coordnate: medaton and decnaton. he medaton  determned  the nterecton wth the ecptc o the great crce pang through the tar and the ceeta poe. It  gven n degree wthn the pecc gn o the zodac. he decnaton  determned  the anguar eparaton o the tar rom the ceeta equator meaured aong the aove-mentoned great crce. It  gven n degree to the north or to the outh o the ceeta equator.  

ekker, “O Atroae and ate,” 1‒1.





here  tte dout that, n tranerrng the data rom a tar t, the ntrument maker reerred to the graduated cae on the atroae. On the one hand, t  thereore o margna mportance or the modern choar to acheve great precon. On the other hand, whe meaurng, t woud e wrong to negect the ntrument’ own dvon. In act, the goa o gatherng data reae at no e than ±.1 mm, uggeted  orode,  a centc mrage whch run counter to the content o the ntrument. It  hard to magne that a medeva atroae maker coud have een o prece and that, n pacng the tar ponter, he wa ree rom an tematc error preent n the graduaton o the ecptc rng or n the tereographc projecton o the rete. he modern choar houd e ated wth meaurng coordnate up to an average precon o ±1° wth repect to the dvon o the ntrument. h degree o precon  comparae to that o the maker and to the nomna precon—the maet ange content mentoned, dregardng trancrpton mtake—o the majort o the medeva tar tae, whch ver edom ncude gure up to .°. In order to undertand what the mt o ±1° mpe, et u conder the oma-Koeker atroae. he overa radu o the ntrument  aout  mm. hereore, the mt mean the at to detect decnaton derence rom aout ±. mm at a decnaton o ° orth up to aout ±1 mm at a decnaton o ° South. A or the other coordnate, the mt requre the at to detect medaton derence rom aout ±. mm at a decnaton o ° orth up to aout ±1 mm at a decnaton o ° South. ua, due to the dtorton o the tereographc projecton, there are no tar paced on the rete outde o the range rom ° orth to ° South. Star Identication he econd tep o the new approach to the data cont, o coure, n dentng the tar on the rete. he centt conder the automaton o th procedure to e the eather n ther cap. everthee, t  preerae to eave the computer wtched o. h  not a orm o noh prde  the htoran. On the programmer, who  edom the ame a the choar, know what the otware  dong and, n partcuar, the weght t gve to each o the man varae on whch tar dentcaton depend. Paradoxca, on a vua procedure nvovng a moderate zed panphere, adjutae or preceon,  reae enough to perorm the dentcaton. he panphere doe not ncude ant tar, whch coud t an awkward comnaton o coordnate. 8  9 

See repectve orode, “A Mathematca Stem,” ; orode, “A Stud,” . Mton . eenz, Precession of the Equinoxes Historical Planisphere (Somerve, Maachuett: Learnng echnooge Inc., 1).

  D f ly lisi slbs



It on ncude rght tar (up to the ourth magntude), among whch were thoe ver ew tar eected  the atroae maker. It , o coure, mperatve to repeat and recheck the dentcaton a ew tme. Aout % o the repreented tar create no troue, ut the dentcaton o the remanng % requre, n addton to the panphere, the conutaton o htorca document. he mot mportant document to dent the tar n the Chaucer-tpe atroae  the tae aed on the oervaton made  John o London n Par n 1 wth an armar ntrument, whch wa reved n 1. In turn, John’ data nuenced the other tae ncuded n the treate on the atroae attruted to the Peudo-Meahaa. A Pau Kuntzch dcovered, th tar tae wa a ource or man ear Engh atroae. It et-known veron  preerved at the Camrdge nvert Lrar (ae 1.1). It  remarkae to note that, when apped to the oma-Koeker atroae, the dentcaton procedure revea the mot nteretng reut wth the hard-to-dent tar. A a rt exampe, notwthtandng ther hape, the two ma meta rdge connectng the ta and the head o the dragon, whch repreent the tropc o Caprcorn, to the ecptc rng, are not tar ponter, a wa ormer eeved (ee gure 1.1). here are no tar, ether gncant or compate wth the Peudo-Meahaa tar tae, n the area where the rdge end. 0 

 

 

Kuntzch’ tar t tpe V. See: Pau Kuntzch, Typen von Sternverzeichnissen in Astronomischen Handschriften des Zehnten bis Vierzehnten Jahrhunderts (Weaden: Otto arraowtz, 1), 1–. See ao: Owen ngerch, “Zoomorphc Atroae and the Introducton o Arac Star ame nto Europe,” n From Deferent to Equant: A Volume of Studies in the History of Science in the Ancient and Medieval Near East in Honor of E.S. Kennedy, ed. avd A. Kng and eorge A. Saa (ew ork, NY: he ew ork Academ o Scence, 1), –1 (); reprnted n ngerch, The Eye of Heaven: Ptolemy, Copernicus, Kepler (ew ork, NY: he Amercan Inttute o Phc, 1), 1–11 (). Camrdge, Camrdge nvert Lrar, . I. ., o. v. he page o the manucrpt  reproduced n unther, Chaucer and Messahalla on the Astrolabe (Oxord: nvert Pre, 1); acme reprnt (London: awon o Pa Ma, 1), unnumered pate etween pp. 1–1. rancrpton o the tar tae are n Water W. Skeat (ed.), A Treatise on the Astrolabe; Addressed to His Son Lowys by Geofrey Chaucer, A.D. 1391 (London: . rüner & Co., 1), xxxv–xxxx; reprnted a: eore Chaucer, A Treatise on the Astrolabe (1391) (Amterdam: Merdan Puhng Co., 1), xxxv–xxxx, whch ncude evera mtake, and n Kuntzch, Typen von Sternverzeichnissen, –. oma, “Poea e cenza,” , dcarded one o the two rdge, ut condered the other a pontng to δ Scorp.

6



TB . The Pseudo-Messahalla Star Table from Cambridge University Library, . Ii.3.3, fol. 70v No.

Name

Identication

 

mrach ate[n]katoz

 4 5   8 9

pate[n]katoz – vente[r] ceth en n ux[u] menkar – nar ceth agen – ron agon agetenar adearan – oc[u][u] v[e] cor taur[] ahaoh – hrc[u] [ve] hu[meru] ag[tator] rg – pe oron ageuze – hu[meru] dext[er] oro[n] ahaor – [n] ore can m[er]d[ona] razageuze – cap[u]d ge[m][n]o[rum] agomeza – n coo can Markep Egregez adran – n ro[n]te eon aart – equ v[e] c[n]gu[u] caaezed – cor eon arucaa – vra coruu duhe – d e[t] vra deneaezed – cauda eo[n] agora – n ce[n]tauro achmec – nhe[r]m e[n]nenaz – e [e]r[e]t[r] [n] the[n]o[n]e aramech – anceator

Mrach, β And aten Kato, χ Cet () aten Kato, ζ Cet ama, α Ar Mra, ο Cet () Menkar; α Cet Agen, α Per Zaurak, γ Er Adearan; α au

0    4 5   8 9 0    4 5   8

Mediation (°:′) Declination (°:′)

() 0:0 Ar 8:0 Ar

:0  :0 S

0:00 Ar :00 Ar 5:00 Ar :00 au 0:00 au :00 au 9:00 au

4:00 S :0  4:0 S :00  49:00  :00 S 4:0 

:00 em

45:00 

:00 em 5:00 em

0:00 S 8:00 

Sru; α CMa

:00 Cnc

5:00 S

Cator; α em

9:00 Cnc

:00 

Procon; α CM ure; ρ Pup ι ma (4) Aphard; α a (5) – () eguu; α Leo μ ma () ν a (8) α ma eneoa; β Leo Agora; δ Crv (0) Spca; α r enetnach; η Ma

:00 Cnc :00 Cnc 4:00 Cnc :00 Leo :00 Leo 0:00 Leo 0:00 Leo :00 r :00 r 5:00 r :00 r 0:00 L 9:00 L

:00  :0 S 45:00  :00 S 8:0 S 5:00  5:00  :00 S (9) :00  9:0  :0 S :00 S 5:00 

Arcturu; α oo

:00 L

4:00 

Capea; α Aur ge; β Or etegeue; α Or

6

  D f ly lisi slbs TB . The Pseudo-Messahalla Star Table from Cambridge University Library (cont.) No.

Name

Identication

9 0    4

aeca – n corona ad[r][a]ne aach ed caaacra – cor corp ahaue – cap[u]d dr[ac]on rahtaen – cap[u]d [erp]e[n]t wega – vutur cade[n] atar – vutur voa[n] den ar – n cgno addgege – cauda gan[a]e

emma; α Cr nuk; α Ser () ed, δ Oph Antare; α Sco a Ahague; α Oph Ettann; γ ra

:00 Sco :00 Sco :00 Sco :00 Sco :00 Sgr 5:00 Sgr

9:00  4:00  :00 S :00 S 5:00  5:00 

ega; α Lr Atar; α Aq β e () ene; α Cg ene a-dgege; α Cg () θ Cap (4) α Equ (5)

:00 Cap :00 Cap 9:00 Cap 9:00 Cap 0:00 Cap

8:00  :00  :0  4:00  4:00 

:00 Aqr 0:00 Aqr

:00 S :00 

Aderamn; α Cep En, ε Peg

0:00 Aqr :00 Aqr

59:00  :00 

ene Aged, δ Cap Skat, δ Aqr Scheat, β Peg Srrah – Apheratz, α And () ene Kato, β Cet (8)

4:00 Aqr

9:0 S

0:00 Aqr :00 Pc 8:00 Pc

9:00 S 4:00  5:00 

:00 Pc

0:00 S

5   8 9 40 4

edene – cauda capr den – nu[or] et oren[ta]or adran ene[er]az – m[u]da eq[u] pega deneaged – cauda caprc[orn] ceach – cru aeraz – n pegao () mentche – hu[meru] eq[u] aat denekatoz – cauda ceth

4 4 44 45 4 4 48

49

ceder

Schedr, α Ca

Mediation (°:′) Declination (°:′)

(9) 8:00 Pc

5:00 

Ns: (1) Wrong trancrpton or :°. See Skeat, A Treatise on the Astrolabe (ct. n. 1), xxxv; Kuntzch, Typen von Sternverzeichnissen (ct. n. ),  n. 1; ennett & Strano, “he So-Caed ‘Chaucer Atroae’” (ct. n. ), . () or Kuntzch, Typen von Sternverzeichnissen (ct. n. ),  n. , entre no.  and no.  are dupcate. he data ugget that the two entre repreent two coe tar, χ Cet and ζ Cet, oth caed aten Kato.

62 () () ()

() ()

() ()

(1) (11) (1)

(1) (1)

(1)

(1) (1) (1) (1)

 “n uxu”  Achernar (α Er), ut the tar coordnate pont eewhere. h tar cannot e θ Er, a uggeted  Kuntzch, Ibid., whoe decnaton n 1 wa ca. ° S. h tar cannot e μ Ma, a uggeted  Kuntzch, Ibid. It  tuated to the Wet, and not to the Eat o Aphard (α a) and eguu (α Leo). h tar, undented  Kuntzch, cannot eong n Leo. he decnaton pont to Aphard (α a). Apparent, th entr contan a trancrpton error. he name Aphard appear a the next entr, no. 1. h tar cannot e Aphard (α a), a armed  Kuntzch, Ibid. he coordnate pont to an “empt” pace. h tar cannot e θ Ma, a tated  Kuntzch, Ibid. It  mot ke μ Ma, a uggeted  ngerch, “Zoomorphc Atroae” (ct. n. ), 1, and ngerch, The Eye of Heaven (ct. n. ), . owever, the decnaton o uch a tar  ca. 1° to the orth. h tar, undented  Kuntzch, cannot eong n the conteaton Corvu, whch  paced aout a u zodaca gn to the Eat. he coordnate pont to ν a. uhe  α ma. Around 1 t decnaton wa ca. ° . A numer  mng n the decnaton o the tar tae. See ennett & Strano, “he So-Caed ‘Chaucer Atroae’” (ct. n. ), . he name Agora  gven to δ Crv and not to γ Crv, a or Kuntzch, Typen von Sternverzeichnissen (ct. n. ), . he peccaton “n centauro”  a cra mtake. h tar cannot e Akra (β Sco), a uggeted  Kuntzch, Ibid. he tar decnaton  1° , and not ca. ° S. h tar cannot e ε e, a uggeted  Kuntzch, Ibid., . he rghtet tar o the conteaton ephnu  β e, the poton o whch t etter wth the decnaton n the t. h  a econd entr or α Cg, wth ght vared coordnate. h tar cannot e ene Aged (δ Cap), a uggeted  Kuntzch, Ibid. In 1, the tar δ Cap had aout the ame decnaton than θ Cap, ut greater medaton. Moreover, ene Aged  correct ted at the entr no. . h tar, undented  Kuntzch, cannot eong n the conteaton ephnu, whch  ocated ca. 1° n medaton to the Wet. he rghtet tar n the area ndcated  the coordnate o the tae  α Equ. he tar name o entre no.  and no.  are nverted. ue to the nveron o entre no.  and , th tar  not a dupcate o β Peg, a ntead uggeted  Kuntzch, Ibid. ene Kato  tradtona attruted to β Cet, and not to ι Cet, a uggeted  Kuntzch, Ibid. Po a wrong trancrpton or :°.

More remarka, the ponter aeed “corvu” doe not ndcate an part o the conteaton Corvu. It pont at the one tar ν drae, aout ° n medaton to the wet o Corvu. o other rght tar can e ound n the area  

he wrong dentcaton  n oma, “Poea e cenza,” .

  D f ly lisi slbs

63

marked  the ponter. Smar, the ponter aeed “den” doe not ndcate the ma conteaton o ephnu. It rather pont at the reatve one tar α Equue, whch  aout ° n medaton to the eat o ephnu. Whe t hep to dcard the roe o the connecton etween the tropc o Caprcorn and the ecptc rng, t  noteworth that the Peudo-Meahaa tar tae ncude doue entre or oth Corvu (no. : “corvu,” and no. : “Agora,” the rghtet tar o Corvu) and “den” (no.  and no. 1, oth aeed “den”). he doue entre are cue that the oma-Koeker atroae e n the tradton o the Peudo-Meahaa tar tae. It  n th tae that the two tar ν drae and α Equue are maeed. he erroneou ae were tranerred rom the tae onto the ntrument. Data Comparison he ver centre o the ana deang wth tar coordnate rede n t thrd tep: the comparon etween derent atroae wthn the ame tradton. At the rt tage o deveopment o the new approach, the pan wa to compare the tar coordnate o the oma-Koeker atroae wth thoe o the other Chaucer-tpe atroae. It oon ecame apparent that to adopt th partcuar ntrument a a man ource o normaton wa meadng. he derent atroae have on a racton o tar n common and the comparon gave mted reut. Moreover, wh houd we agn peca vaue to th partcuar atroae to erve a a touchtone or god tandard or the other? he ntroducton o a reatve super partes term o comparon—the Peudo-Meahaa tar tae—dratca changed thng. or th purpoe, the manucrpt at the Camrdge nvert Lrar wa agan eected a repreentatve o the tar tae or no other peca reaon than t wdepread crcuaton n choar pucaton. On three tar that are preent n the group o x atroae eected or comparon are mng n the PeudoMeahaa tar tae. A or the other tar, the medaton and decnaton derence emergng rom each comparon ndcate how coe each atroae  to the data o the reerence ource. In partcuar, or each atroae t  poe to etah the percentage o tar coordnate derence wthn the random error o ±1° nvoved n the meaurement (ae 1.).

4  5 

he wrong dentcaton  agan n oma, “Poea e cenza,” . β Pere n the Panwck and the oma-Koeker atroae (perhap to e re-dented wth α Pere), κ Oron n the Panwck atroae, and α Pega n the rth Mueum undated atroae.

6



TB .2 Percentages of Star Coordinates Diferences within ±1° Atroae

Star

Medaton

ecnaton

Overa

oma-Koeker, G, orence “Chaucer”, B, London Panwck, H, Oxord Parne, N, Wahngton ndated, B, London unther, H, Oxord

4     9

% 5% 8% 8% % %

% % % 8% % %

% 5% 50% 8% % 8%

he derence revea that the oma-Koeker atroae, wth an overa % o coordnate wthn the mt o ±1°,  the one that depend mot on the data o the Peudo-Meahaa tar tae. It  oowed  the o-caed “Chaucer” atroae o 1 at the rth Mueum, wth %, and the Panwck atroae at the Mueum o the tor o Scence, Oxord, wth %. he other three atroae how a ooe reatonhp wth the tar tae’ data: the Parne at the Smthonan atona Mueum o Amercan tor, Wahngton, wth %, the undated rth Mueum atroae, wth %, and the unther atroae at the Mueum o the tor o Scence, Oxord, wth on 1% o derence wthn ±1°. he comparon eded other reut. A noptc tae, too arge to e puhed, revea other pecuarte o the x atroae. eevant tematc derence n the medaton o Apheratz (α Andromedae) how that at eat our o the x atroae (the “Chaucer” and the Parne have no uch tar) do not come drect rom the data o the Peudo-Meahaa tar tae a t appear n the manucrpt at the Camrdge nvert Lrar. Such atroae depend on another ource—a manucrpt or an ntrument—n whch the proem o the Camrdge manucrpt wth Apheratz wa not preent. In act, the Camrdge manucrpt, entr no. , report the name “aeraz—n peago [c]” or the tar Scheat (β Pega). he oowng entr, no. , “mentche—hu[meru] eq[u] aat,”  ntead the one or Apheratz. rom the ame noptc tae, t  qute apparent that, a or tear nomencature, dentcaton, and potonng, the x atroae eong to at  

or detaed data ee ennett and Strano, “he So-Caed ‘Chaucer Atroae’, ” 1‒1. egretta, due to a trancrpton mtake, a tae rom a to  report the medaton o α Coronae orea n the xth coumn a ° L ntead than 1° Sco.

  D f ly lisi slbs

6

eat two derent u-tradton. On the one hand, the oma-Koeker, the Panwck, the unther and the undated rth Mueum atroae contan the tar ν drae aeed a “Corvu,” ut do not have Agora, the true Corvu. he oma-Koeker and the Panwck ao have α Equue aeed a “den” or “den.” On the other hand, the “Chaucer” and the Parne have Agora or δ Corv, ut nether have the “ae Corvu” nor the “ae ophn.” na, the “Chaucer” atroae at the rth Mueum  extreme ueu n conrmng two trancrpton mtake n the data o the Camrdge manucrpt and n uggetng the poe correcton. h atroae aone among the x contan the two tar β Andromedae and α rae Major. A or the rt tar, the manucrpt’ entr no. 1, “mrach,” report the medaton ° ′ Are. It ha aread een uppoed that th odd datum coud e a mwrtng or ° Are and th  conrmed  the “Chaucer” atroae. he econd tar, α rae Major,  ted n the Camrdge manucrpt at entr no. , “duhe – d e[t] vra.” It decnaton , however, ° orth, a qute ow gure or a crcumpoar conteaton. In th cae, the atroae ha a decnaton o ° orth. A numer  mng n the manucrpt, whch perhap houd have read ° or ° orth. hee two remarkae entre conrm that the data o the “Chaucer” atroae come rom an uncorrupted ource other than the Camrdge manucrpt. The Catalan Astrolabe at the National Maritime Museum, Greenwich, London he potve reut expounded n the ormer paragraph encourage urther reearch. he gve upport to the pan o extendng the data ank and the conrontaton o ear atroae, n partcuar thoe that eong to the “Chaucer tradton.” Wthn th pan, the Cataan panpherc atroae conerved at the atona Martme Mueum o reenwch, London, Card Coecton, appear puzzng. avd A. Kng ha aread noted that, athough the month-name on the ack and ome o the pace-name on the pate are n the medeva daect o aenca, the ntrument dpa the ame rete te o the Chaucer-tpe atroae.   8 

Skeat, A Treatise on the Astrolabe, xxxv; Kuntzch, Typen von Sternverzeichnissen,  n. 1. .A. Kng, “he Earet Known European Atroae n the Lght o Other Ear Atroae,” n Kng, Astrolabes from Medieval Europe, /‒ (/1 and g. /1). Image o the atroae can e een at the atona Martme Mueum wete: http://coecton.rmg .co.uk/coecton/oject/11.htm (acceed March 1, 1).

66



ede the uperca mart and the comparae ze (1 mm n dameter), the Cataan ntrument der rom the other x atroae aread examned. In addton to the “” outne o the rame nde the ecptc rng, the rete dpa the coure o the equnoxe a an eaorate horzonta ar. he ar counter-change x tme and ncude two em-crcuar eement that ma reca the rec o a quatreo decoraton. he coure ar  mng n the other x ntrument examned, and ao n the rete depcted n the two et-known manucrpt o Chaucer’ Treatise on the Astrolabe. he rete o the Cataan atroae ao dpa a egment o the equator rng, whch  preent n the Parne atroae on. Intead, the rete doe not dpa an o the zoomorphc ponter that are a conpcuou charactertc o the Chaucer-tpe atroae. In addton, the ponter o the ntrument have ame hape uua aocated wth ear rench atroae. hee marte and derence rae the oowng queton: d the maker o the Cataan atroae get the tar data rom a manucrpt o the Peudo-Meahaa tar tae? he avaat o a coupe o good pcture o the ntrument made t poe to meaure the medaton and the decnaton o the nneteen tar o the rete wth the requred precon o ±1°. he rt ve coumn o ae 1. ncude: (1) the entr numer o the tar n the atroae; () the trancrpton o the tar’ name; () the tar’ dentcaton (t aer reek etter, and the nternatona three-etter arevaton or the conteaton); () the medaton (μ) o the tar n degree wthn each gn o the zodac; () the decnaton (δ) o the tar n degree north or outh o the equator. Apart rom peng varant, the name engraved on the tar ponter do not rae an partcuar proem. A the name ut two are preent n the PeudoMeahaa tar tae. he rt excepton, “akanu,” unmtaka pont to α Ophuch, whch n the tar tae, entr no. ,  named “ahaue – cap[u]d dr[ac]on.” he econd excepton, “Ahaz,”  proa a corrupton or contracton or Apheratz, ted n the tae, entr no. , a “aeraz – n peago [c]”. O coure, the peng varant and thee two peca cae woud need urther phoogca nvetgaton.

9 

Camrdge, nvert Lrar, . d.., o. 1v, and Oxord, odean Lrar, . awnon . 1, o. r.

67

  D f ly lisi slbs

Once the tar are compared to the correpondng entre o the PeudoMeahaa tar tae, addtona normaton emerge. he ve other coumn o ae 1. ncude: () () () ()

the entr numer o the tar n the tar tae; the medaton (μ) o the tar n degree wthn each gn o the zodac; the decnaton (δ) o the tar n degree north or outh o the equator; the derence n medaton (Δμ) cacuated n the orm: atroae’ e tar tae’ coordnate; (1) the derence n decnaton (Δδ) cacuated a aove. TB .3

The Catalan Astrolabe and the Pseudo-Messahalla Star Table

Catalan Astrolabe

P-M Star Table

Diferences

No.

Name

Star

μ

δ

No.

μ

δ

   4 5   8 9 0    4 5   8 9

atencatoc Adearan Aoch g Aaor Agomeza Adra[n] Aart Agura Achmeck ra Aramech Corona akanu egua Atar ana Ledene Ahaz

ζ Cet α au α Aur β Or α CMa α Cm ζ a α a δ Crv α r η Ma α oo α Cr α Oph α Lr α Aq α Cg θ Cap β Peg

 Ar 4 em  em 4 em 4 Cnc  Cnc 5 Leo  Leo 8 r 5 L 8 L 5 L  Sco 5 Sgr  Cap 5 Cap  Aqr  Aqr  Pc

4 S   45   S  S   8S  S S 5  9  9  4     40   S 4 

 9 0   5 8 9 5   8 9  5  9 40 4

0 Ar 9 au  em  em  Cnc  Cnc  Leo  Leo  r 0 L 9 L  L  Sco  Sgr  Cap  Cap 0 Cap  Aqr  Pc

4 S 4.5  45  0 S 5 S  S 8.5 S .5 S S 5  4  9  5  8   4   S 4 

Δμ

Δδ

˗ 8.0 + 5.0 + .0 + .0 + .0 0.0 ˗ .0 0.0 + .0 + 5.0 + 9.0 ˗ .0 + .0 + .0 0.0 ˗ .0 + .0 0.0 0.0

0.0 ˗ .5 0.0 ˗ .0 ˗ .0 ˗ .0 + .0 + 0.5 + 0.5 + .0 0.0 ˗ 5.0 0.0 ˗ .0 ˗ .0 0.0 ˗ .0 + .0 0.0

6



he normaton aocated wth entr no. 1 o the Cataan atroae “Ahaz” or Apheratz, orm evdence that the ntrument a n the PeudoMeahaa tar tae tradton. he coordnate o the tar are exact the ame a thoe o the tar tae. here , however, conuon among the tae entre no.  and no. . A aread noted n the prevou paragraph, the coordnate o entr no. , “aeraz – n peago [c],” do not pont to Apheratz, ut to Scheat. he coordnate o entr no. , “mentche – hu[meru] eq[u] aat,” are thoe pontng to Apheratz. he maker o the Cataan atroae dd not recognze the nveron o the two ne. e accepted entr no. , that , Apheratz wth Scheat’ coordnate. he mtake pped rom the tar tae onto the atroae. More pecca, t  apparent that the Cataan atroae eong to the ame u-tradton o the “Chaucer” and the Parne atroae. On the one hand, entr no.  o the ntrument  “Agura” or δ Corv. On the other hand, the atroae ha nether the “ae Corvu” nor the “ae ophn.” he ntrument contan two other nteretng entre. When compared to the tar tae, the outne two remarkae mtake o the Camrdge manucrpt. Entr no.  o the atroae, “Adra[n],” once compared wth entr no. 1 o the Peudo-Meahaa tar tae, revea a medaton derence o on –1° and a reevant decnaton dcrepanc o +1°. he uequent entr no.  o the atroae, “Aart,” agan revea a nu derence n medaton and another reevant dcrepanc n decnaton o +1.°. A coer ook at the manucrpt revea that entre no. 1 and no. 1 o the tar tae—repectve “adran – n ro[n]te eon” and “aart – equ v[e] c[n]gu[u]”—contan a gncant ur. Ade rom ther name, entr no. 1 pont to Aphard (α drae), and entr no. 1 pont to an empt pace. he ponter o the atroae, however, repectve ndcate ζ and α drae. he Camrdge manucrpt  corrupt and the atroae—whch receved t data rom another, uncorrupted, manucrpt or ntrument— ugget what woud have een the orgna content o the Peudo-Meahaa tar tae. It  ver ke that entr no. 1 o the tae, “adran,” houd have een ζ drae, wth tar coordnate ver coe to thoe o the atroae. he cre o the Camrdge manucrpt wrote the correct medaton, ° Leo, ut exchanged ° orth wth ° South, thereore producng the decnaton dcrepanc o +1°. A or entr no. 1, t houd have ndeed een Aphard, ut, agan, the cre made another trancrptona mtake. e correct wrote the medaton a 1° Leo, ut added “1” eore the orgna decnaton o .°, thereore producng another dcrepanc o +1°. Such an expanator potenta o the Cataan atroae make no urpre that the percentage o the derence n medaton and decnaton wthn

  D f ly lisi slbs

6

±1° are ver hgh. he percentage are % n medaton and % n decnaton (wthout conderng the two correcton or the tar tae entre no. 1 and no. 1). he overa percentage o % pace the ntrument etween the oma-Koeker and the “Chaucer” atroae. ow can a Cataan atroae e o coe reated to the John o London or Peudo-Meahaa tar tae, and rom whch manucrpt or ntrument dd the maker gathered the data? hee are, or the moment, the unanwered queton. Conclusions he percentage o coordnate derence wthn ±1° outne what can e caed “normatona dtance.” Such a “dtance”  an ndcator o how coe the reatonhp  etween an ntrument and the reerence data ource. h “normatona dtance”  not necear a dtance over tme. I the omaKoeker atroae  the coet to the data ource, th doe not mean that t  the odet o the even atroae tuded. he data o the atroae repreent a reatve athu adaptaton o thoe o the Peudo-Meahaa tar tae, a do thoe o the Cataan or the “Chaucer” atroae. On th ame a, an ntrument at a greater normatona dtance rom the data ource, uch a the unther atroae, te u that the coordnate o the PeudoMeahaa tar tae underwent evera modcaton eore eng meaured ( me) on the rete. Modcaton ma ncude the ntentona purpoe  the maker to update the coordnate or preceon, ut the ma ao depend on man other actor, among whch the at o the maker and the tor o the atroae. In partcuar, the rete o the unther atroae  ad damaged. In an cae, th new approach to the atroae’ data, and epeca to thoe o the ntrument that eong to the ame tradton, appear rutu. Whe a centc approach end—or “dead end,” a E ekker camed— wth an aeged ear o arcaton, the new approach rae more queton than t ove. rom whch manucrpt ource doe the data o the even atroae examned come rom? I uch a ource a nge one? What  the orgn o the uncertant etween Corvu and ν drae? What aout the other uncertant etween ephnu and α Equue? o the other our extent “” Engh atroae eong to the ame two u-tradton deneated  thee even? What  the reatonhp etween the Cataan atroae and the other Engh ntrument? What  the data ource or the other ear Engh atroae, uch a the “quatreo” one? hee and man other queton revea

7



that the new approach to the atroae data  not a dead end, ut a ong path o whch on the rt ew tep have een taken. Acknowledgements Part o the preent artce (Secton ,  and ), ha een preented at the XXX Symposium of the Scientic Instrument Commission, artu, Etona, ‒ Augut 1 and at the  Symposium, orence, Ita, 1‒1 Septemer 1. I woud ke to thank Karen acoa or her knd revon o the Engh text.

Epilogue

∵ Reconstruction of the Plate of Eclipses according to the Description by ʿAlī ibn ʿĪsā Flora Vafea

a f Laae a Taai, a-Aza Uivei, ai, Ep

I i aie Astrolabes as Eclipse Computers: Four Early Arabic Texts on Construction and Use of the Ṣafīḥa Kusūyya, Jae Ta pee, a e, w e eibi e pae f eipe a i e, ai  ʿAī ib ʿĪā’ eipi. Te  e e f e aip Iab, Tpkapı Saa Küüpaei, Ae  3 f. 3–3v ( T/) a e e e f ai, Dā a-Kb, Zakī , f. 2–22 ( Q/). Te  pa f ea e eibe e pae f eipe, a i e e pa i i epaie w  e i ie. A e e f e w aip ave e ifeee, e iiae f e ae eaie, a e paae wi f e w e w.  f e ave ia ii a eviai f e iiia e, wi   aw   ea pee w i ie wa a w i fie, if we eaie ea e epaae, b e biai f b e a ve ee pbe. avi e epeiee f ei fia e f e pae f eipe eibe b a-īūī a b aṭū, I aep ee  e i ie. Te  eea ep i  ee e w e, i e   e ap a b f e ie. weve, ee ae e ipa iffeee i ei vea k,  a: i.

I  T ee wi a bee ae,  a “ea a”, “kw i” a “eae ai  i”, wie e e i  Q i ee, fi  e pe.

  a Vafea, “A-īūī: The Plate of the Eclipses”, Suhayl  (2), 2–3; aṭū’ e i  p. 32.

© koninklijke brill nv, leiden, �9 | doi:0.63/9789004387867_08

 ii.

iii.



 T ie  bee ape  e e f e ie, wie  Q   bee ape; e  ape f  T a bee ie i  Q. A ape  a  ae epaae a a ifee pi i e w aip. Tee ae evea epeae pei e i b aip, e.. “” i  T iea f e e “”, i.e. “ie”, i  Q; “” i  Q iea f e e “”, i.e. “ be eipe” i  T; e e “ّ ” (b) i awa e i  T, a “” (pefae) i e i  Q, weve, eie e fe a eie e ae e i e apppiae e.

I e ie e a I pee bew, I ie  ipae a ifai ie i b aip, i a few ae ai i e wi. We ee wee ifeee i e e, I eee e pae a appae bee e i f a wki e. I ave ie ape  a  i e  avi e pbe f e ifee ivii f e ape i e w aip, a  pee e e ie f ape  a a i ae. A e e “”, wi appea i  Q, ep  e a eipe, I pefee  e e e “” (a eipe  eipe) f  T, i e  keep fi, ie e e “” ( be eipe) i  e ee. A-īūī a e e e f e p “” iea f “” i e eipi f e pae f eipe. I a ae e iiia e f b aip i eie i e appaa. Te ppe f ei e e f e w aip wa   a ie ai  e eipi peee i e  pa f e eaie; i ie  be abe  peae ai  e ii ive i e e pa. Te eae a aa ake a p f ea e f e e – a  a wki e f e evie. ie 3 a   be aae  b ie f a ia piee f i fa-ba  pape-ba  f e pae. ie 2  be  pefae i f e e pa; e e a be aiae i a pai apae ee i e  be  e a i pa i e rete. ie  a a be aiae a e a e ib. Te a bak  peeae ee ee pa  ei ee, ai f e bakie f e ib, e e pae a a e e e rete. Te pi f e bak a pke  a eai i,  a e ee pae ae e ee. Te i f e aiae i  eibe i e e. Afe e i, e eae a 2  Te e “” a ee a e  i eipe appea  wie i  Q. 3  Vafea, “A-īūī: The Plate of the Eclipses”, pp. 3, 33, 3–32.



logu

pef a e e eibe i e e pa f e eaie a veif e fiai f e ie,  e ee f e ee Aabi e a i aai i Ei. Ti   eve a a fai f a fa iia eii f e eaie f ʿAī ib ʿĪā  e pae f eipe, apaie b a pai bewee e epi ie eibe b aṭū a a-īūī, i e a e evi f i ie be eeae a eabie. Arabic Text .ّ ‫�ل‬ ّُ  � � �  ‫ ف‬ ‫س‬   ‫ة‬

4  ّ  

.ّ   .  ّ  

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  .ّ � ‫ى‬      ‫ء‬  ، ‫ء‬ ‫ت‬ّ  ‫ظ‬    ، ٙ   ‫ر‬‫أ‬  ‫ ف‬ّ �   ‫ذ‬  ّ   ّ ‫ ث‬.   ،‫ة‬�   ،�      ،‫آ‬ � ّ .� 

ّ ‫؛ ث‬ٙ ٙɤ   7 6،  ‫ذ‬   5‫ئ‬ .4� �

 … ‫ة‬ : ‫؛‬-- : ‫ي‬ … ّ   : ‫؛‬ � � �  :  ّ  : ‫ّ؛‬  :  ‫شر‬  : ‫؛‬ّ  : ‫ي‬ ‫أ‬ ‫ء‬ : ‫؛‬‫ئ‬ : ‫ء‬  : ‫ء؛‬ :  : ‫؛‬ :  : ‫؛‬ّ‫ط‬ :  : ‫؛‬ : ‫ ف‬: ‫ ؛‬ � : --: ‫؛‬� : ‫ء‬ : ‫؛‬‫ئ‬ : � : ‫؛‬ : --: ‫؛‬ :

           

           2  3        

|3/| ،3/| |2/





ّ  ّ  ‫؛‬  ‫ خ‬ ،� ‫سر‬ٙ   ، �‫أ‬ 8:ٙ  ٙ   � �

5،    � ، 4   �    

  ،ٙ   ‫ى‬   ّ ‫ ث‬.� ‫ة‬� ‫ى‬ ،‫ظ‬ ‫ة‬� ّ  �    

 ،�  ‫ ف‬ ّ  ّ  6،       ،�  7.  ،�  ‫ى‬ �  ‫ط‬ 

‫م‬ �  8‫ ف‬

 ،‫ط‬�   ،  ‫ ف‬� ، �  �

 4�   ،َُ �   .» �   ‫ك‬ «  

.�  6� ،�  ّ� ‫ي‬ 5 �

 ><  � ،ّ   ّ 8‫ي‬  7‫ي‬ �  � �

‫ى‬ ،�  ‫ى‬ ،4 .ّ �   ،» � ‫ك‬ «  4>< ‫د‬

ٙ   : ‫؛‬ٙ  ٙ   � � ّ ‫ ث‬.ٙ  ٙɤ :  � : ‫؛‬�‫أ‬ : � : ‫؛‬  :  : ‫؛‬ : ّ  ّ  : ‫ ّ؛‬  : --: ‫؛‬ : ٙ ٙ ٙ ٙ  : ‫؛‬١٢ :   … � : ‫؛‬-- : -- : ‫؛‬ …    : .  ، �  ‫ى‬ : ‫؛‬-- : ‫ ف‬ : ‫؛‬-- : � : ‫؛‬-- :  : ‫؛‬-- :  : ‫؛‬ : � : ‫؛‬  ،‫ط‬� :  : ‫؛‬: �   : ‫؛‬‫ذ‬  ّ  :  : ‫؛‬ :  ‫ذ‬ ،� : ‫؛‬� ،‫ء‬� : ‫ي‬ : ‫؛‬‫ي‬ �  � � : ‫ي‬ : ‫؛‬‫ي‬ : ّ   ّ : ‫؛‬  : ‫د‬   ‫ذ‬ : ‫؛‬‫د‬   ‫ذ‬ :  : ‫؛‬ :

     2  2  22  23  2  2  2  2  2  2  3  3  32  33  3  3  3  3  3  3    

|3/|



logu

  ، ‫ذ‬  ‫ف‬ ‫؛‬� � ‫و‬   ،‫ر‬‫أ‬ 4   ّ

. / � ‫و‬

|2 /|

‫ك‬ « 45 ‫ي‬ ،44 ‫ك‬  ،4  ‫ ف‬،� ‫ف‬

‫ي‬ � ‫ظ‬�  ،� 48 47 �  ‫ ف‬ 46 .» 

 ّ    ، � 5‫ط‬ ‫ذ‬  ّ   ‫ »؛‬� 4 « 

،5 ‫ى‬ ‫ته‬ ، ‫ك‬ �  ّ  5،�  ‫ك‬ 5‫ط‬ ‫ذ‬ �  ‫س‬� ، 56ِ َ ُ ّ   .� 55    ، ّ  ّ  54ّ 

،� ‫�ش‬ ّ     ، ‫ ف‬، � ‫ف‬ 57 .ّ  ‫ء‬  � 58 .   � ‫�ش‬  ،  ‫أ‬ � ‫ف‬ ،   ‫ف‬

   6َُ ، 5‫شر‬    ،�  ‫آ‬ � ‫ف‬

6    ‫د‬   ‫أ‬  6‫ف‬ .    ،� 

.�  ‫آ‬ � ‫ ف‬ 6 ،‫�ل‬  � �

  ّ  : ‫؛‬  ّ :    : ‫؛‬  ‫ف‬: � : ‫؛‬ :   : ‫؛‬ ‫ي‬ :  � ‫ك‬   � : ‫؛‬‫ي‬  :  : ‫؛‬ :   : ‫؛‬ :   : ‫؛‬  :  : ‫؛‬‫ط‬ :  : ‫؛‬‫ط‬ : � : ‫؛‬�  : �  ‫ؤ‬ � ‫ك‬  : ‫؛‬ ‫ى‬ ‫ته‬ ، ‫ك‬ : ّ  : ‫؛‬ :   : ‫؛‬  :    : ‫؛‬ ّ  : .ّ  ‫ء‬  � �  ‫س‬� : ‫؛‬--: .-- : ‫؛‬.   … � ‫ف‬ : ‫شر‬  : ‫؛‬١٢ :  : ‫؛‬ : ‫ف‬    : ‫؛‬‫ ف‬:  : ‫؛‬ :   : ‫؛‬ :

 2  3                  2  3                  2  3

|3/|





َُ ‫ط‬ 65‫ي‬ 64،‫ط‬‫أ‬    ّ  � �   ‫ف‬

67.ّ  ‫ء‬  ،        ،   �  66‫ض‬  

، ‫أ‬ ،‫ط‬‫أ‬  ‫ ف‬7 ‫ا‬ ،6     68 ‫ف‬

 ،�  ‫ ف‬  ‫ى‬    7 .ّ‫�ظ‬ 7    ‫ف‬ 7.ّ  ‫ء‬     74 .   ‫ ف‬:‫أ‬ �

، � ّ  ، �    ،ً  ‫ط‬‫أ‬ ‫ؤ‬ ‫ا‬ 

 ، ‫ء‬  ّ  ،  �  .� ‫ر‬‫أ‬  

   ّ �  75‫ظ‬ ّ ‫ث‬/.‫أ‬ � ‫ى‬ ‫أ‬ �  �  .ّ  ‫ء‬  � ‫ذ‬     ، ‫ء‬  ،‫ء‬‫أ‬ ‫ ب‬ � ّ ‫ز‬  ،ّ    �  ‫ض‬   ‫ ف‬:� � 76 .‫صر‬   ،   ٙ ٙ ٙ �

 78ّ �   77،     ،  

 ّ   ّ  ،�  8� ‫ ب‬ .7  �  ‫غ‬   8.   ‫ى‬  ‫ غ‬،  �   � 

ّ ‫�ظ‬  ‫ذ‬ ‫أ‬     ‫؛‬� 8ّ ،�     ‫ط‬‫أ‬   : ‫؛‬-- : ‫ي‬ : ‫؛‬‫ي‬ : ‫ض‬ : ‫؛‬--: :‫ض‬ .ّ  ‫ء‬  …   : ‫؛‬ :  : ‫؛‬ : ٢×  :  : ‫؛‬--: ‫س‬ : ‫؛‬ :  : ‫؛‬ : ّ  ‫ء‬  …  ‫ى‬ : ‫؛‬� :  ‫ ف‬  ‫أ‬ � ‫ظ‬ : :‫ظ‬ .‫صر‬   … � �: ‫؛‬�  ‫ ف‬ :       ،   : ‫؛‬-- : ّ …  : ‫؛‬�   :  … ‫ غ‬: ‫؛‬   : � ‫ ب‬: ‫؛‬� : . …  : ‫؛‬ ‫ غ‬  �  ّ   :  …  : ‫ّ؛‬ ،ّ‫�ظ‬    :

                 2  3                  2

|3/|



logu

   8،� �  ‫ط‬  ‫ط‬  ّ ‫�ظ‬  ‫ ُس‬ >< ،ّ‫�ظ‬ 

،�  >‫ ٙɤ<   ‫ ف‬ ‫ �ل‬58 ‫حج‬ ‫س‬    57، ّ ‫أ‬   � 56  6،ّ ‫أ‬  ‫أ‬     � 5   . � 

  ‫؛‬ � 6     ،‫آ‬    ّ  ‫ة‬ ‫ى‬ ‫ظ‬

6.� ّ  ،  �    

64. �  � �    6  ‫ ف‬:� �

 � 66 /،   .‫�ش‬ 65      ّ  

ٙ ٙ ٙ   ، �     67 ّ   ّ  ،‫�ش‬ ّ   ‫ض‬  ، ٙ  68  .ّ  ‫ء‬  ،  ،�  �     ،

 : ‫؛‬ :  : ‫ء؛‬ :   : ‫؛‬ :  : ‫؛‬�    : ٙ  : ‫؛‬   ‫ ف‬ :  : ‫؛‬-- :    : ‫؛‬ّ    :   : ‫؛‬   :  : ‫؛‬ :  ‫حج‬ ‫س‬   : ‫؛‬ ‫حج‬  ‫س‬   :  : ‫؛‬ : ّ ‫أ‬  : ‫؛‬ :  : ‫؛‬-- : � ّ  : ‫؛‬-- :     :� � : ‫؛‬ ‫ ف‬ :  �  � : ‫؛‬�  :  …  : ‫؛‬   :     ،   : ‫؛‬  : :   ّ   ّ  : ‫؛‬ ّ  :   …  ٙ : ‫ى ؛‬   .  ١٢ :

       2  3                  2  3          

|3/|

1

logu

 .�  ّ  7‫ى ع‬    ،�  6  �  7.  ‫؛‬�    �  ‫ض‬       �

/      ،�       ‫) ف‬(:� � 7.ّ     ‫) ف‬(

7‫؛‬  ‫د‬  � � ،   �  ّ 

 ّ  75،ّ    ٙ ٙ ٙ  ‫إ‬/74‫؛‬  �  ّ  ،  ٙ ٙ ٙ     76.� ّ  ، �

‫ي‬ � � 78 77،     ،   

8 . 8‫شر‬   �  7 ،‫آ‬ � ‫ى‬ ّ   ّ� ّ  ،� 84 .‫أ‬ 8  � ‫ط‬� 8 ،  �  ّ ‫ ث‬.86‫ء‬  ّ  ‫ط‬ �   85�   ‫ك‬  ‫ط‬

  . 87 �      >‫ك‬<   ّ  ،�

،� 8     ‫ظ‬  ،�   88      �  : ‫؛‬�  ّ ‫ ث‬: ‫ى ع‬    : ‫؛‬‫ ع‬   :   …  : ‫؛‬‫ض‬    � :  ،�       ‫ ف‬:� � : ‫؛‬ّ     ‫ ف‬ :      ،  ‫ ف‬‫د‬  � �   � ‫ ف‬‫ظ‬ : ‫؛‬ …  :     � �   ‫ظ‬ ،‫�ل‬    ،  .‫ذ‬  …   : ‫؛‬-- : . ٙ ٙ ٙ   ّ   ‫إ‬ : ‫ّ؛‬  ١٢   : .� … �  ّ  : ‫؛‬ :      ،    :� � : ‫؛‬ّ  :  : ‫؛‬ : ‫ي‬ ،ّ   ّ� : ‫؛‬ ،‫آ‬ � ‫ى‬  � : ‫شر‬  : ‫؛‬١٢ :  : ‫؛‬‫ط‬  :  : ‫؛‬ :  : ‫ة؛‬ :  : ‫؛‬ : � ‫ك‬� : ‫؛‬�   ‫ك‬ :     ّ  : ‫ء؛‬  ّ  :  : ‫؛‬-- : �     : ‫؛‬   :    : ‫؛‬  :

       2  3                  2  3            

|22/| |3/|





‫ك‬   �   ‫إ‬ .  ‫؛‬      

     4،ّ‫ط‬ ‫ء‬   ‫إ‬ ‫؛‬ّ   �  ّ  ،ّ   ،�  6    ،ّ   ‫إ‬ .    ،�  5

7.‫�ل‬ ‫ ف‬�  

،�     ‫ك‬ ‫ط‬  ‫ظ‬ ،‫أ‬    8

.  ‫أ‬     ، 

 .ّ  ‫ء‬  ،   ‫ غ‬ ، ‫�ل‬ ّ     

. �    ،�  ‫ى‬/ 

 .‫ى‬ ّ   ، ‫س‬   ‫ى‬  ّ  � � � ‫ر‬ ّ 

      : ‫؛‬    :  ‫إ‬ .  : ‫؛‬  :  : ‫؛‬-- :  : ‫؛‬ : ّ‫ط‬ : ‫؛‬ّ‫ط‬ :       : ‫؛‬    :     ،ّ   ‫إ‬ .    : ‫ ؛‬  ‫إ‬ : ‫�ل‬ ‫ ف‬�   : ‫؛‬ ‫ ف‬�  : -- : ‫؛‬ ‫ ف‬ : : -- : ‫؛‬ : -- : : …  ‫ى‬ ّ  …   : ‫؛‬ ّ  ‫نته‬ :

     2  3              2  2

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logu

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English Translation Treatise of ʿAlī ibn ʿĪsā al-Ḥāsib on the knowledge of how to use the lunar plate and the receptacle for the eclipses. Ma G ave e  i a be i. I e ae f G, e Meif, e paiae—  i i G. ʿAī ib ʿĪā—a G ave e  i—ai, afe paii G a ei i wi wa i e  i, a pae f i Ppe a f i fai: A f e kwee f i pae a w  wk wi i pe, kw a i ib (e ) i ivie i f pa, a i [ppe] af i ivie i 2 pa, wi ep  we ei-a. [A f] e beii f [bei] e ivii  i, we  ake i i  a a  pe i befe  fae, e beii [f bei] f e f i qaa wi be   i ie aei  e pei. [Ti qaa] i ivie i  pa. e, [ai] f e ie a ee f e pei  e ef qaa, e 2 a ae pee, bei e be [f a] i wi e  i viibe. A f e e af [f e pae], i i f e ivii f e  a fai f e  a wi e  e, ie e  i [f e ]. I beii i f e qaa a i   ef, wee “, ” ae wie; e,  e e pae “, ”: e “” (alif ) ep  e  a “”  a fai f a  -i [fai] i ve eve f a -, i e ivii f i qaa i  a ei fai ae pee, a 2 pee , wi ae e  f e i a ei fai.  Ti wi be e ie a wi e  e, f e  i i appea, p  e i f e f . Sbeqe afe a, [ ie] p  e pei f 2 [], a wi [e ] e i aie afe avi eee e 2  f e i a i fai, i [e ivii]  e ib f e  ae pee;   wi e pae f Jae Ta’ aie, e aii f e ake f ai, ae p i aa bake. 2  Te ieae f e ie f e  ei i ake a / f a  f ea a, wi ep  2 /2 a. Te be / f a   e  ivii i a e i ape  bew. Sai f / a ai / f a  pe a, we bai e aiei pei /,  /, 2 /, 3 3/,  2/,  /, ,  /,  /,  /,  3/,  2/,  /, 2 e   e f wi ae wie  e we ef qaa f e ib, a ive e ie f  ei i eaa  afe e. Te e  e f e ae aiei pei, f 2 /  2, ae wie  e we i qaa f e ib a ep  e ie f  ei i ai, i eaa  afe e. I e , I ave wie e iee be f e  a  e ia f e fai, ie i wa i eibe i e e.





e [ib] i e i wi  e pae f e rete [iae] bew e rete. Uea i! ape  e kwee f e rete a i ivii. Te rete i a aie-ike pae, wi a e i e f i ave (e 2). I ae a e pe, a “ie iiai e i f e ” i wie  i. T i e ifai i peee, we e rete i ae  e pae wi e ive a bak aki  i, wi i bew e rete.  e pae beea e rete, ee ae w ie [pae wi] be ive, (e 3) a e ppe f ee ie i e ie f e a i

Fgur 1

The limb

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logu

iae ea e pei. e  i,  e ef ie, wa e ie f e ef qaa, i e bei f e  a wi e  ie a a, a  e qaa afe i, e bei f e  a wi e  ie a i.  e pefae ie f e rete i e ie f falak al-jawzahar (e 2) a  i i wie “falak al-jawzahar”.  i pefae af, ee i a e ie f e ; i i a pie  wi “ie f e ” i ake.  e ie a pi e rete i w ave a bei f e ie wi iee e ie f e i f e , e  e ee f e rete a  falak al-jawzahar, a eiae a i eei, wee e ie i pee,  [i ie] i wie “ie f e ”. Uea a a

Fgur 

The rete

3  I  T e ie i eie a “e pee f e S”, wie i  Q a “falak al-jawzahar”. Te e i e ae, ie falak al-jawzahar  be  e rete, a eie bew, e.. i ape  (ppii ) a  (ppii  i e Appeie A a  f e aie f J. Ta).

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

a bee eibe    a e e f e pae i ae ea f , G wii!  e rete,  i i, ee ae a ivii ai  e be f a i a a ,  e ie 3 a, a  e e ie 2 a, beae e a  i awa ike a.4  e e ie f e pae, ee i a ie ivie i weve pa (e ), f wi bee kw wa i eipe f e , we ee i a a eipe.  e i ie f i ie ee i a bei epeei e iae bewee e w e a e M i a eipe. Ti i wa i  e e ie f e pae.  e bak f i a pae, ee i a aiae iia  e aiae f a aabe (e ).  i, ee ae ie f wi bee kw wa a pae f e a a wa i ef f i, we I eae ai  wa I wi eibe   bew, G wii!  e f i qaa ee ae e ivii f e aie, iia  wa i  e bak f e aabe f aki e aie, a  e ppie qaa i e ivii f e aw. Ti i a  ee  kw f wa i  i pae. Uea i a eae ai, G wii! i ape: T kw w  ake e aie5 I i ake ea a wi e aabe:  pe e pae b  i [a], a  ve e aiae wi  ef [a], a  a wi  ef e ppie  e . Y aie  we e aiae i e eee f aie  a e i f e  pae f e ppe e  e we e. Te,  k a e pie ip f e aiae,  wi eee i fa a e eee f aie; i wi be e aie f a ie, G wii! Se ape: T kw e eape ie f e ai i eqa , a ee ae e eaa [], b wi e ai i f weve , a e i-ie , bei e  e. If  wa a,   kw e [’] aie a ia f  a. P e pie ip f e aiae  e ai aie epi  e ia f  a. Le i aiae fae ie e ,6 i  ee e aw f e aiae ai  e b f e aiae, wi bei iie i a iei. We  kw wee e aw fa  e aiae,  e . Y bei   e ai f e ppe ii vae, f

  Te paae “ e rete … ike a.” appea  i  Q   Te fi ape i  ie i  Q.   “ie e ” i.: e e f 

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logu

Fgur 

The plate: Lunar phases side

wi  ave ake e aw, a wi a bee e f ivii e aw wi ie a  e b f e aiae avee (e ),7 a   Te i f e ie f e eqa ie  e aiae i eibe i eai b a-Ṣūfī, i ape X. f i ea eaie  e aabe ( BNF, Pai aabe , f. 23v–2), ee a Vafea, Le aié ’a-Ṣūfī  ’aabe (P.D. Di, Uivei Pai —Dei Die, 2), App. , 2–3, a b a-īūī, i Istīʿāb al-wujūh al-mumkina fī ṣanʿat al-aṣṭurlāb ( Leie, . 23b, f.2v–3), ee a-Ḥaī, Iīʿāb a-wjū a-kia fī ṣaʿa a-aṣṭāb, aafaū Mḥaa Ib Aḥa Abū Raḥā a-īūī,  e. (Maa: Majaʿ a-ḥū a-Iāia, 22), –.  a Ei aai f a-Ṣūfī e apaie b epaa e a fe e ei e  ie 



Fgur 



The plate: Lunar eclipses side

bewee e e bei f  ae [wie] wi e abjad ea [a ep  e be] , 2, 3, , , .8 Te pii wee e aw fa  i aiae [iiae] e eape ie f aie i . e aiae, ee Jea Ríez-Aiba, “A Teaie  e i f Aabe b Jab be Abi Abaa Iaa a- (aea, 3): Eii, Taai a ea” i Journal for the History of Astronomy (), 2–2; ee –. Te pee f eai e ie i eibe b D. A. Ki i Davi A. Ki, I S wi e eave: Sie i Aia Tiekeepi a Ieai i Meieva Iai iviizai, 2 v., V. 2: Ie f Ma aai (Leie: i, 2), 2:2.   Tee abjad ea  be eiae wi e Geek ea α, β, γ, δ, ε, ς.

9

logu

Fgur 

The hour markings on three alidades from astrolabes (Inv. no. 53637, 33767, 42730) from the Museum of the History of Science in Oxford Courtsy o th usum o th Hstory o cnc n Oxord

We e eaee i befe ia,  e ie wi ae  e aiae  e ie wi i ake wi e abjad ea [a ep  e be] , 2, 3, , , ; a we i i afe ia,  e ie  e aiae f e ie  wi e be f  ae iiae b e abjad ea [a ep  e be] , , , , , 2.  Ti ape: T kw e aw (ae). If e aie i e a °, k a e pie ip f e aiae a wi iiai wii e aw ae fa, a ivie  b a iiai— a e bivii f e aw-; e e wi be e aw a e e  wa. If e aie i °, e aw wi be ea 2 [ii]. If e aie i eae a °, e aw wi be e iiai  wi e pie ip f e aiae fa, wi  ee f ivii. Kw a, G wii!    Tee abjad ea  be eiae wi e Geek ea ζ, η, θ, ι, ια, ιβ.   Te pee eibe i aip T i ieai, wie a i aip Q w a e aw ep  e ae f e ae h f aie, eae i ii. If h=°, e h=2 ii; if h>°, e h