Cleomedes' Lectures on Astronomy: A Translation of The Heavens 9780520928510

Table of contents :
Contents
Preface
Abbreviations
Introduction
Book One of Cleomedes'. The Heavens
APPENDIX: POSIDONIUS ON PHYSICS AND ASTRONOMIE
GLOSSARY OF SELECTED TERMS
BIBLIOGRAPHY
PASSAGES FROM COLLECTIONS IN COLLECTIONS OF TEXTS
GENERAL INDEX
INDEX LOCORUM

Citation preview

Cleonzedes' Lectuves on Astvonomy

I . ~iicwiiiierto .isticlit/: The Hixtni-ic.ill F::o/iltioi! iLf thc H Peter Green

IT. IJ~Neirim~ ill the E ~ s t thr : li/tt,1artioi2of'Giwk ~ i i dl o i / - G ~ w kCi~ilizictioit.~fi(ii~~ edited h)- Anii.lie Kuhrt a n d Susan Syria to Ccirtiiil .-lsiii irjrr .ili~~~ii~di'i; Shent in-\Zhite 111. The, Qi1estin17~f"Ei1crtii~ixiie ": Stiiilizs 111 Lntt'r Giwk Phih~~~ljJ~!~. edited h!J. \I. Dillon and -\. .-\. T m n ~ II: .4trtiCgouosthr Onl'-@'ei/ ciiiil thi. C'ri~irtioiioj-the Hi'N~'r21xt1i. S J ~ I h~!- PRiehard , .\. Billou-s \: Ai History qfllili.rtioirin, h!- R. \Ialcolrn Errington. translated by Catherine E,rrinpn 11. :ittic Lettc~i-C'i~tti'i:~ of229 t o ,S6 B . ( - . . h! Stephen 1: 7i.a~)ofthi, .411i.ii>iltL1 bihz'>h! Lucimo Canfora \X, T h L izni.cbtd Lil~rnry: l L i~~ldtjr 1711. H t - l l e ~ ~PBi/osopi!i, i~t~i ?f .\liiiti. by Jui ia .innas IS. Hi~lltwisticHi,rtol:i,nmi C'i~ltiri~. edited h!- Peter Grcen S . Thr Bt~xtq f the L - l ~ p i r n ~Thr. t t ~ ~Kn!i$i~ition : ?ftiv, Epic. I-lcio in Rook Oire ALrgo~iautica, by J a ~ n rJ. s Clauss ~j'~ip~Noiri~rs' XI, Z+ccs ofPo:xr: .-Ile.nv~de~~~i I ~ J T , I{e/lc/ ~ P l f t ~ l / i ~ ~l'olitic..~, / i ~ t ~1))~ - i n d r e w Stev art 111. 1?1i[7gta.i m d 1~l~i~l~;gics: S~~lf-~1~;fii~tt10it I I I tht' H ~ l l ~ ~ ~ l[ i7 s1 itUi cdited ~ ~ h>- 11; Rulloch. E. S. Grucn, -1. -4. Lonp, and 1.S t e m r t SIII. ficivr S/liiwrkl~trili/to 5rridi.s: Ad \i>zAdpp~.otich to thc St,lei~t.idEiupire. h! Susan Shenx-in-IThite and .hnmi:lie Kuhrt SA: Rt,gioirceli.i?niciril Cbiri~gi,iu /hi, EL.OIIOJI!J, $liliItpi~ili~~~t Uelos, j14-14: B. C., l,!. Gary Reger Hegeiico~-Otto Seugebauer to assign the work to the fourth c e l l h l r ) - . . ~ .but, , in our vie\$-(see 1.8 n. 16), the details of the relexmt test do not justify such an inference. C'nelestin I.q.;'-8y, on the other hand, has been thought to allude to the equation of time. Since this is a subtle concept that Ptolemy ( A ~ J z3.9) . as the first to articulate, this passage u-odd justif!. assigning the Cnelestiir a date no earlier than the middle of the second centllr!,;\.D. (a te~winrispost qutw consistent, as we have seen, with his philosophical culture)." However, the Cleomedean text in question just rehearses a point identical to that made by Geminus (first cent. B.c.) in his Eisi~gfige6.1-4 regarding the length of the day with both texts providing an account ofthe variation in its length that is pre-Ptolemaic." Thus the date of the C~eltstia cannot be cletermined h!- any line of dependence fronl Ptolem!; and if it is post-Ptolemaic (as culh~ralconsiderations would allou ; see n. q above), then this would mean that Cleornedes was either unaware of or indiffer-

''

en t to the .417wirgt~t.

11. For this argument see Eov-en and (;oldstein (1996) 171 n . 27. Ptols t cannot he dated em!-'sfiori~it\\as ca. .I.D. 130-ca. I . D . 170. T h e A l t ~ r ~ g eitself preciscl!. 1 2 . Both Geminus and Cleometies define the day as the i n t e r n 1 from one sunrise to the nest, anti bring into consideration the rising time of the ~ r F$chich the Sun travels along the zodiacal circle during the course of one re^-olution of the cosmos. (For a translation of the passage from Geminus see 1.4, n. 16.) P t o l e m ~by contrast. defines the da!- as the inten-a1 from one meridian crossiny 11)- the Sun t o the next, and focuses o n the time it takes the arc that the Sun tra~.elsduring a da!- to cross the ~neridiancircle. I n effect. Ptolerny isolates the trigonometric contribution of the Sun's motion to the variation in the length of the day (that is, to the equation of time) 11) subtracting the effect of latitude. 1.4.72-89, fiar from h o n i n g Cleomedes' reliance on Ptolemy. So C~~,'~elestii~ presents a11 account of the length of the tia! that Ptolemy clarified and made precise. 13. See Ugra (2000) 168 Frith 11. 16 for this general conclusion.

T h e C'mlesti~iwas read almost esclusidy as an astronomical handhook until around 1 9 0 0 , ' when ~ German classical philologists began to define the historical context of the treatise through Q~~elIt~~!fi~nS[li~,q. the procedure of "source hunting" by which the ideas in lost works were reconstructed from purportedly later residues." Since Cleomedes admitted using rnateseen sinq)l!- as rial from Posidonius (n. 3 above), his work u-as so~neti~ues a repository of Posidonian doctrines and treatises, or, in more nioditied claims, as an amalgaln of earlier Stoic literature and Posidonian components.'" But since almost every Cleomeclean sentence could he linked with some Stoic or Posidonian fragment, as well as nit11 passages in nlanuals of elementary astronom!;'~ interpretations based on the parallels gathered from such sources inel-itably left its author identitied genericall!- as a postPosidonian Stoic scholastic with an interest in astronomy They did not succeed in placing him in any specific historical and intellectual context. In the early 1920s Karl Reinhardt adopted a more promising approach." H e identified what he called the "inner form" of Cleomedes' rq. Sce %dtl(ryy2) 2-5. Neugebauer (1975) 959-965 continues this tradition. T h e ~stronum!- in the CjAr/i~stii/did, 11o\tever, ensure its \un-ival in late ;Intiquity a h e n most other Stoic scholastic material \\ as lost. r j . On this older literature see 7 h d d (2004). 16. Cleomedes' Stoicism generall!- conforms to the lmdy of doctrine associated mith this school's major figure in the TJellenistic periocl, Chr!.sippus (z80/76--zo8/4 B.(:.); see Algra (199j) 268-270, and the sur-\.e! at Goulet 9-1 I . .+art from the theory of lunar illumination in 11.4 (see 11.4, n n . I , X and 19). Posidonius is not identified as the exclusire source of any of the hmdarnental theories mentioned in the Cnelfitiir, although, as 15-e argue helo\v, he esercisetl a strong influence o n its general principles and methociolog.. Cf. also n. 52 1,elon. 17. See the parallels and si~nilinin 'I'odcl's edition of the Cj/c,lcsti;r,and at Gouict 11-1 j.

18. See Reinhardt (ryzr) 183-207, and the recapitulations at Reinharcit (1926) 124, with 11. 2 , and (1953) 68j-686. For some discussion of his r i e \ \ s sec Tocid (2004).

treatise by drawing on a Posidonian fragment (F18EK; translated and discussed in our Appendix). n-hich, along with some associated texts,'" posits a hierarchical relation between the two major components of the Caelestiii, physical theory and astronomy."' Physical theory according to this fragnlent, deals N-ithmatter, causal relations, and teleological explanation, while astronomy is defined as an activity that uses geometry and mathematics to analyze the shape, size, motions, and interactions of the principal heavenly bodies.'' T h e two disciplines might address identical topics (for example, the sphericit)- of the Earth, the size of the Sun, or solar and lunar eclipses), but will conduct their demonstrations in syste~naticallpdifferent ways. For while astronomj- will be based on observations, it will acknowledge physical theory as foundational. Thus in the all-important explanation of the motion of the heavenly bodies, physical theory supplies the "first principles" ([/l-khni) that astronomy has to adopt and folloll-." T h e distinction, and hierarchical relation, posited between physics and astronomy in FI 8EK is, as Reinhardt saw, respected throughout the C'iielesti~r,where physical theorj- is achowledged as defining the cosmolog?presupposed in astrono~nicalobservations and calculations. T h e treatise in fact opens (1.1.20-149) with a lengthy demonstration that the cosmos 19. 011this material see I. G. K d t i (1978a) and Comm.134-136 T h e texts in question are Diog. Laert. ;.13~-13j (= F254 Theiler). Sen. Ep. 88.25-28 (FqoEK; F447 Theiler), and Strabo 1 . 1 . 2 0 and 2 . j . 2 (F3h and 3c Theiler). Cf. also Theon E.vpos. 166.4-10 and 188.1j-24 (on which see Appendix n. 30) and 199.9-200.12. 2 0 . T h e reader may now wish to consult the .\ppendix. T h e relevance of F18 to the Cmlestin \{-asalso noted at Todd (1989) 1368-1369, and has recently been briefl!- discussed by .Ugra (2000) r ;S-177 21. Positi. F18.j-18 EK; cf. Sen. Ep. 88.26. 22. F18.46-jo EK; see .ippendix n. 8, anti also Appendix n. r for Gerninus' concern with the same issue. For the same autonom!- of physical theor!- see Straho 2 . 3 . 2 , and Sen. I$. 88.28. F18.46-jo E K and Straho 2 . j.2 also refer to the theory of planetary motion in eccentric circuits found at Cdestia 11.5.102-141.

(the realm of astronomical obsewation) is a finite material continuum surrounded by unlimited void. In line with FrSEK, its analysis and ariguments focus on matter, causal relations, and teleology. Also in that opening chapter, the stability and sphericity of the cosmos are said to be dependent on the centripetal motion of the elements, and while this particular physical theory goes undemonstrated (cf. 11. 6 above), its foundational status is obvious, and it is later cited as the basis for the Earth's stability at the center of the cos~nos(I.6.41-43).'' Then at I. j.126-138 the properties of the lighter elements, air and aether, are identified as the cause of the sphericity of the cosmos, while elsewhere the differing density of the elements selTes to demonstrate both how the Earth and the heavenly bodies are organically sustained by a mutual interchange of matter (1.8.79-9 j), and why different heavenly bodies move at different velocities (11.1.334338). Finally the lunar theory of 11.4-6 consists of an opening chapter on the phj.sica1 theory of lunar illumination as a prelude to an analysis of lunar phases and eclipses. In all these cases physical causality, as Posidonius claims in general terms in FISEK, serves to define the cosmological structure within which astronomical obsen-ations are made and ~ t i l i z e d . 'But ~ the most explicit, and philosophically most interesting, links benveen the Posidonian program in Fr8EK and the Cirelcrti~iare to be found not in physical theory so much as in epistemology and methodology

2 3. In Fact, this physical assumption determines the w a y that obsen-ations are described tl~roughoutthe treatise. 1f7ithoutit, the same phenomena (such as the risings and settings of the Sun, as well as the lengths of daytimes and nighttimes) that in 1.5-6 are said to entail the sphericity and stable centrality of the F,arth could he explained by the rotation of the Earth and the stahilitj. of the Sun, as Posidonius recognized in his critique of Heraclides of Ponhis at F18.39-42 EK (see Appendix and cf. 1.6 n. 14). 24. .it the w n e time, physical causality is esernplified at C'~t,Ie.rti~1.1-4 through the motion of the Sun, and the diurnal and seasonal changes that it causes. See fiirther i p p e n d i ~n. 1 3.

Phmical theor!; Fr8EK argues (lines 30-32 and 12-46), cannot be directl!- established from "the phenomena" (that is, from the evidence of primaril!- celestial obsen-ations), since, in a famous phrase, these can equallj- well be "sax-ed" by other "llypotheses." This undesirable possi-

hili ty is exemplified (F18.; 9 -42 EK)by the coslnolog. of a mobile Earth and ilnrnohile Sun that had been hypothesized on the basis of the phenomena by Heraclides of Pont-us (a pupil of Plato). Posidonius, to borrou. language from \f: 1: 0. Quine," can thus be wid to have regarded a " ~ ~ ~ l d e r ~ l e t e r i i l ithe n i ~theory ~ g " of the basic structure the p h a m 1 1 ~ n as of the cosmos in that the!- can support diverse and even conflicting accounts. For Posidonius, "h!-pothesis" is thus a derogatory term for any theory that, while in principle foundational to cosmoloa; is mistakenly formulated only on the basis of observations. Posidonius' aim was to eliminate h!-potheses of this type entirelj- from scientific reasoning.26 Cleomedes' treatrnent of these central themes in the philosophy of science is, 1 5 contrnst, indirect and unreflective. H e never overtly addresses the status and limitations of astrononl!- as an obsen-ational science, apart f r o m acknodedging at one place (1.1.1;~-I7 j) that a spherical and geo-

static coslnology cannot be established conclusidy "from the phenome m " but only from thc theor!. of the centripetal motion of the elements." I I e is, hov ever, concerned with the --a!-

that obselmtions of the heav-

ens, ifused uncriticall!; can lead to false theories, and in one place (I.j.1-6) articulates this concern with explicit reference to the Stoic concept of the criterion of truth.

In Stoicism this criterion is defined as the "cognitive presentation" j. See (Juine (19-ji. 26. On the specid role o f F18.iz-;o K ' in estahlishing this position see the .\ppendix r c ) j - r c ) o . 1;. Cf. n. 2 3 she. and for the iignificance of density for the Earth's sphericity anti stal~ilitysee, respectix-el~-, I. j.6-;and 1.6.41-43 (vith 1.6 n. 14). brief references in chapters that other~viscpresent arguments based on observations. I

certlfi~ble."In effect, it posits

,I

fit betneen h u ~ n a nr e m m ancl the content

with which it n-as presented-one

that is proof against misleading (or

n o n c o g n ~ t ne) pl-esentat~ons.~" .It 1'11 earher p a n t in hls expos~tlonof Cto~c phdosoph) Cleornedes m m t have mtroduced t h ~ sdoctrine, probrotation. Chapter 3. T h e latitudes of the Earth have differing seasons caused by the motion of the Sun in the zodiacal circle. Chapter 4. T h e lengths of daytimes and nighttimes differ at differing latitudes because of the motion of the Sun in the zodiacal circle. (Dig~.e.ssioiz:T h e torrid zone of the Earth is uninhabitable.) Chapter 5. T h e shape of the Earth is spherical. C h a p t e r 6. T h e E a r t h is a t the center of the cos~nos.

Chapter 7 . Digi-essiorz: Posidonius' and Eratosthenes' tneasurements of the circumference of the Earth. Chapter 8. T h e size of the Earth is discountable in observations of all heavenly bodies except the Aloon.

* T h e outlines here and at the heginning of Book X o (page 98) are included for the sake of the reader and do not belong to the translation proper. T h e division of the Caclestin into books reflects its original structure as tu-o lecture courses (see 11.7 n. j ) , but the dirision into chapters dates only from the editions of the Renaissance, and, while, generally logical, and supported h>-marginalia in manuscript sources, it has been revised for 1.1-4; see Todd ed. C~elestiirPiut+ n, and also 1.1 11,j8, 1.2 n. I j, and 1.4 n , I . C:leomedes himself refers to l o p ("discussions," perhaps single lectures). which in some cases correspond to our existing chapters; see 11.2.29-30 (identifying 11.6 as part of 11.4-6), 11.4.136-13? (identifl-ing 11.j), and 11.j.1 jo (identifying 11.6).

3: Tosmos" is used in many senses, but our present discussion? concerns it with reference to its final arrangement13which is defined as follows: a cosmos is a construct formed from the heavens, the Earth, and the natural substances within them.+ This [cosmos] encompasses all bodies, since, as is demonstrated elsewhere, there is, without qualification, no body existing outside the cosmos.' Yet the cosn~osis not unlimited, but

is limited, as is clear from its being administered throughout by Nature. F o r it is impossible for Nature to belong to anything unlimited, since n'ature must control what it belongs to.

I . O n the title of the treatise see Introduction n. I above. 2. I.e., the present chapter, which is a preliminary overview of the structure of the cosnlos; see further n,j 8 below: 3. dinkom~isis:cf. SlVF 2.526- j27 and 2. j j 8 where it identifies the distribution of the elements in a fully established cosmos. Cf. also n. 6 below. 4. This is a standard definition; e.g., S I T 2.638 (192.3 5-36), Posid. F I ~ E K , PS.-hist. Dc mundo 391bg-10, and drnten 127.14-1 j. j. Cleo~nedesmust already have demonstrated that the cosmos is a finite continuum; cf. also lines 126-127 below. At lines 69-73 belou; and a t I. j.128-I 34 he alludes to the conditions that maintain this continuum.

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C1eontede.s' T h e Heavens

11: And

that the cosmos has Nature as that which administers it is evident from the follo\i-ing: the ordering ofthe parts within it;hthe orderly succession of what comes into existence;- the sympathy of the parts in it for one a n ~ t h e rthe ; ~ fact that all individual entities are created in relation to something else; and, finall!; the fact that everything in the cosmos renders very beneficial services." (These are also properties of individual natural substances.) So since the cosmos has Sature administering throughout, it is itself necessarily limited, whereas what is outside it is a void that extends without limit in every direction. Of this [void] the [part] that is occupied by body is called "place," while that which is not occupied will be void."' zo: UTeshall now briefly surninarize [the argument] that there is a void: Et-ery body is necessarily present in something; but the thing that a bodj. is present in, given that it is incorporeal and as such without physical contact," must be distinct from what occupies and fills it; we therefore speak 6. These "parts" are elements (cf. 1.4.244 and I.j.8) in an "ordering" (tmic.; cf. dintnxi.r at 11.1.3~9)in the cosrnos; see lines r 16-119 below (with n. 43), and I.j.126-13;. 7 . This is elsewhere referred to as the "continued stability" (ilinmor~?)or "presenation" (sitii-iir) of the cosmos; see 1.2.2-3, 1.8.98-99, and 11.1.399. 8. S y p a t h y in Stoic cosrnobiolo~-yis a ps>choph!-sical interaction between bodies: that is, sympath?- is not a metaphorical concept but defines the physical relation between lix-ing things. 9. "Provides" (pnrekhestkni) carries an inherently teleological sense, particularlya-ithreference to the Sun? p m e r (e.g., I.3.86,91, g j , 97,104; 1.4.1j; 11.1.362 and 371); cf. 1.3 n. 17. 10. O n the comple~nentar!- Stoic theories of place, space and void (the most important evidence for m-hich is at S W 2. jo3-506) see Algra (rgqj), especialljch. 6 (with Cleotnedes discussed at 268-270). O n Cleomedes on the x-oid see beTodd ( 1 ~ 8 2m) d I n ~ o o d(1991) 2 j;-2 jq. Innood tries to drdn d dlst~nct~on tween Cleomedes and the earlier Chq-sippean theory, but rUgn (1y9 j) 269 argues convincingly that Cleomedes is rendering orthodox Stoicism in defining place as that which is occupied by body I I. "Has no physical contact" ( m p h e s ) ; cf. Epicur. Hdt. 40 and P)&. 86 for the same term used to define incorporeality

T h e Heavens 1.1 /

23

of such a state of subsistenceE-namely a capacity to receive body and he occupied-as void." 25: That bodies are present in such a thing can be seen pri~narilyin the case of liquids (i.e., all liquid substance).14 (h) U'hen, for example, we extract the solid from a vessel that contains liquid and some solid body, the liquid converges on the place of the object that has been extracted, and is no longer seen at the same level, but is reduced by an amount equal to the size of the object that was extracted. (h) Conversely, if a solid is placed into a vessel full of liquid, the amount of liquid that overflows is equal to the volume of the solid imported, and that would not happen unless the liquid had been present in something that had been filled by it and was capable of being occupied by body." (c) In the case of air, too, the same thing must be understood to occur. In fact, air is forced out of the place it occupies whenever a solid occupies that place: n-hen, for example, we pour anything into a vessel,]%e in return 1 2 . "State of subsistence" (hzipostnsis) is more specific than "esisting"; see LS 1.164. It is therefore appropriately used of the void, lvhich is "something" (line j7 with n. 22), although conceived of as incorporeal (lines 65-66), Its suhsistence comprises positive properties that constitute the way in which it "exists"; see line h8 belo\\; ~vherethe generic verb hupnl-khei~lis used. Elsewhere, the vcrh hphbnsthni, is used both of corporeal esistence (11.1.3~8, related to h~~postirsis, 364 and 402), and of a geometrical abstraction (1.3.33). 13. To call void "occupied" here (as a t line 18 above) is to treat it as a general concept of space, rather than as the capacity to be occupied by hod!; its formal definition. See hlgra (199j) 69-70, and 269 n. 26. 14. Because of this reference to any type of liquid, we h a w translated h~irlor. in the passage that follows (as at lines 74-78 below) as "liquid" rather than "water." I j. ( 4and (h) recall the standard argument for place as the "extension" (dins t ? ? ~between ) the limits of a container; see Arist. Phys. 2 I I ~ I ~ 7.- This I commonsense theory, which rejected, was widely discussed hp his commentators. Philoponus (e.g., 117 phys. j82.10-j83.12) essentially adopted the Stoic concept of place as occupied void, although he rejected extracosmic void. 16. Something "solid" can be poured, inasmuch as water is "somewhat c o n pact" (see 11.4.36); it is unlikely (cf. n. 18 belou-) that pliable solids (e.g., salt) are also envisaged.

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Cleomedes' T h e Heavens

perceive the air1: inside it escaping, and especially when the aperture is

'

narrow. 39: M'e can also conceive of the cosmos itself moving from the place that it currently happens to occupy, and together with this displacement of it we shall also at the same time conceive of the place abandoned by the cosmos as void, and the place into which it is transferred as taken over and occupied by it. T h e latter [place] must be filled void. If, according to the doctrine of the most accomplished natural philosophers, the whole substance [of the cosmos] is also reduced to fire, it must occupy an immensely larger place, as do solid bodies that are vaporized into fumes.'" Therefore the place occupied in the conflagration by the substance [of the cosmos] when it expands is currently void, since no body fills it.'o But if anyone claims that a conflagration does not occur, such a claim does not confute the existence of the void. For even if we merely conceived of the substance [of the cosmos] expanding, that is, being h r ther extended (granted that there is no possible obstacle to such extension), then this very thing into which it would be conceived as entering in its extension would be void, just as of course what it also currently occupies is filled void. 55: So those who claim that there is nothing outside the cosmos are

17. "h-" here translates p i ~ r l r m n ,n-hich is clearly being used in a nontechnical sense; on its technical sense see 1.5 nn. 34-3.7. 18. T h e vessel involved here may be a clepsylra, which had a narrow aperture at the top and snlall perforations at the bottom. A liquid in \vliich it was immersed entered through the perforations until the aperture a-as plugged, and air escaped at the top as this process occurred. Its exit could thus be "perceived in return" (the verb is n77ti-ln7ribni2esthiri) by touch, and perhaps aurally, if it made, say, a whistling sound. 19. Cf. 1.8.83-90 for this principle applied to the Earth 20. . U p (199j) j r 1-3 36 makes the case for Posidonius having believed that the extracos~nicvoid was only large enough to accommodate the expansion of matter caused by the conflagration.

T h e Heavens 1.1 /

zj

talking nonsense.?' T h e very thing that they term "nothing" obviously cannot staid as an impediment to the substance [ofthe cosmos] as it expancls. -4s a result, when the substance expands, it will occupy something,?' and what is on each occasion occupied in a natural [process] will be filled by the object that occupies it, and will become its place, which is void that is occupied (i.e., filled) by body. This [filled void]" will duly become void M-henthe substance [of the cosnm] is again compressed (that is, contracted into a snlaller volume). 62: NOWjust as there is that which has received body, so also there is that which is capable of receiving body; the latter, which can both be filled and abandoned by body, is void. Now it is necessary that the void possess a state ofsubsistence. But our way of conceivingvoid is entirely without qualification, since void is incorporeal and without physical contact, since it neither possesses a shape nor has one imposed on it, and is neither acted on in any m y nor acts,24but is without qualification capable of receiving hody. 68: Since the void exists in this way, it is also not present at all within the cosmos. This is clear from the phenomena For if the substance of the whole cosmos were not naturally linked throughout, then: (a) the cosnlos could neither be held together and adtninistered throughout by Xature, nor could its parts have any sympathy relative to one another;?' (17) we n-ould also be incapable of seeing and hearing, if the cosnlos were not held

I I. For iristotle's position (cf. n. 29 below) reformulated in this way see :&X. Aphr. Q ~ i i t c ~3t..1 2 , roj.30-3 j and 106.32-107.4 (tr. Sharples [1g94] 74-75)? and Si~nplic.172 iI", M P ~ O 2 8j . 2 1-24 and 117 plys. 468.1-3. 2 2 . For the void as "something" (ti) see SJ~F2.331, and Brunschwig (1988) 96-99. Lines 64-6; helo\v define its ontological status. 2 3 . Here again (cf. n. 13 above) "void" is being used in the sense of space. 24. ".-Icting" and "heing acted on" (poiein and paskhei,~) define body for the Stoics; see Sl'F 1.90 and 2.363. T h e sense of "acting" here is that of causing an etfect; see 1.3 11, 17. 2 j. There is a similar argument at SGF 2. j43.

2

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C'leon~eiles-'T h e Heavens

together by a single tension (that is, if the pneulna were not naturally linked throughout); for if there n-ere intervening void spaces, our senses would be impeded by the1n;'"c) ~esselswith narrow apertures would also, when im-erted in liquids, be filled n-hen the liquid passed through the void spaces; but this does not in fact occur, because the vessels are h11 of air, and this air cannot be em-uded hecause their apertures are enclosed by liquid.'And there are countless other [phenomena] that rve need not mention n o n by which this [thesis] is demonstrated. It is therefore impossible that there be void present within the cosmos. 81: LAristotleand the nlenlbers of his school do not admit void even outside the co~mos.~"'Thevoid," they argue, "must be a container of body; but no body exists outside the cosmos; so neither does void."?" But this is simplistic, and exactly like someone saying that since a-ater cannot be present in places that are dry (i.e., lack water), there can also be no container capable of receiving water."' So it should be admitted that "container of a body" is used in two senses: as that which holds body and is filled hp it, and as that which is capable of receil-ing body. 89: "But," they say "if there were void outside the cosmos, the cosmos would mm-e through it, since it a-ould have nothing that could hold it together and support it."" But our response \.\-illbe that the cosmos 2 6. ;Ues. Aphr. Llc iril libi: maiit. I 39.14-1; argues that if light is a Id!; then if there were an interstitial void, the air n - o d d be unevenl!- illumi~latedh!- the light present in the pockets of the void. O n pneurna in vision see 11.6.178-18.7, where its peculiar tenuity (or inherently rarefied state; cf. I . j n. 34) dlows it to be refracted by the water in a full container xithout causing any overfloa. 2;. This would not he a problem for liquid poured into an upright T essel, o r entering a clepsylra, of which the latter is more likely the situation k i n g descrihed at lines 31-37 above. 2 8 . See line j j-61 above v i t h n. 21. 29. See Arist. De cir~/oz.;qa12-14, and Simplic. Iil iieci~th284.21-24. 30. O n the raliditj- of the notion of an unactualizetl possibility underlying this counter-claim see Sorahji (1988) 133-13 j. 31. For this argument see Ales. Aphr. at Simplic. Iil deirrelo 286.6-10 and Sirnplic. 177 pby. 671.4-13 (= 517: z.jjz). T h e fact that here and below (see n. 34)

T h e Heaven5 l.I

/

27

cannot "rnove" t h r o u g h t h e w i d , since i t tends toward its o\vn center, and has as dovm t h e [direction] toward which it tends;'! for if t h e cosld m o s did n o t have its center and d o w n as identical, it ~ ~ o u "rnove" t h r o u g h t h e void" (as will be demonstrated i n o u r discussion concerni n g m o t i o n toward t h e center).

96: T h e y also claim that "if there were void outside t h e cosmos, t h e suhstaiice [of the cosmos] 15-ould, by expanding t h r o u g h it, h e scattered and dispersed t o a n unlimited e ~ t e n t . " But ' ~ o u r response will be: (n) T h e [substance of t h e cosmos] c a n n o t h e acted o n in this u,a!-, since i t has a holding power that holds i t togetherji a n d thus p r e s e ~ ~ it. e s AQso,(h) t h e

Cleornedes responds to the ~ n a mthrust of ~irg-un~ents that a e knon nere torn~ulatedh! Alexander of Aphrodisias (fl, ca. . L D . zoo) could not in itself prow that he \vas a contemporar! of this Peripatetic (pim Algra [1q88] 169-1 j r and [ ~ q q j269; ] now retracted at Algl-a [ ~ o o o171-~;z), ] since such argximents could have predated ;Uexander. Cleornedes' connection n-ith Alexander confirms only that he belongs to an era terminating around A D , zoo, a-hen polemics between Stoics and Peripatetics a ere common; see Introduction nith n. 4. 32. See further lines 161-r;j below. O n this arLprnentsee Hahm (19;;) I 19, ;Ugra (1988) 169 -I jo and \lblfF (I 988); cf. also 11. j 7 belon-. 3 3 . This conditional sentence (lines 02-04) has sonieti~nesbeen deleted because of incomplete knowledge of the inmuscript tradition; see Crrclestiir 'Ibtid ed. ad loc. B u t it is integral to the reasoning, though \\hen the receix-ed test at line 93 says that the cosmos \ \ o d d he borne "donmvarcls" (kilti). that qualification can be omitted, since the void has no dov-nn-ard direction; see lines I jo-I j r below. 34. Cf. .-\les. .+hr. at Simplic. I12 ( / P i i ~ e z86.10-23, l~ and at Siml~lic.I12 p h ~ s . 671.8-13 (= .CIF 2.jj2); also, derivatively, Themist. I12 ply-. 130.13-1; (= S1'7; 2. 553). h i s t . P l y x z r jarz-24 had cited dispersal "in all directions" (pnutpi), though only 'fhemistius uses the phrase "m-ithout liinit"/"to an uriliinited extent" (cir ~ p c i m r )found in Cleomedes (at lines 9; and r r 3-1 14 helon-). Alexander did concede that the Stoic "holding power" (lwis), introcluceti in Cleonledes' response, might prevent the cosnlos from splitting into pieces, but thought that 1 s displaced. p v e r no help when the cosmos ~ ~ being 3 j. -1s at lines jo ancl 7 2 above, and 98-99 below, .mueklvi12 (literally "to hold together") also means "to make continuous" through the physics ofthe Stoic dynanlic continuu~n,conveyed here by the hexis ("the holding power").

28

/

Clcomedes' T h e Heavens

enclosingvoid does not act at all,'" ~vhereasthis [substance] conserves itself through the exercise of its surpassing power," as it is compressed. and again as it expands, in the void, in accordance with its natural changes-expanding

into fire at one time, nhile setting out for the gen-

eration of the cosmos at a n ~ t h e r . ~ ' 104: Simplistic too is the [Lkistotelians']claim that: "if there is m i d outside the cosmos, it will have to be unlimited; but if the void outside the cosmos is unlimited, then there will also have to be unlimited hodJ;."'" T h e reasons are: (I*)the void's being unlimited does not imply that body is also unlimited, since the concept of the void does not cease anywhere, whereas being limited is in fact included in the notion o f l ~ o d ~(1,); ~there ~) also cannot he a "holding power" for what is unlimited: for how could something unlimited be held4' bj. anything? T h e [Alristotelians]also make other similar claims. 36. Cf. lines 66-67 and n, 23 aho\.e. 3;. This power (dmamis) surpasses those attributed later to intracosrnic hodies such as the Earth (1.8.82-9 j), the Sun (11.1.3 57-+o3), and the AIoon (11.3.61-6;). 38. T h e Stoic cosmogony is the result of the e~olutionuf a creative originative fire (e.g., SliC I.IO;, 171; z.;;t. 102;; see Pease [ r y ij] 011 Cic. De /wt. rieoi: 2.57); as such, it can be described as the nlanifestation o f a biological "impetus" (for which Cleomedes uses the verb hoi.miii~). 19. See Alex. Aphr, at Simplic. Iiz de cm10 285.32-286.2 (= SVF 2,j3j), and cf. Arist. PAYS.203hl j-30. 40. This notion jeniroin), like others in the treatise (1.8.21-26; 11.1.1j 5-170; 11.3.1-4 and 34-3 j), isa puli~ifii~nq, idea, reached by rudirnentar!- reasoning ancl requiring further refinement. Thus here n-e cannot naturally form a notiorl of body that is not finite (Sorabji [l9881140 suygests Arist. Phy. zoqhj-7 as a precedent), but need a dernonstratiun (at lines 133-139 helon-) that an infinitel!- enlarged cosmos is inconceivable. In the (,irclestinCleomedes shou s no interest in the origin of such notions; that is, he does not identify them as "nanlral" or "co~nmon," or see them as "preconceptions" (pi&p.rei.Q. (On this feature of Stoic epistemoloa- see Todd [ I Y ) Tand ~ ] Scott [1988].) They are comparable to other arguments in the Cirrle.rtin that are of li~nitedvalue because they are based only on observations; see Introduction n. 31 and n. j 4 below. 31. Perhaps ckbrsthai (line I 10) should be erneritled t o . r ~ ~ ? ~ e k l ~given t ' ~ t hthat ~i. a hrwis is n-hat makes [the cosmos] continuous (cf. n. 3j).

T h e Heavens 1.1 /

29

That it is necessary that there be void outside the cosmos is evident from what has already been demonstrated. But that it is absolutely necessary that this void extend without lisnit in every direction from the cosmos, we may learn from the following [principle]: everything that is limited has its limit in something different in lund, different, that is, from the thing that is l i n ~ i t e dTo . ~ ~take an obvious example: in the whole cosmos air, because it is limited, ceases [to be air] at two bodies difFerent in kind, aether and at er.^' Similarly, the aether ceases at both the air and 112:

the void, the water at both the earth and the air, and the earth at the water. Our bodies too are similarly limited by something different in kind, their surface, and this is i n c ~ r p o r e a lIt. ~is, ~ then, necessary that if the void enclosing the cosmos is limited rather than unlimited, it ceases [to be void] at something different in kind. But nothing different in kind from the void, at which the void ceases, can be conceived ~ f . ~ T h e r e f o the r e void is unlimited. I 23: For even if we did conceive of something different in h n d from the void, by which it will be limited, this [other void] will have to be filled, and what fills it will be body. And in this way there will have to

42. In the Lito~nist-Epicurea~i tradition this principle is used to demonstrate that extracosmic void is infinite, and that it is occupied by infinitely numerous t~odies;see Epicur. Hdt. 41, Lucr. r.qj8-967, and cf. Arist. ply.^. zojhzo-22. 43. By "ceasing" here Cleornedes means that the elements cease to he called hy their g i ~ e nnames. However, this does not i~nplythat these four elements are distinct ho~nogeneousbands or layers; in fact the ,\loon, which is at the "juncture"(suni~pbi'/ of air and aether (1.2.37-38; 11.3.83-Q), has its appearance age'ected by not being in the "pure" part of the aether (11.3.88-90). O n the pradations in the density of the Stoic aether see Todd (2001). 44. On the incorporealitj- of surface (epiphmein) see Plut. De romm. not. 1o8oE, and the discussions a t LS I. r 63, r 6 j, and 301, and by Brunschwig ( I y 88) 28-30. 4 j ;hother Peripatetic arLprnent(cf. lines I 10-1 I I abol-e)is that such a void . ro j.27-3 j, AIex. is simply an imaginary conception; see ,Vex. Aphr. Q ~ a e s t 3.12, Aphr. at Si~nplic.01d i , ~ m l o285.26-27 and 286.23-2 7 , and Todd (1984). Thorp (1990) I 59-164 discusses the Aristotelian basis for this position.

30 /

C'lrom~iles'T h e Heavens

be body outside the cosmos-something that physical theory does not suggest, since all bodies are enclosed by the c o ~ m o s . From ~ " this it is evident that the external void cannot be limited anywhere. Therefore it is unlimited. 130: Indeed, just as it is thought that everything that is limited is enclosed by something (otherwise it would not be limited), so too the void, if limited, is necessarily enclosed by something. IZ'hat could this be? A body? Impossible, since there is no body outside the cosn~os.But even if there were a [body], it again, since it is limited, will have to be enclosed by a void. And again this T-oidwould, if it is not going to be unlimited, be enclosed by another body that would itself in turn be enclosed by another void, since this body too must hare boundaries. This [process would go on] to an unlimited extent, and so bodies will come into existence that are unlimited both in number and in size. None of this is possible.'. I 39: Thus if the extracosmic void is limited, and at all events enclosed by something, yet not enclosed by b o 4 it will he enclosed by some. what will this be' Time? Surface? Alekt077?~%omething i ~ o r p o r e a lSo thing else just like them? But it is implausible that the void be enclosed by any of these. Indeed, there M-illhave to be another void that encloses it, and this, if it is not unli~nited,will have to he enclosed by another void, and this by another to an unlimited extent. So by refusing to admit that the extracosmic void is unlimited, \ye shall be brought round to the necessity of admitting an unlimited number of distinct voids! That is utterly

46. Cf. lines 5-7 above. 4;. For the Epicureans an infinite number of bodies m s , of course, possible (see Epicur. Hdt. 41-42), although a n infinitely large body was not (Epicur. Hdt. 5;). 48. O n extracosmic time as inconceivl-lhlesee alread>-:kist. Dr nrda z;yalq-r 8. T h e surface is presumably to be disti~lguishedfrom a surrounding void, nhich has been excluded the preceding arLgurnent. .hextracosmic lid~uiz(literall!"the expressible," the carrier of the meaning of a proposition, and a n incorporeal; see 1I.j n. 18) would have nothing for which it could express a meaning.

T h e Heavens 1.1 /

31

a b ~ u r d . ~So" it is necessary that we agree that the void beyond the cosliios is unlimited. 150: Since the void is unlimited, as well as being incorporeal, it will not hale an upu drds or a downwards [dlrectlon],nor a front, back, r ~ g h t , left, or center, for these direction^'^) (seven in number) are obsesved in relation to bodies. Thus while none of them exists in relation to the oid, the cosnlos itself, being a body, necessarily has both an upwards and doxvnwards [direction], as well as the remaining directions. So they say that the \vest is its "front," since its impetus is westward, and that the east is its "back," since it is from there that it proceeds f o n ~ a r d . Thus ' ~ the north will be its "right," and the south its "left."i'

158: There is nothing obscure about these directions in the cosmos, but the remaining ones [namely, up and down] confused the earlier natural philosophers considerably, and numerous errors occurred in this area, since they lvere unable to grasp that in the cosn~os,which is spherical in shape, the exact center is necessarily dow-n~vardsfrom every direction, n hereas what extends from the center to the limits and right up to the surface of the 4phere is upuards. T h e two directions coincide in the cosrnos (that is, both the center and the downwards direction are identical), though in bodies that are made oblong in shape they are separated, whereas this is not the case with spherical bodies, where instead they coincide. This is because [bodies] with spherical holding powers necessar-

49. This is because the concept of the void is "without qualification" (line 6 j a h ~ - e )this ; ~vouldbe untrue if blocks of it were separately distinguished. jo. "Directions" (skhesei.9; the terrn literall!. means a relational state, appropriately enough since the directions are defined from an arbitrarily defined point. j r . T h e impetus (home; cf. 11. 3 8 above) of the cosmos here is that of the is thus sphere composed of aether, which contains all the heavenly bodies; kosl~~os 1jeir.g used, as it often is, in the same sense as o~rianos(the standard terrn for "heavens"). This impetus in^-olves a dailyrotation from east to nest around a fixed central Earth; cf. 1.2.1-4. 5 2 . See 1.6 n. ;on these six non-central directions and the arguments for the centrality of the Earth in the cosmos.

ily tend" i n t h e direction of their center f r o m their surface, and s o have as do\l-nnards t h e jtlirection] tom ard which they tend. So t h e cosmos too, since i t is spherical in shape, has t h e same property, that is, its downwards direction and center are identical because these directions coincide i n i t at t h e same [point]. [ T h e sphericity of t h e cosmos] will b e t h e p r i n n r y aim of o u r demonstration i n o u r discussion concerning motion toward t h e center, b u t for n o w we shall demonstrate it in simpler terms, o n t h e l m i s od!- of n.hat is presented t o us in p e r ~ e p t i o n . ' ~

176: ( ~ l )41o f u s , a t 11 hatever latitude of the E a r t h we m a y he," clearly see t h e heavens located a h o w o u r heads, while everything around t h e m appears t o us t o he sloping an-ay T h e n as n-e proceed t o a n y o t h e r terj;. 'I'his links the geometry oftht: sphere and Stoic ph!-sical theory sphert it \\.it11 this ic~ilhod! xi11 11,n e the kind of "holding poner" (hc~.u.\;it h ~ endmvs shape. and makes it "tend" (ileltci~l;cf. lines c)1-9z ahove) in a centripetal direction. For some inclication of the physics that applies this principle to the cosmos see 1.5.116-138. ;+ See 1.j.1-6 r h e r e the limitations of thii argument are noted in more elahargument only for the sphericity of the orate terlns. Proposition (g)i s a i.oiii~/iisi;~e FJ I .tb, bnsed on the e\ itience of changing horizons (we I. j.107-108 ~vithI.5.49-

;i 1)ut ) it. can onl! "sug~est"(cf. 1.5.1) the iphericity of the cosmos, or, in effect, pro\-itie a prclimin;)~!notion of it (we n. 40 d h r e ) . 5 j. Strictl!. speahng, the latitude iklii~~ic) of an ohser\er's localit!- is detined 11) the elewtion (or inclination) of the north celestial pole above the northern horizon. But (see I.'ipre I ) thih k ~ i i i i~i ~cc1u;il to angle ZC)(J,a-hich measures the distance alony the obsen-er's rneriiii,in from his zenith to the celestial equator. This angle is in turn equal to anglc OTE, the ohsen-er's latitude, that is, the ano.ular distance measured along a meridian nf longitude from the terrestrial equator to the parallel circle pasiing through the ohserver's locality; cf. Ptol. Alvr. 2.6. Tn stantlard usage anlony geographers. the distance from this parallel to the equator can be called a kliimi. ;inJ is usuall! g i i w ~in stades (e.g., Straho z.j.;, 2.5.15-16. ;incl z.5.3c)-+o), although for- Ptoleti1~-it is ~ 1 arc 1 @\-er1in degrees. In his Gcogiuphicr (or C ~ e ~ , p p k i u iIII i i ~ ~ ~ ~ t oPtolern!i:)') ativanced the study of geogand pli~tos(longitude and latitude; r.nph!- ]!l- appl! ing scientificdI!- the terms 1ni.40~ the wme terms he used in the Abi/i/gi..it h r celestial coordinates) as coordinates to represent. respecti\el!,, east-weit 311~1n ~ r t h - w u t hdistances reckoned in decrees on (a nlap of) the Earth: cf. Seugeh'iuer (rg;j) 934.

T h e Heavens 1.1

/

33

restrial latitude ~t all, U hat u n t ~then l appeared to he 5lopmg an a) is o~er our hedds. T h ~ us ould not occur unless the hear ens M ere located ,~ho\e the Earth m e\ er! d~rection(thdt

IS,

unless the exact centei- of the cos-

extendmg from it to the h e a mos 11 ere donnu ards, n hile the [d~rectlon] ens

ere up14 ards).

(I?)

11~0,M hen on

J

sea I o) age u e h'n e no land

sight, the hear ens appear to us to be touching the n'lter in horuon. Rut on reaching the place

M

,i

111

circle at our

here the heal en5 appeared to us to

he toudling the xi ater, the) are ~ n s t e x\isihlj l located or erhead. and this occurs continuousl! throughout the o! age. So if it 15 ere pos51ble to s a l around the mhole Earth, or go around it b j some other means (~ssuining that no p u t of it is u n ~ n h a l x t ~ ~ b l erie ) , 'rtould ~ l e x n that the heaxens 'we located aboxe eT er) p'irt of it. -2nd so the center of the cosmos is s ~iell as 1' center. But our I e s ~ o nconcermng the rnoat once dou nn ~ r d as tlon of h e q hotlies to the center" nil1 establish t h ~ smore eflectii ely.

1 9 3 . 'Fi\ ~ e parallel circles 'Ire drawn

111 the

h e a ens. one, 15 hich n e

cdl the equmoct~alclrcle, d n ides the heai ens ~ n t ohi o equal p ~ r t sv, h11e on e ~ t h e rs ~ d eof this ,Ire

trio

that ,Ire sm,~llert h m it, but equal to one

another. 7 he! are called "tropics," since e drdu them through the trop~ c apoints l of the Sun.

o others are also drawn on e i t h e ~ude of these,

of 11h1ch the northern is called "'lrct~c," 'ind the one oppo5ite to it 56. For Cleometles (lines 110-211 and 266-26; belmr) the torrid zone isuninhabitat~le. j;. Only in this reference (cf. lines y+y j and 173-174 alxxe) to this forthc o n ~ i n gdemonstration is the phrase "of heav! botlies" atlded, although it a p p a r " in ijther references to centripetal motion a \ the physical principle unilerl!.i~lg the sphericit!- of the Earth and the cosmos; see G e m . Lwg. 16.2. S t r a h 1.5.2, anti l t ~ 11.22-13.9 ~. is a related, hut special, case; T h e o n E.~pos.I2z.r 1-16. ( P t ~ l . ~ j 1.7. see \\i)lff [1y88] 499 n. 31.) But Cleomedes and theye other authors must still mexn that NN the elements in the cosmos hare n centripetal motion, i.e.. that the!are all "hea\-!-" in that sense. See further 1.5 n. 38. 58. 1.1.ri);-173 formed a separate chapter in all earlier printed editions. Rut they are a g c o p p h i c a l appendix to ch. I, while lines 270-2 73 helow form 311 01)vious conclwion, and lines 262-269 complement 1.1.3-16 I)! introducing a teleological principle.

"antarctic." These differ for different [obsen-ers] depending on differences in latitude, since they become larger and smaller, and ultimately disappear.'" Tl'here they do not [both] disappear, one of them must be out of sight, while the other is aln-a)-svisible. Five parts of the Earth are located below the intervals in the heavens that are distinguished by the circles just des~ribed:~" First, the one enclosed by the arctic circle; second, that located below the interval between the arctic circle and the summer tropic; third, the one between the two tropics, which has the equinoctial circle located above it at its exact center; fourth, that between the winter tropic and antarctic circle; fifth, that enclosed by the antarctic circle. 209: T h e natural philosophers call these parts of the Earth "zones," and say that while each of the outer ones is uninhabitable because of icy cold, the one at the exact center is uninhabitable because of blazing heat, and those on either side of it are temperate since they are each tempered by the torrid and frigid zones adjacent to them. So by further dividing each of these temperate zones into two with respect to the hemisphere thought to be the upper [region of the] Earth, and the one thought to be the lower, they say that there are four inhabited zones."' TTe humans. ~ ' the people of whotn there are direct reports, inhabit one of t h e ~ e , and called "circurnhabitants" (pel-ioikoi) another. Though the latter are in the same temperate zone as us, they inhabit the region that is thought to be j9. Here, in the nest paragraph, and at 1.2.79-80 it is assurrled that the arctic and antarctic circles are defined; that is, that the ohsen-er is not at either pole or at the equator. See Figure 2. Note that Figures z(a)-(f) are not true perspective drawings. I l e ha\-e instead in this case and others like it chosen to adopt a style of representing the sphere that is trad~tionalin classical astronoln!; and distorts perspective in order to fiacilitate comprehension. 60. On these zones see Arist. J l r t r o l : 36zajz-j6zbg, S I T 1.649, Ach. I q g . 62.20-63.j,Aiatea 96.23-97.6, and Plin. 17H 2 . 1 7 2 . Posidonius challenged this folk geography; see I.+yo-146. 61. O n these see Ach. Isilg-. 6 5.1j-66.2 j,.-lrzlten 97.7-23, and Gem. isizy. I 5.1-2. See Figure 3 . 6 2. Gem. l s q . I 6.1 calls such inhabitants "co-hahitants" (smoikoi).

T h e Heavens 1.1 /

3j

belou the Earth." T h e "contrahab~tants"(mztozkor) inhabit a third zone, and those antipodal to U\ a fourth, and while they [both] o c c u p ~the contratemperate zone, some of them (our contrahabitants, also called "dressed by the shoulder" [ n n t i m o ~ ] ) , occupy "~ the region a b o ~ ethe Earth, whereas those occupying the region below the Earth are antipodes."' To explain: the footprints of all who walk the Earth must face directly toward the center (that is, the exact center) of the Earth, given that the exact center of the Earth, because ofits spherical shape, is donnwards. Hence it is not our circumhabitants who become our antipodes, but inhabitants of the contratemperate zone in the region below the Earth-the ones who are located directly opposite us, nith their footprints directlj. opposite T h e footprints of our circumhabitants do not, however, point toward ours, but toward those of our contrahabitants, so that again these [tn o groups] become antipodal to one another. Our antipodes become contrahabitants of our circumhabitants, since such relations resemble those of friends and brothers, rather than those of fathers and children, or slaves and masters; that is, they 63. This "region" (klimn heing used in the sense of a broad band of latitudes) is "thought" (dokolin) to he "below the Earth" from the perspective of the northern temperate zone. Based o n lines I 53-1 $8 above, an ohsen-er in this zone who looks toward the n-est has his 0 ~ 1 1region and that of the contrahahitants "above the Earth" (or to his right and left), while the other two regions are 1)elow it. 64. X contrahabitant who (following lines I 57-1 j 8 ahox-e) faces west will (to use a militarl- term) be "dressed" (or aligned) to "our" (southern European) left, a n d me to that person's right, assuming geographical S!-mmctry (sec n. 66 belux{-). 6 j. T h e use of the Greek "antipodes" as a collective noun for these inhabitants seems preferable to "contrapodes." 66. But n-hile the theor>-of Nature (see lines 262-269 beloa-) Inay require s o w e equivalently inhabited antipodal zone, it could not guarantee that its geograph!; and the footprints of its residents, would correspond, unless land masses were suitahl! distributed in each hemisphere by some teleological principle, as may have been the case for the Stoics (see 1.4 n. 32). On the ellduring illusion of exact antipodality see Quine (1987) 121-124.

convert,"- in that \ve become circumhabitants of our circumliabitants, antipodes of our antipodes, and similarly contraha1)itants of our contrahabitants. 2 3 5 : Yet in relation to each of these [groups] u-e have something in cornmon, as well as distinct. In relation to our circumhabitmts we have in common, first, inhabiting the same temperate zone; second, h a ~ i n g winter, summer, and the other seasons at the same time, that is, ha\-ing identical lengthening and shortening in daj-times and nighttimes.""~ut there is a difference in their da!-times and nighttimes: when it is daj-time in our zone, it must be nighttirne in theirs, and vice versa, although this is put too looselj-. For it is not by precise reckoning that the Sun begins to rise in their zone when it sets in ours, since in that case the nighttime in their zone 1%-ould be long when the da!-time in ours was long, and their seasons, that is, the lengthening and shortening of their da!.times and nighttimes, v-ould be the reverse of ours. But in fact, as the Sun goes round (i.e., encircles) the Earth, which is spherical, it shines its bright light on the [put" on which it casts its rays each time its course takes it over the Earth's curvatures. So while it is still visible above the Earth in our zone, the circumhabitants necessarily see it rising, given that it goes round an Earth that is spherical in shape, and, as it goes over the Earth's cur\.atures, it rises at different tirnes for different [ohseners]. 2 5 2 : In relation to our contraliabitants we have in common: first, that n-e both occupj. the upper hemisphere of the Earth; second, that we have daytimes and nighttimes at the same time, although this is also put too

6;. T h e logical comersion i~ilplieclhere is that of strict reciprocity, n-hereh! j. \\-here the reciprocit!- of relatires (t[cpi.osti) can c o w - the I-elation,excluded here, h e n w e n slave and master. 68. "Da! time" ( b ? m e i ~and ~ ) "nighttime" (iiirx) \I ill be used for the inten-als from sunrise to sunset, a n d sunset to sunrise, respectively. Cleonledes uses the term i~irkhthPnrei-oir("inten a1 of a nighttime and a daytime") for the interxal from one wnrise to the next: see 1.4 n. 16.

aKh is true if and only if bRa. Contrast .lrist. Ciit. 61328-;a

T h e Heavens 1.1 /

;;

looselyh" since there is shortest da!-time for them \\.lien there is longest da!.tiine for us, and rice versa,-" given that in relation to them our seasons, that is, the lengthening and shortening of daj-times and nighttirnes, are reversed. But Lve hare nothing in common with the antipocles.

111-

stead, everything is re\-ersed: we occupy one another's lon-er regions of the Earth, and their seasons, that is, their daj-times and nighttimes, in terms of the lengthening and shortening of daytinles, are the reverse of ours. 262:

T h e theory of Nature teaches us that circumhalitants, an-

tipodes, and contrahabitants nlust exist, since none of these [ groups] are described hy direct reports.-' TT> sinlply cannot travel to our circurnhabitants because the Ocean separating us from them is unnavigable and infested by Ixasts; nor to the inhabitants of the contratempel-ate zone, since we cannot tra\.erse the torrid zone. Yet the regions of the E k t h that al given are equally temperate are necessarily inhabited to an e q ~ ~extent, that Nature loves Life, and Reason requires that all [parts] of the where possible, be filled n-ith anir-rial life, both rational and irrational.

270: To be demonstrated next is \\hat causes difFcrent parts of the Earth to he frigid, torrid, and ternperate;" and why for inhabitants of thc contraternperate zone the seasons, that is, the lengthening and shortcning o f the claytimes, are reversed.-' 69. Cf. lines 240-241 above. 70. It was cornmonl~assumed in antiquit!. that the shortest nighttime is ecluCll to the shortest daytime, although, as Neugrl~auer(1969) 158 n. r points out, atmospheric conditions make the shortest da!.tinie longer t l ~ nthe shortest nighttime. 71. This "theory ofnature" (phusiologii~)includes the explanation for the cosmos heing spherical and geocentric (lines 191-192 above; also I. 5.126-13): ancl 11.6.41-43). which in turn determines the Earth's relation to the Sun's motion in the ccliptic (1.2.73-80; cf. 11. I,361-386). Cf. also Gem. I > q . I 6.1y - 2 0 OII the symmetry of habitable zones in a spherical Earth. 7 2 . See 1.2.80-82 where this proicct is completecl. 73. This is the program for 1.3;see 1.3.1I 1-1 14;see 1.4 n. r on its continuation.

CHAPTER T W O

I : As the heavens revolve in a circle above the air and the Earth, and effect this motion as providential for the presen-ation and continuing stability of the whole cosmos, they also necessarily carry round all the heavenly bodies that they encompass.' Of these, then, some have as their motion the simplest kind, since they are revolved by the heavens, and always occupy the same places in the heavens.? But others move both with the motion that necessarily accompanies the heavens (they are carried round by them because they are encompassed), and with still another motion based on choice' through which they occupy different parts of the heavens at

I . T h e "heavens" here consist of the element irith?l- (cf. 1.4.87-88), that 15, they are a hand of rarefied matter with a natural tendency to sphericity (cf. I.j.131-13;) and circular notion (SYF 2.642). (This sentence therefore supplements the ifescription of the dznkosnr&ic. at 1.1.3-16.) T h e term nstl-n, which can refer onl!- to the fixed stars, will be translated as "heal-enly bodies," when, as here, it refers generically to both the fixed stars and the planets. 2. Hence they are used to define celestial latitudes; see 1.3.44-51, 3. This motion is "based on choice" (kil~?sispl-oiril-etik?)because in the Stoic system planets are endowed with reason and thus self-rnorimted (cf. Cic. Dr 11at. ilroi: 2.4j and 2. j8), though such choice is exercised strictly within the limits of line 2 ) of the heavens; this, as it \!-ere, the "providential motion" (kin~i.rppl-oi~oitik~ allous planets some ~ndependencerelatne to the motion of the fixed stars. See further Todd ( r o o ~ ) .

T h e Heavens 1.2 / 39 different times. This second motion of theirs is slower than the motion of the cosmos, and they also seem to go in the opposite direction to the heavens, since they move from west to east. 12: The first [set of bodies] is called "fixed," but the second "planets," since these appear at different times in different parts of the heavens.+The fixed bodies might be likened to passengers who are borne5 along by a ship, yet remain in their assigned places in relation to the overall space.6 The planets, by contrast, are like passengers who move in an opposite direction to the ship (toward the stern from positions at the prow) with a relatively slower motion. They could also be likened to ants creeping on the basis of choice on a potter's wheel in a motion opposite to [that of] the wheel.; to: T h e total number of the fixed bodies is i m m e n ~ ebut , ~ only seven planets have become known to us,9 although it is unclear whether there

4. For this general distinction see also SW 2.6 jo. This elementary definition, given the Stoics' preoccupation with etymology (cf. 11.5.82-86 and 92-IOI), was probably designed to draw attention to the literal meanings of aplavi and plan& merza/plarzitai, "non-wanderers" (sc. fixed) and "wanderers" (sc. planetary). j. T h e stars "are borne" (pheresthai, in a passive sense), since, unlike the planets (cf. n. 3 above), they do not initiate their own motion. Pheresthai switches back to its middle voice sense ("move") in the comparison with the planets. 6. "Space" (khirn) is defined by the Stoics ( S W 2 . jo3- jo6) as the larger area within which something has its "place" (topos). See Algra (199 j) 263-281 on this concept. 7. For the comparison with displacement in a moving vessel see Ach. Isag. 39.16-20 and Hygin. De astlnn. 4.6; and with ants crawling backwards on a wheel Ach. hag. 48.16-18,Aratea 97.33-98.1, andVitruv. Dearch. 9.1.1j. Bodnir (1997) 2 0 0 n. 29 links Cleomedes' analogies with his acceptance of planetary motion in eccentric circles (cf. 11.j.139-140). 8. For this conventional claim see Arist. De caelo 2gza11-12, P ~ . - ~ b i sDe t. mundo 392a16-17, and Sext. Emp. PH 2.90 and 97. 9. For the number of planets as a basic assumption of astronomy see Dercyllides at Theon Expos. 200.2-3. (This passage could reflect Posidonian ideas, as I. G. Kidd [1978a] 11 suggests, particularly if Dercyllides can be dated to the first decades of the first century A.D., as Tarrant [1993] 11-12 and 72-76 argues.) O n the "Chaldean" planetary order followed here (as opposed to the "Egyptian," in

40 / C'lromeiles' T h e Heavens are still more. The one held to he farthest aw!; the star of Saturn, named Pbirii761z (The Shining One), completes its on-n circuit in a period of 30 !-ears in accordance with its motion that is based on choice. Below it is the star ofJupiter, named Phitrtbi12( T h e Radiant One), n-hich completes its own circuit in a period of 1 2 years. Below this is Pur-oeis (The Fiery One), the star of llars, which has a relatirel! disorderly motion,1° although it too is held to complete its own circuit in z !-ears j months." T h e Sun is thought to be belon this, and thus at the center of the other planets." By going round its on11 circuit in I year it demarcates the seasons b y this motion. n hile it prox~desthe da! s h! the motlon that accompanies the heavens. Belo\v this is the star of Venus, and it too has a period of I !-ear; xvhen it sets later than the Sun, it is called Hespei-os (ET-eningStar), but \\-hen it rises before it, Hp6.spho~-os(Daw-n-Bringer), which some also like to call Ph%spboi.os(Light-Bearer). Below Venus is the star of JIercur!; named Stilbii~(The Gleaming One); they say it goes round its particular circuit in I !-ear. Below this is the \loon,13 closest to the Earth of all the heaven1~-bodies, in that accepted theor): places it at t h e junction of the air and the aether, which is \\.h!- its own body is also I-isi1d~~ n u r l y .The ' ~ illuminated part of it has its luminance from the Sun,

\L hich the Sun immediatel!- hllon-s the 1Ioon rather than being centrallj- located) w e P r i a u s (1973) 213-21; ~ 1 1 .-\ulac d ( 1 ~ 7 5124 ) n. See also 11.; n. z. Cleomedes giws the siik~i~i~irl period for each of the sewn planets. that is, the time it takes for each planet as seen from the E;irth to return to a +en srar. For the .ymilic planewry periods, that is, the periods from one conjunction (or opposition) with the Sun t o the nest, see I1.;.8-10. O n tile epithets applied to the planets see Pease ( I y j j) on Cic. L)e i~ict. ileoi: 2. j 2-5 3. ro. Cf. Plin. 1-H2 . ; ; . 'l'his motion is od!- "relati\-ely" disorderl!; given lines 43-46 helow: though Cleoriletles doe5 not explain \\-h!- he regards it as such. 11. called a 1icikhth8nlt.mil (the term used at l i r m 72-89 helow). O u r tcrms "claytime" and "nighttime" for h87liei~~ and i1rl.v (cf. 1.1 n. 68) distinguish the periods of solar ~llurninationand darkness lvithin m y such "da!.." j. T h i s is the situation at the Hellespont (54°K); see A l c l ~ Isirs-.. . 57.2-6, Hipparch. 117 A4ii~t. LT E I [ I ~ OPS~. I ~ 1.3.7 c I ~ .(26.1 6-2 j), Schd, ill AIW.i'iJt.301.3-5 a n d 305.9-306.:. and Ptol..4/m. 2.6, 109.17-18. Cf. 11.1.442, where g hours is given for the rhortest nighttime at the Hellespont. 6. \'i7ith this paragraph cf. Gc111. I.sq. 6.34-39. 7. T h a t is, the centrd circle of the zodiacal hand, as is explained at lines jz- j3 belon-. 'She Sun appears to go "through" it, in the sense that it fo1lon.s it in its course. 'That is, this zodiacal circle is the trace of the heliacal circle on the zodiacal [,ancl, and is sometimes itself called the "heliacal circle"; cf. I.r.46-jr, and 1.2 11. 18.

intersects with the equinoctial circle at two points, while touching each of the tropics at one point. It intersects with the equinoctial circle and adjacent parallel circles more directlyx but abuts on the tropical circles inore obliquely, that is, at a more inclined [angle]. Because it produces acute angles in this latter way, it becomes the cause of [the Sun's] approaching and distancing itself from the tropics more slo\\-ly.T h e Sun, that is, as it eEects its lengthy course through the zodiacal circle, distances itself from the tropics more sloli-ly, whereas at the equinoctial circle, where the zodiacal circle is more upright, it effects its approach and withdrawal from it more abruptly." Providence, in other words, has manellously fashioned the relation of the zodiacal circle to the tropics in such 8. Here we hare revised Todd's text by deleting at line 34 a phrase seemingly ~ ) same ua!. as "nmre designed to explain n no re directly" ( d P B O ' ~ ~ Pin~ jthe obliquely" ( . ~ ; h a ~ i & ~ ~which o s ) , is explained in the nest clause b!- the phrase "at a more inclined [angle]" (27;; iYtihivdPwo~). T h e deleted phrase is tia; &\l;/ou , almost at right angles." But this is obriousl!- untrue S& 7iP& dPB& Y ~ ~ ~ &'Le., of the angle in question, which is approximately ~ 3 ' 1 ~Neugebauer ". ( I y j j) 961 n. 4 recognized the problem, and proposed deleting y c d a s ("angles") and translating the phrase as "almost as a straight line." H e explained this as meaning "under a constant angle, in contrast to a changing direction fiarther alra!- until tangential contact with the tropics." and noted an identical Latin expresion ("paene directim") at AIart. Cap. 8.878.However, the common phrase r p & ZpH& m-ould then whereas yovL'cr; is have to be used unprecedentedly to mean zP& ZPB& YP~pILLU;'. norrnal1~-understood in this phrase, as at C i i e l d i / 11.j.70. ;Use, the Greek for "in d r i a v yPapp+~.l>!- a n a relation to a straight line" xould presumably be . ~ ; p & o~ with the standard phrase for "in a straight line," ET' & ~ / a ; Jypapp+) (e.g.. 11.6.182). T h e adjective dp0& also normally refers to lines that are perpendicular to one another. 11% suspect that tia; 6X;you & i 1 ~ dpi-)&s;/tol,hs was deriwd from a gloss, designed to balance the genuine gloss on .;;hay&~~os,its i n t r ~ ~ s i ~ e status suggested by its a\vhvard location after the main verb r;p~sti. (For another deleted gloss see 11.j.14~-146.n-ithII.5 n. 32.) T h e glossator was perhaps either impressed (consult Figure 6) by the near equality of the angles of intersection at C and D, or else \vas exaggerating the angle ofintersection a t these points in order to sharpen the contrast uith nhat happens at A ancl B. In either case, the thought is so poorly expressed that we decline to attribute it to Cleornedes. 9. See Figure h.

T h e Heavens 1.4

/

53

a way as to ensure that changes in the seasons occur inlperceptibly rather than abruptly. l 0

44: T h e time intenrals between the tropics and the equinoctial circle are not equal either: from the vernal equinox to the summer solstice there are yq1/2days; from the surnmer solstice to the autumn equinox 9z1/: days; from this equinox to the winter solstice 88; and from the winter solstice to the vernal equinox

ll

49: So the problem arises: given that the four quarters of the zodiacal circle are equal, why does the Sun not complete its passage through them in an equal time? Now the answer to be given is that if the Sun effected its course through the zodiacal circle itself, it would go through all its parts in an equal time. But the heliacal circle is in fact located below the central circle of the zodiacal band, and at a position much closer to the Earth. Yet if, despite being located below the zodiacal circle, the heliacal circle had the same center as the zodiacal circle, the Sun would also go through the four parts of its own circle in an equal time, since then the diameters drawn out from the tropical and equinoctial [points of the zodiacal circle] would also divide the heliacal circle into four equal parts. But in fact [these tsvo circles] do not happen to hare the center. Instead, the heliacal circle is eccentric [relative to the zodiacal circle], and for this reason is not divided into four equal [parts] by the diameters just mentioned. Rather, its arcs are unequal, since only circles with identical centers h a ~ earcs equally divided by diameters, whereas circles that do not have the same centers do not.'?

62: So since the heliacal circle is eccentric, then if it is divided into 10. Cf. 11.1.396-399, and Cic. De vat. &or: 2.49. I I . See F i p r e ?(a). Other sources report a year of 36 jl/+days, with 88'/8 days in the period from the autumn equinox to the summer solstice, and 9o'A days in that from the winter solstice to the spring equinox. See Gem. I.sug. I .S 3-16, Ptol. ill?^. 34,' 33.2 1-2 4m& 33720-2 3384 (with Hipparchus' prior authorit!, inyokecl a t 238.3-q), and Theon Ekpos. 1j3.6-12. 12. For similar demonstrations see Gem. 1.r~ig.1.31-34, Theon Expos. I j3.16rj8.11, and 1Iart. Cap. 8.848-849.

54

/

C'ko7~edes'T h e Heavens

twelve [parts], just like the zodiacal circle, there will be unequal sections of the heliacal circle located below equal sections of the zodiacal circle. Its largest section will be that located below Gemini, its smallest that be1 o ~Sagittarius:" that is also why [the Sun] goes through Sagittarius in the shortest period, but through Gemini in the lengthiest, since it is at its greatest height in Gemini, but closest to the Earth in Sagittarius, while proportionately [distant] in the other signs. So consequently the Sun's circuit is also eccentric since it does not always move at the same height,14 but in accordance with its course it moves both on high and back toward [points] closer to the Earth." 72:16 Nor are all the intervals of a nighttime and a daytime equal to 13. A ziiiiio?~maJ- he either a zodiacal constellation or a zodiacal sign (a dfidekictintorion or one-twelfth part of the zodiacal circle; see n. 17 below). Here Gemini and Sagitrarius are zodiacal signs. 14. "Height," here and elsewhere, translates b~cpsos,which in cases such as this refers to the distance of a celestial body from the center of the cosmos, the Earth. I j. See F i p r e 7(b). 16. -1s noted in the Introduction (nn. I I and 12) in connection with the dating of the C'nelestiir, the a r p r n e n t at lines 72-80 here parallels Gem. I.si~g.6.1-4. and both passages offer a less sophisticated analysis of day lengths than Ptolemy 'S at ;ilmngest 3.9. AUm,C;c~ninus uses the periphrasis "a nighttime and a daytime added together" (to siuznviphoterov i l l i s kiri bi.mri-n) instead of Cleomedes' term "interval of a nighttime and a da!-time" OiickbthHniei-oizi.His passage is as follows: "[I] 'Day' is used in two senses: in one sense it is the inten-a1 of time from a rising of the Sun to a setting, but in the other sense 'day' is used for the interval of time from one rising of the Sun to the nest, [ 2 ] In the second sense the da!- is [identical with] the revolution of the heavens iriiil the rising of the arc that the Sun traverses as it moves in the direction opposite to the heavens during their revolution. [j] That explains wh! a nighttime and a da!-time added together is also not precisely equal to every nighttime and daytime. Instead, while their lengths are equal relative to perception, relative to precise reckoning there is some slight and imperceptible variation. [q] 'The reason is that while the rerolutions of the heavens are in equal inte~valsof time, the risings of the arcs that the Sun traverses during the revolution of the heavens are not. T h a t explains why a nighttime and a daytime added together is not to every nighttime and

The Hea\en\ 1.4 / 55

one another by precise reckoning, as is supposed, but only in relation to perception. 'That is because the revolution of the heavens themselves is necessarily less than everg- interval of a nighttime and a daytime, given that in a whole course the heavens complete their 0u.n circuit more quickly than in the interval of a nighttime and daytime that the Sun proceeds through as it goes in the opposite direction to the heavens. For when the heavens have come right round to the same point, the Sun is not yet observed in the east; instead it is only when the arc of the circle that the Sun in accordance with its motion based on choice completes during the inten-al of a nighttime and a daytime is elevated that it too is of the zodiacal circle, which seen in the east. So if all the &dekizt~.n?o?-in" are equal, also rose in an equal time, every interval of a nighttime and a daytime would consequently be equal as well. But in fact the summer signs rise upright and set obliquely, and as they rise upright the period of their rising is longer, and so the parts of them through which the Sun goes in the i n t e n d of a nighttime and a daytime rise proportionately more slowlY1Qut the opposite occurs with the winter signs.'" Thus the revolutions of the aether are equal, but the intervals of a nighttime and a daytime are not, at least on the most precise reckoning.

go: T h e Sun, as we have said,'() approaches the tropics and withdraws fi-on1 them rather slowly, and for that reason spends a longer time near da!rti~ne added together." In the final sentence of sect. [4] we deletepm7 ("erery") before the first use of "a nighttime and a daytime added together" to create the required parallel t)enveen this sentence and the first sentence of sect. [3]. Yso, the supplenlent "" should hare the form is? in Greek, not bo17 (Aujac), again as in the first sentence of [j]. I;. As the technical term for the zodiacal signs, that is, for those twelfth parts of the zotliacal circle that are ~larnedafter certain constellations, we leave ildekitri~noiio77transliterated, as also at 1.7.2I , 1.8.38, and 11.1.3 19 and 3 28. For the definition and identification of the dicleknt?mol-inas zodiacal signs see Gem. 1si/g. 1.1-4. 18. See Figure 8. 19. See Ptol. .lh.2 . 7 on rising times. 20. Lines 30-40above.

5 6 / Cleomedes' T h e Heavens them. Also, the parts below the tropics are not uninhabitable, nor are those still further south. Syene2' is in fact located [directly] below the summer tropic,22and Ethiopia farther south than this.23Talung his key from this [evidence], Posidonius believed that the whole latitude below the equinoctial circle was also temperate.?lAnd where the reputable natural philosophers had claimed that there were five terrestrial zones, he alone claimed that the one they called "torrid" was inhabited and temperate. That is, he argued thatZ5(a) if the [latitudes] below the tropics are not uninhabitable, nor those still farther within them,26despite the Sun's spending longer there, how could the [latitudes directly] below the equinoctial circle not be much more temperate, since the Sun approaches this circle rapidly and again distances itself at an equal speed, and does not spend a prolonged time at that latitude, when moreover, as he says, (b) the nighttime there is always equal to the daytime, and for this reason has a length appropriate for cooling ? (c) Since this air is also in the exact center (i.e., most voluminous [part]) of the [nocturnal] shadow, there will be rains and winds that can cool the air, because even i n Ethiopia rains reportedly fall continuously in the summer, and espe2 I. Its contemporary name is Aswan. T h e same location is assigned it at Plut. De def O K ~ I I and A Strabo 2.5.7. See also 1.7.71-72. 22. See 1.5.59-60; 1.7.71-72; 11.1.211-212 and 270. 23. T h e Ethiopians (located in modern Sudan) were often identified (e.g., by Homer Odyssey 1.22-24; cf. Iliad 1.423) as the most equatorial race in the known world, just as they had been the most peripheral on a flat Earth; see Gem. Isag. 16.28 with Aujac (1975) 152 n. 3. 24. Posidonius, in addition to lines 90-131 here (= FzIoEK), addressed is. treatise sues involving zones at Fq9.1-145 EK; cf. also F209 and F ~ I I E KHis on this subject, On the Ocean, was known to Strabo. 2 j . T h e three explanations that follow may be "alternative possible hypotheses" (Kidd Comm. 136), but they are not mutually incompatible as are the explanations of paradoxical eclipses anonymously proposed at 11.6.168-177 (see 11.6 n. 21). I. G. Kidd (1978a) 14 mistakenly tries to use such multiple explanations to support his interpretation of Posidonius' philosophy of science in F I 8EK as an activity based on hypotheses. See Appendix, especially n. 7. 26. I.e., closer to the equinoctial circle.

T h e Heavens 1.4 /

j7

ciall! at its height, and these are also thought to be the source from which the S i l e floods during the summer.!109: That, then, is Posidonius' position. .Ind if this is the situation with the regions below the equinoctial circle, then the seasons will have to occur there twice a year, since the Sun is certainly at their zenith twice, inasmuch as it causes two equinoxes.'" 11 3: 'Those who oppose this opinion of Posidonius argue [as follow-S]. ((2) .is far as the Sun's spending longer at the tropics is concerned, his doctrine mould haw to be sound. Yet, in addition, the Sun distances itself a considerable amount from the tropics, and so the air below them also cools off a considerable amount. As a result, those latitudes can be inhabited. But it distances itself just slightly from the equinoctial circle (v hich is half;! het\+een the tropm), and effects a rapid re1 ersal of direction to\\ 'ird ~t.'" (17) T h e [Imtudes] below the troplcs receir e annual u11id5from the frlg~dzones, and these moderate the extreme heat from the Sun h) cooling the air.'" But the) cannot penetrate as far as the O n (c) see Straho 2.3.3 (F49.j1-61 EK) and 2.3.3 (F49.134-13j EK). 2 8 . This parenthesis could be an implication that Posidonius himself drew, or C:leomedes' interjection, hased o n 1.3.88-89 and 98-106, and lines 8-13 above, \\.here the \-crnal and a ~ ~ t u m n equinoxes al are distinguished. T h e reasoning is that although the "seasons" at the terrestrial equator are not distinguishable by the usual criterion of the length of the daytirnes and nighttimes (defined by the Sun's return overhead and by- its departure; cf. lines 234-23 j below), they are definat~l~. different in temperature, and in this respect form two pairs of seasons \vhich are defined by the Sun's rehlrll to an equinox and departure for a solstice. l his claim reinforces the a r p ~ n e n t for s eq~latorialhabitabilit!- in @-id that precede, hut in such genel-a1 term? that it is probably best taken as a Cleornedean aside. r q. Since the distances involved here depend on the size of the Earth, this obsenation may reflect some debate about the distance between the terrestrial tropics and equator; see Strabo 2.2.2 (Posid. Fqq.10-36 EK) with f i d d Chrnw. :z;-zrH. 30. See Straho 3.2. j (Posid. T22EK) on Posidonius' account ofannual ("etet attributecl to an earlier Stoic, sian") winds. At .-;li.ittcu 97.1-6 this a r p ~ n i e n is I'anaetius (ca. 187-109 B.[,.). 27.

, >

equinoctial circle. If thei do, then the Sun, g n en the length of its course, MIII make them hot, Indeed flaming hot. (L) T h e equ,dit! [helom the equinoctial circle] of nighttime to daytime would not by itself have the gii en t h ~ the t Sun has 1' 11 mdefinahle pon er, pov er to cool the ~ I Ithere, and at all times sends out its ray toward that latitude in a perpendicular and intense form, since it certainly does not significantly slope awaj- from that latitude. ( T h e natural philosophers suppose that most of the Great Sea, which is centrally placed in order to nourish the heat-enly bodies," is inserted at this latitude.)" Thus in this case Posidonius does not seem to adopt the correct rien-. 132: But on [Posiclonius'] hypothesis" that the whole Earth is inhahited, some habitations v-ill he encircled with shadows (pei-iskioi), others shadowed unidirectionally (heti~i~~skioij. and others shadowed hidirectionally (mnpbkkioi). Encircled v ith shadon.s are those hahitations helonthe poles where the year will he [equally] divided into daytime and nighttime, the equator will be the horizon, and the same six signs of the zodiac will always be abo1.e and below the Earth.:4 Shadows there accordin& describe a circle, and make people "encircled with sliadom-s," since in latitudes below the poles the heavens re\-ol1.e just like millstones." Shadon-ed unidirectionall!- are the temperate habitations, since wlzenei-er the Sun is in the south, people in the northern zone hare shadows that slope ton ard the north, n hlle those In our contratemperdte zone have nil1 be those them slop~ngto\\ arc1 the wuth.'" Shadon ecl bidirection~~lly 31. On the equatorial ocean as excluded from Posidonius' geograph>-see

F I I ~ E Kwith Kidd Co~mn.4 j9-461. 32. "Inserted" (hlrpobitNt..ctbiti/ rn;I!. hare teleological implications linked to the geographical s p n i e t r ! bet\\ eel1 terrestrial zones (on which see 1.1 11. 66). ;3. Fz IOEK ends at line 131, but Theiler (F184) correctl!- includes lines I 32-146 as a logical extension of lines 00-1 3 I . For its classification of zones see Strabo 2.5.3; a11dAc11. Isirg. 66.28-67.6: also,cf. Ptol..-Ih~.2.6,at 102.9, 10;.14. a n d I 14.23, and see 1.6 n.10. 34. See further lines 2 2 5 - 2 31 heion. 3 j. See Figure c)(a). 36. See Figure ~ ( I I ) .

helon- the equinoctial circle: for when the Sun 1eax.e~the equinoctial circle for the south (that is, the ~vintertropic), their shadows slope toxvard the north hut when it travels to the summer tropic from the equinoctial circle, they would point to~vardthe south.'- T h a t , then, is [Posiclonius'] distinction between the zones of the Earth. 147: But what tnust also be realized here'qs that lvhile daytime lengthens and shortens over the same time period for everyone occupying our temperate zone, the addition anti subtraction [of claytime] is still not equal at all [latitudes]. Instead, there is a major contrast hetween them, with some having a minimal addition and subtraction, others aver!- large one, m d still others an intermediary one. T h i s is caused 11)- the heavens' not sloping equally at all [latitudes], and the north pole not being elevated [e\.er~-where]an equal number of degrees from the horizon, hut just nlini~rlall!. for anyone living in the south, more for anyone in the north, and an intermediary amount for anyone in t~etween.

156:'" T o explain. Those trawling to the south from the north necessarily ha\ e the north pole at a lower elevation and the heavens with less of a slope, while the opposite holds for those going a\va!- from there to the north. T h a t is because o n the Earth [directly] below the equinoctial circle each o f t h e poles, as u e ha\-e said,40is ohsen-ed on the horizon, and all the parallel circles have equal sections above and below the Earth. T h e r e the axis [of the cosmos] is also the diameter of the horizon, and there are n o stars that are either alm-ays risible or al~vaysout of sight. But because of the spherical shape of the Earth, those who come toward us from the mid-torrid zone ha\,e our pole elevated, have altered horizons, 3.; See Figure g(c). 38. "Here" 1m1st refer to lines 1-89 ahore, the opening ciiscussion of the lengths of daytimes. Lines 147-2 3I form in effect a supplement to lines I 8-2 9 ahox. based on the scheme of terrestrial latitudes recapitulated from 1.3.1-68. 39. (X.1.3.6-12 and 15-18, where the situation at the equator is also taken as the point of rekrence. Only here (lines 161 and 164) is the axis of the cosmos (on v-hich see (kin. ITS. 4.1) mentioned. 40. :It 1.3.0, 23-24 and 5 2 - 5 4

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and ha\ e the axis [of the cosmos] no longer as the diameter of an! [horizon] because the slope that del elops as the h e a ens are ele\ ated abox e the plane depends on the elel ation of the pole. 166:~' There are also diEerent Arctic circles at different [northern] latitudes depending on alterations in horizons. This is because the uctic circles enclosing the stars that are almays visible at each latitude must be described by the pole and the distance [from the pole] each latitude's h ~ r i z o n . ~So' for people living near the mid-torrid zone (that is, south of us), the arctic circles are very s~wallhecause the heavens slope minimallTV, and the [north] pole appears minimall!- elevated above the horizon. But for people in the north (that is, near the frigid zone) it is necessary that the arctic circles be very large, the pole hale 1' significant ele~atlonabove the honzon, and the heahens coilsequentl! slope to an extreme degree. But for people rlght in bent een the north and the south (and this includes the Greeks and e\ eryone at the s a n e lat~tude),~' all the [pheno~nena]just descr~bedoccur to an intermediar> degree. 179: Those parallel circles that are dnided b! the horizons ~t each l a t l t u d e are, therefore, also d n ided equally In the mid-torr~dzone, but unequally at the other latitudes. T h e larger and sinaller sections above

41. Cf. a-ith this paragraph 1.3.32-3 j anti 44-68. 42. T h e idea behind "be described" (g/-icphesthlri) seernr to be that, as the celestial sphere makes its daily rotation. ?he x c t i c circle is traced on the celestial sphere by the northernmost point of the horizon. T h e text that we hare translated restores a deletion in Todd'i edition and adds a supplement, so that at line

"at" the horizon, and for "at" we hare supplied a preposition that defines locality much as it does in the standard p l ~ r ~ ~"in s e sthe north/southl' (np& ( i p ~ 7 ( j i 1 & ! ~ ) . In so ernending we reject the possihilit!- that the Greek as it stands can mean that the arctic circles are "drawn by the pole m d the distance to the horizon" ("dessines par le p61e e t la distance il'horizon." Goulet). T h a t is the kind of meaning clearly needed by this text, and we hare tried to elicit it ~1it11minimal intervention, though we concede that the solution nu!- not be entire]!. satisfactory 43. Given 1.3.39-tz (cf. I.; n. g), this latitude would he 36"X.

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and below the Earth will balance out at those latitudes, and in this way the lengthenings and shortenings of daytimes will also balance out 1)roportionately.4i 184: Those living adjacent to the mid-torrid zone do not have daytimes that significantly lengthen and shorten, since there the heavens slope ~ninimall!; and cause a slight variation in the division of parallel circles into unequal [sections] by the horizon. But people at the latitude adjacent to the frigid zone have an extreme variation in the lengthenings of daytimes and nighttimes, since there the heavens have an extreme slope, and also because the pole has a significant elevation above the horizon and for this reason makes the arctic circle there extremely large, resulting in its not being far distant from the summer tropic. T h e horizons at those latitudes consequently divide the parallel circles unequally in so extreme a disproportion that the lengthenings and shortenings of daytimes also imolve an extreme variation. 197: For example, in Britain, when the Sun is in Cancer and causes the longest daytime, the daytime reportedly consists of 18 equinoctial hours and the nighttime of 6,4i so that over this time interval there is light at this latitude during the nighttime, since the Sun runs alongside the horizon and sends out its rays over the Earth. (This of course also happens at our latitude, when the Sun approaches the horizon, since its light is well in aclvance of its rising.) So in Britain too there is light during the night, so that even reading becomes possible. In fact this is said to be absolutely necessary because, due to the section of the summer tropic below the Earth being minimal at this latitude, the Sun at this time effects its course alongside the horizon uithout going too far below the Earth. 44. O n this "haldncing out" (wnmeti-m)x e hnes 2 3 2-2 39 helon. Oher the course of a year each latitude n-ill receive in principle (cf., hoxverer, 1.1. n. 70 and 11. 51 helow) an equal amount of light and darkness. 4 j . See 11.1.+4+ At Ptol. L & ~ . 2.6, 113.6-9 the parallel at 580N ("through the southern part of Ireland") is assigned a longest daytime of 18 hours. For less precise data see Gem. Isng. 6.7-8, and Plin. XH 2.186.

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208:'~In the island called Thule (said to have been visited by Py-

theas, the philosopher from 3larseilles) the whole summer tropic is reportedly above the Earth, and in fiact it beconles the arctic circle at that latitude.': ITlnen the Sun is in Cancer there, the daytime will last I month, if all the parts of Cancer are also always visible there; but if not, then to the extent that the Sun is present in the parts of that sign that are always visible. 2 1 3 : For ~~

those proceeding to the north from this island other parts of the zodiacal circle in addition to Cancer will hecome always visible in due proportion, and this means that as long as the Sun is going through those parts of the zodiacal circle that are [always] visible above the Earth at each latitude, it will be daytime. 218:L ~necessarily ~ d there exist latitudes of the Earth where the daytime is 2 and 3 months long, and 4 and j months, too.'" L41so,'0since directly under the pole there are 6 signs of the zodiac above the Earth, then as long as the Sun is going through these signs, which are alu-aysvisible, it will be daytime, since here the same circle is the horizon, the arctic circle, and the equinoctial circle. T h a t is. people at Thule hare the summer tropic coinciding with the arctic circle, but people still hrther north have the arctic circle exceeding the sumner tropic relative to the parts [of the heavens] leading to the equinoctial circle. and this occurs proportionately. But for those directly under the pole the equinoctial cir46. At Ptol. L-ll?n. 2.6. 114.9-11 Thule, an island north of Britain, perhaps identifiable n-ith Iceland or parr of Scandinwia, is assigned a latitude of 63"N, with a longest daytime of zo hours. T h e latitude at which the longest daytime is . I I j.8-16). For the claim by Pytheas (probably a month is 67"N (Ptol. A 1 h ~2.6, late fourth century B.c.) that the arctic circle and surnmer tropic coincide at T l u l e see Strabo z. j.8, Kidd CO~JZTJI. 74 5-746. and Roseman (1994) 104-109, n-ho translates and discusses Cleomedes' report (lines 208-2 ro = Pytheas T z j Roseman) and its context. 4;. See Figure ~ o ( a ) . 48. Cf. n-it11lines 213-219 Ptol. .1/77z. 2.6, I I j.8-I 16.20. 49. See Figure ~ o ( b ) . jo. Cf. with lines 219-231 Ptol. . - l h 2.6, r 16.21-117.9.

T h e Heavens 1.4 /

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cle assumes all three relations: it is the arctic circle because it encloses the stars that are always visible, since at this [latitude] absolutely no star sets or rises; it is the horizon because it separates the hemisphere of the heavens that is above the Earth from the one below the Earth; and it is the equinoctial circle because it alone divides daytime and nighttime equally at that latitude, and while everywhere else too it is the equinoctial circle to an equivalent degree, it is no longer either a horizon or an arctic circle. 2 3 2 : These, then, are the variations in the lengthenings and shorteni n g of nighttimes and daytimes, although the darkenings and illuminations of the air are made equal at all latitudes. In the mid-torrid zone, that is, nighttimes are always equal to daytimes, but at the other latitudes this kind of equalization is achieved differently: that is, the longest daytimes at each latitude are made equal to the longest nighttimes," and neither the darkenings nor illuminations of the air exceed one another, but the year as a whole divides them equally. 239: T h e cause of the whole variation in the cases just described is the Earth's shape, which is spherical, as a fortiori is the whole cosmos itself. In other words, none of the [phenomena] just described could occur with other kinds of shapes. IVe shall demonstrate next that both the whole cosmos, and its niost significant parts, do have this shape." 51. Since atmospheric coilditions make the longest daytime longer than the longest nighttime (see 1.1n. TO), this assumption of exact symmetry does not in h c t hold true. 5 2 . T h e Earth's sphericit)-had previously been assu~ned; see 1.1.22+24 j-246, 1.3.2-3, and 1.4.163.

CHAPTER FIVE

that must n o t b e m a d e a criterion for its shape, since everything does n o t in I : S o w sight alone seems t o suggest that t h e cosnlos is a sphere,] b u t

h c t usually appear t o us as i t [really] is.? I t follo~vsthat i t is o n t h e basis of n-hat is "clearer" (that is, w h a t is presented c o g n i t i ~ e lt~o ,us)' that, i n

accord with what is patently implied,+ we should a i m t o arrive a t things Cf. I.r.r;(i-191. n-here cosmic sphericit? \\-as demonstrated on the basis is presented in perception." or, as here, "sight" (opsi.9. 2 . O n the Stoic concept of the criterion of truth, and the met11otlolo~~sumnlarizecl in this opening paragraph. see also the Introduction. 3 . T h e terminolog~in the phrase 'rpo to11 i,iriri~esti,i.oii kiri kirtnleptikGs h i n z i ~ ~ ~ ~ V I ~ ~ ~ O W isI Eused I ~ ~ elsewhere I I hy Posidonius; see 7'81.2, F1j9.z and F169.4j EE;, and cf. I j d d C'OINIIZ. 74 U-h11rightly calls it a "criterion." T h e words katill2ptikiispl?iliilon~i.i~irthat gloss "clearer" also embed!- the technical Stoic term for a cogniti\ el! reliable sense presentation, the kiitirliptiki.ph~~~~ti~siic (see Introduction n-ith n. 19). 4.This translates katn t ? i ~~ I J I I I I I I I I I I I J I I E ~I I k o l o z t t h i m a, phrase difficult to interpret nithout a context for its use. Presumably the implication (nkolol~thia)is I ~ e c ~ ~human u s e reason recognizes "apparent" (the literal meaning ofpiwri~oi)rciri.) it 2s clear or evident, and our trnnslation "patentl!-" is designed to reflect this throu$ alternatire lang~~age. Thus at lines I z 6-1 38 helon- (which are anticipated at lines 6-9 here) there are t u o inferences (or "transitions"; cf. metioutes, line X ) I.

of

"U hat

T h e Heakens I.j

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65

that are not in and of themselves fully displayed. Accordingly, if we demonstrate that the ~ n o s solid t (that is, the rnost compact) part of the cosinos, the Earth, has a spherical shape, we could easily learn 1))- a transition from this to its remaining parts that they are all spherical, and in this way that the whole cosmos too has this sort of s l ~ a p e . ~ 10: There haw been numerous differences among earlier natural philosophers about the shape of the Earth: some, by following only the sense presentation based on sight, claimed that its shape m-as flat (i.e., a plane);'' others, who supposed that water would not be stationar!. on an Earth that did not have a "deep" (i.e., conca\,e) shape, said that it had just that shape;' others claimed that the Earth \vas shaped like a cube (i.e., square); others that it \vas shaped like a Our school, as well as from the sphericit!, of the Earth to that o f t h e air and aether (and thus the U hole coilnos), ancl these ;Ire grasped T-iaphysical theor)- and its geometrical nianifesrations. In the main Imdy of this chapter too (lines 2 0 - 1 13) implications are grasped as "evident" within more restricted contests in the arguments for the i~koloutl~ii/il. despite its F,arth's sphericit); and so the phrase k m / ti.11phi~ii~ow~ei~i'i~ use here in connection n-it11the larger cosmological picture, has completely g m era1 application. 5. T h e Structure of the cosmos is i t d f u n o l ~ s e ~ ~ ~ that i h l eis, . it is one of the ~ I t is tlisthings "not in and of themselves full!- clispla!-ed" (W? ~ o t o t l l r it'k,i7/lilil?). played to the extent that \ve can see the air anti acther. I)ut their sphericity can only be inferred crith the help of $1) sical theory (see lines 128-134 helow): it cannot I)e inferred fro111the phenomena alone, as c;in the sphericity of the Earth (we lines 104-1 I 3 helom). 6. \iThile the Hat-Earth co\molog. is associated a-ith I I o m e r and earl!Creek thought (e.g., h!- G e m . Isi~g.I 6.28), the present test ma! app1)- to the Epicureans (on \+horn see Furley [19y6]),who kit 11.1.2-5 are sirnilarl!- tiescritwl as ha\,ing inferred the Sun's size from its "~isualsense presentation"; see also 11.1. 11. 101. .; Uernocric~is(DK 68Ay4) thought that there \\.as a central hollo\5 on a flat ancl oblong Earth. 8. For other shapes see Ptol. .-161. 1.4, I 5.23-16.; for the cylinder, and T h e o n for the cone and c)-lincler. See E.Y~IUX. 120.23-121.1 m d Eucl. P ~ N P I4.26-6.14 I. drcii: 1.24. also the Epicurean polernic at Cic. De /m.

all the scientists and most of the Socratic school, affirmed that the shape of the Earth was spheric'd." 2 0 : Now since no other shape beyond those mentioned could be appropnately attached to the Earth, the follow ing disjunction 1%o d d be necessaril) true: the Eiiith 11e r t h c r j k t ( I . ? . , ir plirne), orronwi'e ("deep'?), oi-stjrtnw, oi~pj~imni~1~71, oi.sphericir1 in shirpe. So having posited this disjunction as true, then by going forward on the basis of what the logicians call "the fifth undemonstrated [arLgumentconstructed] through multiple [disj~incts],"~~ we shall demonstrate that the Earth has a spherical shape. That is, we shall state, as indeed we shall demonstrate, that the E m t h is u ~ i t h e i . f l / t , nor C O ~ ~ I PZ W, S ~ I Y ~, ~ o r p y ~ . i l r / ~ TITe i d u l shall . then conclude that it is nbsolutcljl~nec.es.slrq thiit t h E~n i t b be spheriiirl. 30: T h a t the Earth 1s not 1' plane n e may learn from the [follon 111g arguments]. (4 If it were flat (i.e., a plane) in shape, then there would be a single horizon for all peoples: for it is inconceivable hen; if the Earth had such a shape, horizons m-ould alter. And given a single horizon, the Sun's risings and settings, and thus also the beginning5 of daytimes and s not nlghttunes, n odd occur a t the same time ex er! n here. But t h ~ does in fact happen; instead, in terrestrial regions the variation in the [phenornena] cited is clearlj-rerj. considerable, in that the Sun sets and rises at different times at different places. For example, the Persians who live in the east are said to encounter the onset of the Sun 4 hours earlier than the Iberians who h - e in the west." This [variation] is also proven y. For the Stoics ("our school"; cf. Posid. TX-jEK)see SI~F2.648 and Posid. F18.20 and Fqy.6-; EK; for Plato see Pbmio 1 0 8 ~ - 1 o y a 6(R-ithFurley [1y8yb] 2 3-26), T h e "scientists" (hai ilpo tdii ~iricthi.wrot6ir) include, but are not restricted to, mathematical astronomers (see 11.6.122 ) . 10. O n this ar~urnent sce S1 F ' 2.241 (80.1;-20) and 2.24 j (82.34-83.3), and Sext. E ~ n pPH 2 . 1 j8. It has the form "either p or q or r," "not p and not q," "therefore r." T h e way that "not p" and "not r" are demonstrated in this chapter is via the Stoics' "second undemonstratcd ;tr~mment"(e.g., SCT 2.242, p. 81.1-1 2 ) , their equivalent of nroii~istoNciu; see n. 2 8 below. I I. For the Iberians as the westernmost inhabitants of the known \\-orld see lines 42-43 and 78 helow, and II.1.-tjg-q61; also Strabo 1.4.j and Aujac (1966)

T h e Heavens 1.5

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trorn other [pheno~nena] but particularl! trorn the ecl~psesof the heal enl! hodies, mhich, though they are eclipsed el erjm here o\er the same time

per~od,are still not detected at the same hour. Instead, the [heal -

enl) hod!] that is eclipsed among the Iberians in the 1st hour is detected as undergoing an eclipse among the Perslam in the jth hour, and proportionatel! elseuhere

"

(17) If the Exth's shape mere flat, the pole

aould he seen h! eler!one ~t an equal d ~ s t m c efrom the horizon, as nould the same arctic circle. Nothing like this is present in the phenomena, ~nstead,the elex ation of the [north] pole is seen as I er! small for the inhabitants of S ~ e n eand for the Ethiopians, yet as \ e r ) great among the Britons, and proportionatel? at mterx ening Iat~tudes.''(L) For ioineone lea\ ing tor the north from the south soirle of the stars that 'Ire seen 111 the south are concealed, and others prex iousl) out of sight come to be seen in the north, and the opposite happens to anyone M ho

184. Strabo 1.4.j and others usually cite India rather than Persia as the easternmost location. 1 2 . T h e sphericit!. of the Earth is hest demonstrated from the obsen-ation of lunar eclipses at ditferent times and locations; see Ptol. r ? h . 1.4, I j.12-13 and Tlieon Evpos. 1 2 I .j-I 2 . Plin.H '\. 2.180 uses both lunar and solar eclipse, in his argument for the Fkrth's sphericity, but because of lunar parallax, a solar eclipse \rill ditfer for different obsercers "at the same hour," and in some cases will not be seen at all. It is unusual in antiquity to find conlparisons of the Sun's rising times at different longitxcldes. i t is worth noting that Cleornedes' estimate of a +hour difference between Persia anti Iberia (Spain) n q - be hasetf o n reports of a lunar eclipse that \vas ohservecl simultaneously at Arbela on Sept. 2 0 , 331 B . L . , during :ilesander's campaign and at Carthage. Ptolemy (Geag. 1.4) says that the eclipse occurred in the 5th hour (of night) at Arbela and in the 2nd hour at Carthage, U hich would make the tiifference hetu-een times of sunrise there roughl!. 3 hours (though it should onl!- be about 21/4 hours). Pliny's report (1.H z.r80), ~vhichis better so far as it goes, maintains that the eclipse took place in the 2nd hour at Ahbela,hut says onl!- that it was seen at the same time that the .\loon rose (that is, at sunset) in Sicily See h'eugebauer (197 j) 667-668 and 938. 13. Syene is at the latin~deof the northern tropic (I.a.93, and lines jg-60 l>elo\v),uhile the Ethiopians are probably at the latin~tleof Aleroe, the southernrnost latitude identified in lists of latitudes; see 11.1.4;t0-441.

68 /

C'lroii~crlcs'T h e Heal ens

nlight go south from the north." None of thls v ould happen ~fthe Earth h,1d a flat shape that caused 1' smgle horizon. Therefore the Earth does not ha\ e t h ~ ss11'1pe. (d) Daj tlmes m o d d also turn out to be of equal length for everyone,[' although entirely the opposite is present in the phenomena. 57: (69 Indeed, if the Earth had a shape that was flat (i.e., a plane), the ( I ) People whole diameter ofthe com~osn.ouldhe ~oo,ooos ~ a d e s !Loo1i.l'~ at Lysimachia have the head of Draco 01-erhead, while Cancer is located above the area of Syene. ( 2 ) T h e "arc [of the meridian]" between Draco and Cancer is l/,; of the "meridian" passing through L!-sirnachia and Syene (as is demonstrated h>-sundials). [(?) S>-eneis zo,ooo stades from Lysimachia.I1y4) I/,; of the whole "circle" is '/, of the "dia~neter."~" 14. I t 1.3. I 2-43 the y'hericit! of the Earth \i as identified as the cause of these variations. 15. T h i s is a consequence of there I~einga single horizon; see lines 30-39 above. 16. This argument concerns the size of the ~ O S I / I U S . not tlic Earth (see Goulet zoo n. 162 against Seugebauer [ I L ) , ~ ]961-961 plus fig. ($7 a t 14o6), and must that invoked a bizarre costiiology ( L originally have \ ) e m a i . c d i r c . t i o iiiiizl~sicirlic~~~ milinr to Ptoleniy; s c e L i l / ~I . ~ , I I . I + - 2 4and cf. n. 2 1 helon) i n v hicli a flat Earth has the hewens parallel to it, rather t h m encirclinp it. This is the structure impliecl h!-assumptions (;) and (4)heion: i.e., if ofthe flat Earth's extent is ro.ooo stacles, its total extent is joo,ooo stades, or the same as that of the healens, lvhich must therefore be parallel to it. Hence "arc." "meridian," "diameter," and "circle" need to he used in quotation marks in this passage to reflect their etiolated me;~iiingwhen applied to such a nonspherical cosmology Floa-ever, by ha\-inp n. 2 I below). Clethe flat Earth surrounded l ~ ya sphere in tliis a r ~ i p n c n (see t onledes. or his source. has misrepresented tliis reasoning. TIence the figures in this passuge should be used I\ ith caution in historical or geographical reconstructions; for attempts 3t these see, for e w n p l e . 1 - e u ~ e b a u e r(1941). Collinder (1964), and Goulet 2 0 0 11. 162. see Introduction 11. j8), ~ v i t hfour I;. I f h a t follon-s is a "procedure" (t~pl~iiiiiis: overt assuinptions and an implicit axiomatic principle (see 11. 2 2 \~elo\v). 18. This is to anticipate the information given at line 68 helon-. ~ y This . is because the diameter of a circle is taken to he a third of the circur~iference,as at 1.;.118-1:o, and 1 1 . 1 . z y y j o o and 321-322.

T h e Heavens l.j

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63: So if, by hypothesizing that the Earth is a plane,'u u e produce perpendiculars to it from the extremities of the "arc" extending from Draco to Cancer, the! will [by (I)] touch the "diameter" [of the Earth] that measures the "meridian" through Syene and Lysimachia." Thus the distance between the two perpendiculars will be zo,ooo stades, since [by (')l there are 2 0 , 0 0 0 stades between S!-ene and Lj.sirnachia. So since [by (2) and (q)]this distance is '4of the whole "diameter," the m-hole "diameter" of the "meridian" will be ~oo,ooostades. So if the cosmos has a "diameter" of ~oo,ooostades, it will have a "great circle" of 300,000 stades2'-in relation to which the Earth, although a point [in relation to the cosmos], is zjo,ooo stades [in circumference], while the Sun is much larger than this, although it constitutes a minimal part of the hea\ ens.- ' ? 3

20. In the calculations of the size of the Earth or the Sun in I.; and 11.1,the sphericity of the Earth and the cosmos are, of course, implicitly assumed. 2 1 . See Figure I I . In order to reflect the misleading reasoning in this passage (see n. 16 above), the shapes of the flat Earth and flat heavens in this figure are finite and circular. They shoulrl he indefinite in shape and extent. As Ptolem!; Alm. I .3, I 1 . 1 4-24, argues, if both the Earth md the heavens are flat, the heavenly bodies will move in a straight line "to infinity," with no plausible eaplanation available for their rising and setting, or for their rectilinear motion ever heing re\-ersecl. Thus the problem that Cleomedes should be posing a flat-Earther is that the cosmos is infinite, rather than, as is concluded here, minuscule. z r . T h e calculation is implicitly based on the axiom that two quantities haw the same ratio to one another as the equimultiples of these quanta t ~ k c nin corresponding order (cf. Eucl. El. j prop. I 5). Tlmsif d is the diameter o f a circle, and c is its circumference, then il:r :: 1:3 :: 5 X zo,ooo:15 X zo,ooo. T h e sul~sequent calculations of the circumference of the Earth, and the size of the Sun, also rely on this axiom (see 1.7 nn. y mtl 2 1 ; 11.1 nn. j 8 and ;3), \rhich is known to have interested Posidonius (see 1.7 n. g). Perhaps the present a r p m c n t . more appropriate1)- articulated (see previous note), was originally Posidonius' ren'l/i.tio nd abswillrm of the theory of a flat Earth. 23. T h e comment follon-ing the dash may he Cleomedes' insertion, since if he, rather than any source, is responsihle for misunderstanding the cosmological assumptions of this argument (see n. 2 I above), he could now be drawing on Eratosthenes' calculation of the size of the spherical Earth (I.;.~oy-110). and allutiing to the later calculation ofthe size of the Sun (cf. II.r.;zq-325).

;o

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C'lro7~cries'T h e Heal ens

Surely it is obl-ious from this [argument] too that the Earth cannot be a plane? 76: That the Earth also does not have a "deep" (i.e., concave) shape may he seen from the following [arguments]. ( ~ 7 ) ' ~ If its shape were like this, daytime would begin for the Iberians before the Persians, since the protrusion [of one side] of the Earth would obstruct [the Persians] xvho are close to it, without impeding the line of sight for [the Iberians] who are at a greater distance away .lfter all, when any hollow object is out in the Sun, the part of it on the Sun's side is in a shadow when the Sun rises, whereas the part directly opposite is illuminated." So if the Earth's shape were concave, the outcome would be same throughout the n-hole world too: that is, people in the west would encounter sunrises earlier. But in fact the opposite is present in the phenomena. (It) _Ilso, if the Earth had this sort of shape, then for people in the south, the north pole uould he visible at a significant distance above the horizon, while it uould be obstructed for people in the north by the protrusion [of the side of the Earth closest to them]. And bj- the same token, given this shape, more stars would alu-ays appear visible to people in the south, and consequently their arctic circle would be larger. Entireljthe opposite to this is present in the phenomena. (c) Those living in the deepest part of the concavity ~vouldbe unable to see the six zodiacal signs above the Earth, and thus not even half of the equinoctial circle. For example, when we descend to a deeper place and look back toward the heavens, we see a small part of it, not the whole hemisphere.'"d) Sighttimes u-ould also alu-ays exceed daytimes, since the arc of the hea~-ens located below the convex part [of the Earth] xi-odd fir exceed the 24. Ptol. Alm. 1.4, I j.16-I; briefly notes this argument. 2 j . This use of any hollow object to illustrate the consequences of the Earth being holloa- is in line with Stoic accounts of concept formation "b!- analo~y"; see, for example, S I F 2.8; (with a parallel at 19.1j-16). 26. As at 1.8.130-132, valleys rather than subterranean locations (cf. 11.1.3844) must be intended here.

T h e Heavens 1.5 / 71 arc located above the concave part, assuming that the Earth is at the exact center of the cosmos. 98: If the Earth were cuboid (i.e., square), the result would be a daytime consisting of 6 hours and a nighttime of 18, given that each side of the cube would be illuminated for 6 hours. But if the Earth were like a pyramid too, each side of it would be illuminated for 8 hours.27 102: So if the phenomena demonstrate that the Earth has none of these shapes, it is necessarily spherical in accordance with the fifth [undemonstrated argument] from multiple [disjuncts].But it can also be demonstrated directly that the Earth is spherical by starting out in the same way from the phenomena, given that precisely the same [phenomena] that demonstrated that the Earth had none of the [non-spherical] shapes listed above demonThat is, horizons on the Earth alter, and the strate that it is ~pherical.?~ following are not observed as being identical everywhere: the stars in the north and the south, the elevation of the pole, the size of the arctic circle, and the lengths of nighttimes and daytimes. All these phenomena clearly demonstrate that the shape of the Earth is spherical. For it is impossible for any of them to occur with a different shape,29but it is possible for properties of this kind to be displayed only in association with a sphere. 114: when at sea we are about to approach land, our line of 27. Ptol. Alm. 1.4,' j.19-23 also mentions a triangular and square shape, and notes that they would be subject to the arguments against the Earth's having any polygonal shape. 28. T h e reasoning at lines 30-101 has been "indirect." T h a t is, if "p entails q" is the direct argument (i.e., given phenomena entail that the Earth is spherical), then previously the argument form was "not-q entails not-p; but p; therefore, not not-q," i.e., modus tollens (see n. 10 above). In other words, nonspherical shapes are eliminated because they entail impossible phenomena. 29. For these arguments used to eliminate nonspherical shapes see lines 30-39, 44-49, and 54-56 above, and cf. 1.4.239-242. 30. This is an elementary application of the argument from changing horizons at lines 30-39 above. Cf. 1.1.183-190 where it is used in a slightly different form as a preliminary proof of the sphericity of the cosmos.

;z

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C'lmn~eiles'T h e Heavens

sight first encounters ~nountainpeaks, while everything else is obstructed by the Earth's ~ u n - a t u r e . Next, ~' as we go 07-er the curvatures, we encounter in the course of the journe! the sides and spurs of mountains. A l n duithin the boats themseh es, x ~ h e n15 e ascend the mast and get above the obstructing curvatures, we invariably see those parts of the land that dre invisible from the decks and the hold. Also, when a ship leaves land, the hulls disappear first, although the masts are stdl lsible; but u hen it '~pproachesland from the sea, then, b) the same token, the masts are seen first, xr hile the hulls are stdl obstructed b j the c u n ature of the u ater. V1 these [phenomena] ~ n d ~ cthrough ~ ~ t e irtuall> geometrical demonstrations that the shape of the Earth 1s spher~c'~l.''

126: It is necessx!,

then, that the air enclos~ngthe Earth also be a

sphere, since exhalat~onsfrom the u h o l e of the Earth rise and flou together, and thus fashion the same shape for the air too." (Solid bodies can also, of course, have numerous configurations, but in the case of a substance that is composed of pneuma o r of fire,'+ wherever [such types of matter ] exist independentl!; nothing like this can happen. T h i s is because they reach the shape proper to their- nature h!, being "tensionized," that Is, b! bemg stretched equall! in all directions from the exact center [of the Earth], since their substance is rnalleable, meaning that nothing

If the Earth has 1' "cun-aturr" (kici-tiiilit: here and a t lines 118, 1 2 0 , ancl since cunature, define sphericity (cf. 1.1.24; and 2 jo), this argument contains apetitlopi.ii~i.ipi~.Ptul. . - l h . 1.4,I 6.13-18 argues more carefully that the surface of the sea causes the land to appear to "rise up" as we approach it. For other versions see Plin. A7H 2.164. Straho 1 . 1 . 2 0 (= Posid. 3b Theiler), and Theon Expos. 12 2.17-123.4. 32. Cf. alqo 1.8.17-18 o n geornetrization. 3 3 . O n terrestrial cshalations cf. SI F ' 2.5 2 ; (I 68.2 j-2 h). and see 1.8.;9-88. l'he arpnient from here to line I 38 was outlined at lines 6-9 ahol-e;see notes 4 and j al~ove. 34. Pneuma is a compound of air and fire (e.g.. SI F 2.442), and so the nvo elements identified here. the air and the aether, can also form a realm of matter describable as "con~posedof pneurila or fire," since they represent pneuma in its purest for-rn,unafhcted h-! solid matter. 31.

124 above), then,

T h e Heal ens I.j

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73

solid exists which would configure them differently3') Since the air is spher~c,~l, so too 1s the 'lether, since [the 'lether], being In turn hie to enclose the

m d n e ~ t h e hemg r bent into angles h! m! thmg

5011~1,nor >

ha\ ing m! thmg forcmg ~tinto some shdpe u ~ t m h e \ en lengths,'

15

it-

t xr hole cosself neces5anlj a sphere. So it 1s absolutel) necessar! t h ~the mos too h'ne such 1' shape." I 39:

It 1s also entirelj plmalble that the most complete of hodles has

d c o m ~ o is s the most complete of ,111 the most complete of shapes. L k ~the bodies, u hile the sphere 1s the most complete of a11 shapes. For the sphere , no other can enclose ex ery s h ~ p et h ~ ht ~ the s same diameter as ~ t but shape can enclose a sphere that has a diameter equal to it."' So it is ahsolutel! necessary that the cosrnos be a sphere. 3 j. I'neuma holds the Stoic cos111os together 111. "tensional motion" (see 1.1.7z-73). TIence non-solid matter is next said to haw a sphericit!- that results from being "tensionized" (toizoiathni), i.e., from the oscillation of pneuma from the center to the periphery of the cosmos ant1 hack to produce a "stretching effect" (the literal meaning of taizos). 36. Ptol. . i h . 1.3, 13.21-14.16 argues that the aether (for hi111 irn~nutnl,le)is spherical just because of its homogeneity and I)ecause it is occupied h!, ohserva11l~-spherical bodies. 3 7 Sec 1.1.166-168 for the contrast lxtween splicricit! anti shapes ith uneven lengths. ;X. See also S1 7: 2 . j47 and 681, and Posid. FIIEK. for t h ~ sconclusion. Uthough the present argument emphasizes the relative density of the elements. dntl the c d p ~ c ~ ot t ! the I~ghterones for pneummc, or tens~onal,motlon. ~tneed not contl~cta i t h the ea-ltel p r ~ n u l ~ (1.1.94-9 le j, 173-I;+ and r o r - ~ c ) ~t)h. ~ t ,111 the elements ,Ire c e n t r ~ p e t ~Furle! ~ l . (1993) defends such 1' s! stem ot d\n,uiit l~ghterI ~ o d 1's. \ \ i ~ l t t(1988) 497-5 33 ~11d$39- j42. ho\\e\er, suggests t h ~the le5 push the he,nler ones to the center m d mole clround the111 In J ~ortex-like motion. 30. For this claim see PI. EIII. 33111-7. lrist. L)esmlo 2861125-33. Cic. L)? i ~ t . h i : 2.47, S I T 2.1009 ( z c ) c j . ~ j - ~ q ) ,and cf. Ptol. .-///H.1.3, rj.r+zo. Cleoliicdcs' \.ersion holds for the fir-e regular solids; see Eucl. El. I 3 props. 13-1 8.

CHAPTER SIX'

TT'e shall establish that the Earth occupies the exact center of the cosmos, by which it is enclosed, by again' starting out from the procedure based on the fifth undeinonstrated [argument constructed] through multiple [disjuncts]. T h e following disjunction, that is, is necessarily true: T h e E N ~r h ,i c h is eelzcon~pirssrtlOy the cosmos, is cithei- i n its m s t , or- its r e s t . 07. its ~ z o r t h 01, , its south. or bigher t h m its center o r l o w r - o r it occupies its ex. i othe ~nct centel: But, as we shall demonstrate, noue of t h e @ r o p o s i t i o ~ ~ . ~ p fto Imt is t m e . Therefore, it is im.cs.riri:y t h n t t l ~ eEriith occl~pythe srlztei. of'the COSI?l 0s. 9' That it is not in the east is clear from the following. (g) If it were in the east, then shadows from objects illuminated at sunrise would be I:

I . This whole chapter can he compared with Ptol. .-h. I. j, which is diagrammaticalli- analvzed at Pedersen (1974) 39-42 T h e argrinients here also assume the thesis of1.8, that the radius of the Earth is negligible in relation to the distance from the Earth to the Sun, or to the edge of the cosmos, i.e., that the obsen-er is effectively at the center of the Earth. T h e theses of 1.6 and 1.8 are thus comentionally linked; see Eucl. Pham prop. I (10.11-12), Gem. Irng. 16.29, and Theon E.vpo\. 12o.11-12. 2 . See I.5.23-26. 3. .It Ptol. .-ilmI.. j, 17.4- j such displacement is described as a case of the Earth's not being on the axis ofthe cosmos, hut still equidistant from both poles.

The Heavens 1.6

/

jj

shorter, hut at sunset these uould be sent out farther, that 1s becduse hen objects that glre out 11ghtare nearby, shado~rs[cast bp them] are shorter, hut u hen the! are more d~stant,shadous are In\ , ~ r ~ a benlarged lj In proportion to the d ~ s t a n c e(I,) . ~ If n e \\ere closer to the east, all the [heal enly bodles] n ould appear larger to us as the! 15,

rise, U hde

on settlng (that

as the! continually v, ent farther au a!), they n o d d appear smaller.' (c)

T h e first SIY hours of the daytme mould also be er! short, smce the Sun T\

ould reach the zenlth rapldlj, \I hereas those hours after the s~xthn ould

he lengthened, gnen the greater distmce from the zemth to the \\est." None of these [obsenations] IS present Among the phenomena. Therefore the Earth 1s not farther east. Yet b! the same token ne~ther1s ~tf ~ r ther to the vest, othern~seall the [obsen at~ons]\+oultlas a result be the opposlte to those just descr~bed 22.-

But if the E x t h u ere fa-ther north, then u h e n e ~ er the Sun rlses,

shadons trom objects ~llummatedb) ~tU ould as a result extend 111 the dlere in the south, sh~clovs 15 ould also rectlon of that reglon. And ~f it 1% slope southm ards, both mhen the Sun uses and n hen ~tsets. In fact none

ot t h ~ occurs, s but at the equlnoxs, v, hen [the Sun] nses, shadou s slope settlng [point], and rzhen ~t sets, ton ard \r here ~tsets at the equ~noct~al the! slope tonarci rr here ~tr~sesat the equlnoct~alrlsing [point]. But at 4. T h e longer shadous will, g i \ w (L;) below, also he cast for a longer period of the daytime. 5. Cf. I'tol. L-fl/w.I . 5, 18.5-8, anti in the Cizch-tin cf. 1.8.32-3 j . 6. Ptol. .4h.1.5, 17.9-18.4 notes only the elimination of the equinox, here left implied. .; Ptol. L41/v/.I. j, 18.12-10.8 describes this as a case of the Earth's being on the axis of the cosmos hut tlisplaced toward one of the poles. H e rejects it h!. using the same evidence of the altered visibility of zodiacal signs usecl here at lines 33-35 against the Earth's k i n g "higher" or "1o~vt.r"than its central position. T h e latter c;ws are identical with the present case of displacement toward one ofthe poles, and this seems to he acknouledged in the summary at line 40 h e l o ~~vhen only "four regions" of displacement are noted. T h e six catalogued in this chapter M ere perhaps intended to correspond to the six noncentral directions identified at 1.1.1jo-1.~8.

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Cli~omr~iec' T h e Hear ens

inter solstices n hen [the Sun] sires, [shadou s slope] tov drd n here it sets at the summer s~lstitialsetting point, and U hen it sets, [the) slope] to\$ard v here it rises ,1t the summer solstltidl rlslng [po~nt].But \then, hack < u p Xfrom the south, it rises [at surnmer solstice\]," shadon-sslope toward where it sets at the winter solstitial setting [point],

but a h e n it sets, they slope tom ard ~111ei-e~t rlses at the uinter solstitial r~siilg[point]. Thus [over the course of a year] the shatlom s foriil a chi~ s m u s . "Therefore the Earth 1s not In an) of these regions.

3 3 . If the Earth U ere h ~ g h ethan r the center, then the half of the heal ens a l ) o ~ ethe Earth uould not be ~ i s i b l e nor , \ ~ o u l dthe

SIX

~od~acal

signs (I.e., 180degrees), nor half of the equmoctial circle, hut less than

,111 these

[nould be 1 isilde] . l 1 Hence nighttimes too v ould as a reault

dn 1' ) 5 be longer than daj-t~mes.But if the Earth r$ere lov er than the center, the result n oulcl he the complete opposite to n hat has just been descr~bed,since the hemisphere abox e the Earth ould be larger." [ T h ~ s does not happen.] Therefore the Earth is at neither a higher, nor a lower, position. 8. T h i s supplement tr~inilates61a ~ p ; ? ; w ~proposed ,, for a lacuna in Cirdcrtiir e ~ I . ~ ) dapparatus d, criticus at T .6.29. .l\er11 is neccled here to complenlent ; i & , G t ("thence," i.e., hack again froin the \outh). y. T h i s gloss is needed to I x h n c e "at \{inter solstices" (line 28), and is i n plied h!- "back up." 10. This chiasmus, or "decussation." in\ olt-cs t\vo cliagonals for the solstitial shadons; see Figure 1 2 . T h e illustration could he Positlonian, given that at I.+ I 32-146 (cf. Figure g) zones are defined in terms of shatlons in a passage that c m he :~ttributedto him; see 1.4 11. 33. r I . Throughout this paragraph the ohserl er is assumed to he at ground l e d . O n the special conditions under which less than 180degrees are seen in this position from a centrally located Earth see 1.8.1~;-I3 2 and 1.8 n. 33. I 2 . \ l o r e than I 80" would be isihle k o n i a centrall!- located Earth if the Earth were large enough. or the cosrnos suficiently sniall: see 1.8.134-139 anti 1.8 n. 34. and II.6.12z-138 and 11.6 11.16. Also, under norrnal conditions, the refraction of light h>-the air at the horizon enables m!- terrestrial ohsen-er to see slightly more than half of the celestial sphere at any time.

T h e Heatens 1.6

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77

40: It has been denmnstrated that the Earth 1s not In an> of the four regions [rnentloned abc)~. e].l Therefore

it

1s necessar! that it occup! the

exact center of the cosmos. (I11 addit~on,the Earth

IS

the heal lest of the

bodies in the cosmos, m d so must occupl the [place] farthest dot! nu arda, n hich [in a sphere] 1s dlso identical n ith the exdct center.)I4

13. See 11. ;above. 14. This refers to the centripetal motion of the elements (the demonstration of n-hich was lmstlmned at 1.1.yf-gj, I 73-174, and 191-192; see Introtluction n. h), n.hich mill establish that the Earth is stable at the center of a spherical anti stable cosmos, and so rule out saving the phenomena introduced in this chapter (like many of those in I.j and 1.8) by a different cosmological arrangement (see Introd. n. 23) Ptol. ,4h.1.j-6 (his equivalents to C~7elcstu71.6 and 1.8) are immecliatel!, followed by a demonstration (I.;) that the Earth is immobile h!- a ph>.sical theory broadly similar to the Stoic theory of centripetal motion; see IThltf (1988) 498-502.

CHAPTER SEVEN

I : Natural

philosophers have held numerous doctrines about the size of

the Earth, but two of these are superior to the rest. Eratosthenes' doctrine demonstrates its size by a geodesic procedure,' while Posidonius' is less complicated. Each [philosopher] takes certain assun~ptions[as bei n g the case], and t h e n arrives at demonstrations via t h e implications of the assumptions. T h e first [doctrine] that m-e shall discuss is Posidonius'.' 7: H e states that (PI) Rhodes and Lllexandriaare located below the same meridian.' (D$ I ) Meridians are the circles drawn through the poles of the cosmos, and through a point that lies at the zenith of each of those I. Our translation reflects Gratwick (199j) 178 11. I . IIXile the procedure here that term cannot mean "geometrical." since Posidonius as is called gr~ow~rti-lkos, v-ell as Eratosthenes (ca. 276-194 B.c.) employs geometry. 2. For literature on this calculation see Kidd Comm. 718-729; add Taishak (1973-74) and Gram-ick (19gj). See also Fi~mre13. In this calculation and that of Eratosthenes below the unit of measurernent used is the stade. Since it was never standardized, its value is difficult to deter~ninefrom the ancient sources, and it cannot he readil!- translated into motlern T-aluesfor comparative purposes. For further discussion see Lloyd (198;) 233-zj;r, and the literature cited at Chnzilez (2000) 2 I 6-2 17. 3. This \%IS the standard riev (Ptol. A7n. j.3, 364.9-10 and Strabo I.j.;; cf. Toonier [l9841 z j j 11. 16), although Rhodes is in h c t 1'50' west of Alexandria.

'The Heavens 1.7

/

79

[observers] who stands on the Earth. (Thus, while the poles are the same for everybody, the point at the zenith is different for different [observers], which is why infinitely numerous meridians can be draum.) Rhodes and Alexandria, then, are located below the same meridian, and ( P 2 ) the distance between the cities is held to be j,ooo stades.+ Let it be assumed that this is so. (DeJ2) All the meridians are also included among the great circles in the cosn~os,since they divide it into 2 equal parts by being drawn through its poles.' IS: Now with this assumed to be the case, Posidonius next (P?) divides the zodiacal circle (which, since it too divides the cosmos into 2 equal parts, is [by def 21 equal to the meridians) into 48 parts by dividing each of its ~16dekatimor.inhinto quarters. Now if the meridian through Rhodes and Alexandria is also divided into the same 48 parts as the zodiacal circle, then its sections will be equal to the sections of the zodiacal circle just identified. T h e reason is that (def j) when [ z ] equal magnitude~are divided into equal [parts], their parts must also be equal to the parts of what has been divided.;

4. ''IS held" ( S O K E ~ (14-1 ) j; also line 43 below) here i~nplies"generally believed on good authority"; cf. 1.2.26-2 j and 11.3.18 for this sense, and 1.4.197and 11.7.1 for figures cited on external authorit5 without 199, ~ I . I . + ~11.3.10, I, resen-ations. Kidd COVIWZ. 726, however, calls the ~lurnbergiven in (Pz) "hypothetical," and claims that the whole Posidonian calculation reported here is designed to illustrate "the hypothetical method rather than the accuracy or certainty of the figures." But even though Posidonius uses a method of calculation that can be identified independently of the numbers used (see n. 9 below), that does not make the numbers cited "hypothetical." There is a significant ditference between using numbers that have some reasonable credibilitl; and arbitrarily (or hypothetically) stipulating nulnhers to facilitate a calculation (as at 11.1.27427-5 in Posidonius' measurement of the size of the Sun). T h e number in (Pz) is clearly of the former kind. See also 11. I I belou; j. O n the definition of great circles see 1.3.j6-62. 6. O n this term see 1.4 n. 17. 7 . Compare Eucl. El. I , ,Yet. wnm. 3 (j.11-I 2): if equals are subtracted from equals, the remainders are equals.

80 / Cleomedes' The Heavens

27: S o u -with [(PI)-(P?)] assumed to be the case, Posidonius nest says that the star called Canobus, which is located in the south at the rudder of &go, is very bright.%(This star is not seen at all in Greece; that is why Aratus does not mention it in his Phnenon~eifn.)But for people going to the south from the north, the star starts to be seen at Rhodes, and once seen on the horizon immediately sets along with the revolution of the heavens. But when u-e reach Alexandria by sailing the j , o o o stades from Rhodes, this star, when precisely at the meridian, is determined as being elevated above the horizon of a zodiacal sign, that is, [by ( P I ) and (Q)] 1/4b of the meridian through Rhodes and Alexandria.

38: S o w it is necessary [by (PI) and (P;)] that the section of the same meridian located above the distance separating Rhodes and Alexandria also be '/,g of that meridian, because the Rhodians' horizon is also distant by of the zodiacal circle from that of the Ale~andrians.~ S o since [bp (P41 the portion of the Earth located below this section is held to be 5,000 stades, the portions located below the other sections also consist of j , o o o stades. _Indin this way the circumference of the Earth is determined as 240,000 stadesl"-$[by (P211 there are 5,000 stades bemeen 8. O n Canobus (sometimes spelt Canopus) ( a Carinae), the brightest star after Sirius, see Aujac (1975) 132 n. 6 (on Gem. Isng. 3.1j), and E d d Comm. 72 j-726. 9. In Figure 13, since RI' is parallel to X1; angle .?&'V = a (Eucl. El. I prop. 2 9). Since triangle APV is similar to triangle RTI;angle RTaA = angle APIT= U . T h e three ratios that are identical in this calculation (cf. I. j n. 22) are 1 4 8 :: I/, didekat?mol-io7z:fullcircle :: j,ooo:24o,ooo stades (on the numbers in the latter see n. 4 abol-e). Since the same basic principle or axiom underlies Eratosthenes' calculation (n. 2 1 belon-), Posidonius could be the source for both reports in this chapter. H e was certainly interested in relations between ratios; see Galen hst. log. 18 (cf. F191.13-I j EK), and 011the asion~atizationof such relations, see Hanhnson (1994) 73-74. 10. Strabo 2.2.2 reports "about iperi) 180,000 stades," i.e., joo stades per degree of the circumference. This implies a distance of 3,; 50 stades between Rhodes and Alexandria, the figure that Strabo 2.5.24 says that Eratosthenes calculated by the use of sundials.

T h e Heavens I.;

/

81

Rhodes and Alexandria. Otherwise, [it will be determined] in proportion to the [true] distance." That, then, is Posidonius' procedure for dealing with the size of the Earth. 49: Eratosthenes' [calculation], by contrast, involves a geodesic proBut cedure, and is considered to possess a greater degree of ob~curity.'~ the folloving [asw~nptions],when stated by us as presuppositions, will clarif! 111saccount. 51: Let us first assume here too [cf. (PI)] that (Er) Syene and Alexandria are located belom the same mer~dian;[second] that (E2) the d~stance , that (E?) the hetueen the t u o clties 15 5,000 stade\.13 T h ~ r d [assume] rays sent domn from different parts of the Sun to different parts of the Earth are parallel, as georneters assume to be the case.'+ Fourth, let the folloming assumption demonstrated by geometers he made: that (E4) straight lines intersecting with parallel lines make the alternate angles equal.'' Fifth, [assume] that (Ej) the arcs [of a circle] standing on equal angles are similar, that is, have the same proportion (namely, the same 11. T h e gloss "true" is justified here, since the figure of ~ , O Gspades G is onl!. "held" (i.e., widely believed) to be true (see lines 14-1 j and 43). Kidd C'unrm. 716-72; again (cf. 11. 4 above) sees the m 3 e a tin line 46 as evidence of Posidonius' u i e of "hypothetical method." But aside from an uncertainty as to whether this ca\eat \\.as entered h-! Posidonius or Cleomedes, for Posidonius to admit qua11titati~-e corrigihility (cf. also 1.4.208-213 and 11.3.40) would scarcell- slio\r that he "a-as not primarily interested in figures or in accuracy" (Kidd Conu~r.7 2 7). In since the same basic principle or axiom underlies the two calculations reported in this chapter (see n. 2 1 belou), it is even conceivable that Posidonius \+as the source for both of them. I 2. 011 Eratosthenes' calculation see Figure 14. For discussions see the literature cited at L1q.d (198;) 231 n. j j; note especially Taisbak (1973-74), Newton (1980). Rawlins (1982a) and (198zh), and Cratwick(19gj). For fi~rtherliterature see Gonzilez (2000) ~IL+-zI;. 13. Syene is in fact ahout 3" east o f Alexandria. 1;or ( E r ) and (EL) see also Straho 2. 5.7, where (Er) is qualified as "approximate." 14. Cf. also 11.1.197-zoq for this assumption. r j. Eucl. El. I prop. 29.

X2

/

C I P O ~ I / PT~hCe SHeavens '

ratio) to their own circles, as is also deinonstrated by geometers.'"For example, when arcs stand on equal angles, then if one of them is onetenth part of its own circle, all the remaining arcs will also be one-tenth parts of their on-n circles.)

64: Someone who has mastered these [assumptions] would have no difficulty in learning Eratosthenes' procedure, which is as follow^.^' H e says that ( E I ) Syene and Alezandria are located below the same meridian. So since (drf: 2 ) the meridians are included among the great circles in the cosmos, the circles of the Earth located below them are necessarily also great circles. Thus the size that this procedure demonstrates for the [arc of the] circle of the Earth through Syene and Alexandria will be in a ratio with the great circle of the Earth.'" 71: Eratosthenes says, and it is the case, that (E6) Syene is located below the summer tropical circle.'"^ when the Sun, as it enters Cancer and produces the summer solstice, is precisely at this meridian, the pointers on the sundials are necessarily shadonless, since the Sun is located vertically above them. (This [shadowless area] is reportedly 300 stades in diameter.)"' Rut i n rllexandria a t the same hour pointers on sundials do cast a shadow, since this city is located fi~rthernorth than Syene. Nou-

16. Compare Eucl. El. j def. I I , U hich concerns segments. 17. As befits a pedagogical treatiie, the basic method of calculation is summarized in advance, as at lines 2 1-26 abow. 18. Lines 104-106 below- ofter the justification for translating the correlatives here ( ~ ~ X K O . . ST. ~ ~ ~ K Oas~ referring ~ T O S )to a ratio. 19. For this location see 1.4 n. 1 I . For the absence of shadon- at Syene at the . summer solstice see Ach. Isng. 67.5-6. Plin. LYH2 . I 83, Ptol. A 4 h 2.6,10;.16-20. and S t n b o 2 . j . ~ ro. Onl?- Cleomedes, here and at 11.1.211-213 and 270-273, provides this T-alue.Three hundred stades are %, of 240,000 stxies, or g,, of 180,000 stades, the tv-o figures for the Earth's circumference attributed to Posidonius (see n. 10 above). Neugebauer (19;j) 6 j j - 6 j 6 , however, suggests that the figure of 300 \?-as derived from the tiernonstration h?- water clocks that the Sun is TjOof its o u - t ~orbit (see I I , I . I ~ ~ - Iwith ~ I )z40,ooo statics / 750 = 320 stades, rounded off to 300 staties.

T h e Heavens 1.7 / 83 since [by (EI)]the two cities are located below a meridian (a great circle ) ] ) , if we draw an arc from the tip of the pointer's shadow on [by (def: z the sundial at Alexandria round to the base of the pointer, this arc will be a section of the great circle in the sundial's bowl, since the sundial's bowl is located below a great circle. 84: If we next conceive of straight lines produced through the Earth from each of the pointers, they will coincide at the center of the Earth. So since [by (E6)] the sundial at Syene is located directly below the Sun, then if we also conceive of a straight line going from the Sun to the tip of that sundial's pointer, the line going from the Sun to the center of the Earth will be a single straight line. If we conceive of a second straight line drawn from the bowl at Alexandria, that is, from the tip of the pointer's shadow up to the Sun, this line and the first one will be parallel [by (E?)], since they extend from different parts of the Sun to different parts of the Earth. 94: Now a [third] straight line extending from the center of the Earth to the pointer at Alexandria meets these parallel lines, and as a consequence [of (E4)] makes the alternate angles equal. One of these [angles] is at the center of the Earth where the lines drawn from the sundials to the center of the Earth coincide. T h e other is where the tip of the pointer at Alexandria and the line drawn from the tip of the pointer's shadow up to the Sun through the point where the line touches [the tip] coincide. T h e arc drawn from the tip of that pointer's shadow round to its base stands on this second angle, while the arc extending from Syene to Alexandria stands on the angle at the center of the Earth. 103: Now the arcs are similar to one another, since [by (EJ)] they stand on angles that are equal. Thus the ratio that the arc in the bowl [at Alexandria] has to its own circle is the same as the ratio of the [arc] from Syene to Alexandria [to its own ~ i r c l e ] . ~T'h e arc in the bowl is certainly determined as one-fiftieth part of its own circle. So the distance from Syene 2 1 . There are in fact three ratios here that are the same: I: j o :: %, circ1e:full circle :: ~ O O jo,ooo O : ~ stades. Cf. n. 9 above.

84 /

Cleomedes' T h e Heavens

to LUexandria is necessarily one-fiftieth part of the great circle of the Earth: namely [by ( E 2 ) ] j,ooo stades. Therefore, the [great] circle [of the Earth] totals 2 ~ O , O Ostades." O And that is Eratosthenes' procedure. 111: Also, at winter solstices sundials are positioned in each of these cities, and when each sundial casts shadows, the shadow at Alexandria is necessarily determined as the longer because this city is at a greater distance from the winter tropic. So by taking the amount by which the shadow at Syene is exceeded by that at Alexandria, they also determine this amount as one-fiftieth part of the great circle in the sundial. So it is evident from this [calculation] too that the great circle of the Earth is 2jo.000 stades.!' Thus the diameter of the Earth will exceed 80,000 stades, given that it must certainly be '/i, of the great circles of the Earth.'+ 1 2 1 : Those n-ho say that the Earth cannot be spherical because of the hollows occupied by the sea and the mountainous protrusions, express a quite irrational doctrine.!' For neither is there a mountain determined higher, nor a depth of sea [greater], than

Ij

stades. But 30 stades has no

as 2 jo,ooo stades. For 2 j2,0o0 stades see Galen 111.rt.log. 1 2 . 2 (26.21-z;.~), l'lin. .VH2.24;, Strabo 2.j.; and 2.j.34. Tlieon Opo.,.. 124.ro-rz, andyitrul: D P N I Z ~ . 1.6.9. 23. See Figure I j. Bouen (2002) notes that Cleornedes, in relying on Eratosthenes' figure for the size of the Earth in other arguments (1.j.;~;II.1.zy429 5). may be indicating that he considered it superior. If so. the point of his mentioning this new computation (the work of an unidentified "they") Inay be that it replicates and c o n f i r m the one attributecl t o Eratosthenes at lines 6+1ro. thus making the procedure common to both more relialde than Posidonius', which (see n , I r abul-e) used reported and questionable information for a crucial premise. 24. For the diameter as y of the circumference of the circle see 1.5.62-63, and II.1.29j-301 and 320-323; also G e m . Isi,'? since there oh\ iouslj cannot be sex era1 centers belonging to a single sphere. This means that the pointers on all the sundials that can be marked out on the Earth have precisely the ratio [to the heliacal circle] they nould ha\ e even if they were conI;. See also Ptol. L.ih~i. 1.6, 20.13-19. Theon E.vpos. rz8.j-11 (after emenclation), and Calcid. 112 T i t n . I I 1.8-1;. 18. Iliad 8.485-486; cf. also 1 1 . 6 . 2 2 - 2 3 . 19. Sec 11.6.4-8. 2 0 . They represent the diurnal course follo\r-et1by the shadow cast by the unilluminated portion of the Earth, and so, in the literal sense of the x r h used (s~r?~lpe~.iilosteiil). they "corne hack home [to their original position] by going round with" that larger shadon-. 2 1 . T h e sphere is "conceived" or "imagined" (i~ourmei~?) (cf. line 77 below, and I1.1.72),since it is like the limit of a hod!; which in Stoic o 1 1 t o l o ~"subsists in mere thought" +at' iyiizoini1 psilcn): cf. S1F 2.488. 2 2 . T h e sentence in angle brackets has heen transposed frorn lines 66-67 above, where it interrupted the argwnent.

The Heavens 1.8 / 91 tracted into a single point.23So since there is no part of the Earth on which a sundial could not be set up, the whole Earth has the ratio of a point to the Sun's height and to the sphere conceived of from it. 79: N o problem need be raised here about how the Earth, with the status of a point in relation to the size of the cosmos, sends nutriment up to the heavens, as well as to the bodies encompassed by them, despite the heavenly bodies being so large in number and size.24That is because the Earth, while minuscule in volume, is vast in power in that virtually alone it comprises most of the substance [of the cosmos]. So if we imagined it totally reduced to smoke or air, it would become much larger than the circumference of the cosmos, and not only if it became smoke, or air, or fire would it become much larger than the cosmos, but also if it were reduced to dust. (We can, for example, see that even wooden objects that disintegrate into smoke expand almost without limit, as does vaporized incense, and every other solid body that is reduced to vapor.) And if we imagined the heavens, along with the air and the heavenly bodies, contracted to the compactness of the Earth, they would be compressed into a volume smaller than it. Thus while in volume the Earth may be a point in relation to the cosmos, since it has an indefinable power (that is, has a natural [capacity] to expand almost without limit), it does not lack the power to send nutriment up to the heavens and to the bodies in them. And this [process] would not cause the Earth to be totally expended, since the Earth itself also acquires something in turn from the air and the heav2 3 . Goulet (204 n. 206) claims that here Cleomedes has forgotten the principle underlying Eratosthenes' calculation of the size of the Earth in 1.7: that shadows vary depending on the latitudes at which sundials are located. But the present argument turns on the observation that in defining the paths of shadows in sundials, no account need be taken of the size of the Earth; see Ptol. Alm. 1.6, 20.16-19. 24. Terrestrial exhalations are celestial nutrition in Stoic cosmohiolog~.;see, for example, SVF 2.6 jo (196.8-1 I), 663, and 690, Posid. FIoEK, and cf. Cic. De

92

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C'k.07~1edes'T h e Hear ens

ens. For "the way up is the way down" (to quote Heraclitus)," given that substance [of the cosmos] is naturally disposed to be completely transformed and changed by yielding in every W-ayto the artificer for the administration and continuing stability of the whole cosrno~.~" 100:So while the Earth has the ratio of a point to the height of the Sun, some use arguments of the following kind to establish that it does not have the ratio of a point to the sphere of the 21oo11.'- (4 T h e distances of the [lunar sphere] from the fixed stars are said not to appear equal at every latitude, but larger and smaller at the same hour for different [observers]. Yet this would not be the result if the straight lines drawn from the Earth to the height of the ,\loon were equal, for then the distances of the [lunar sphere from the fixed stars] would also appear equal. (I,) T h e eclipse of the Sun is also adduced as a sign2%f this [conclusion], in that it is not eclipsed to an equal extent for all [obseners], but it is frequently eclipsed totally, partially, or not at all for different [obsen-ers].'" This would not result if the Earth were a point in relation to the height of the 31oon rather than being at an [obse~~ationally] significant distance.

DK zzB60. This "craftsman" (dt;n?iozi~~os) is fire, or an "artificer" (tekbnifios)(e.g., SJ'F 2.103 2). T h e active principle in Stoic physical theory also "crafts"; see SIVF 3.300. 27. See Plut. De fiu. 92 I D (cf. Chernis5 [ I y 511 I 38) on "certain rnathematicians" who were said to argue that there is no lunar parallax. T h e question of lunar parallax (that is, v-hether obsen-ations taken on the Earth's surface can for practical purposes be treated as though they were taken at the Earth's center) is different from the question about whether the Earth is at the center of the lunar sphere. Note that Cleornedes speaks of the E,arth as having the ratio of a center to the solar sphere, but does not think that the Earth lies at the center of this sphere (cf. 1.4.53-62). Cf. also Ptol. Alm. 4.1, esp. 266.1-4. .histarch. DL'm p . prop. 2 (352.5-6) does not allow for lunar 1)arallaa. 28. A sign @mcion) is an observable indication of something that is not tiirectly obsen-able (cf. si.meiootni at 11.1.216).On the elaborate theorj- of signs in Stoic epistemology see Burnyeat (1982). 2 9 . That is, it is often the case that a siiigk solar eclipse is obserwd as total or partial by different observers, W-hileheing invisible to everyone else. z j. See Heraclitus at 26.

TheHeavens 1.8 / 93

And this is why the Moon conceals [the Sun] either totally, partially, or not at all for different [observers]."' 113: Some use the following arguments to claim that the Earth does not have the ratio of a point [to the size of the cosmos]." 114: (a) They say that when elevated our sight observes objects that are not observed at ground level but are concealed beneath the horizon, and it does this to an increasing extent the higher it is elevated; therefore the heavens are not divided equally from every part of the Earth, and this is considered evidence that the Earth does not have the ratio of a point [to the size of the cosmos]. Our response snust be that this [kind of observation] is caused by the sphericity of the Earth's shape. Thus even if the Earth were one spade in size, the result would be identical, just as long as the Earth is centrally located [in the cosn~os]and has a spherical shape. (And of course it could not be claimed that an Earth of such limited size did not have a ratio of a point to the cosmos!) So in this case the Earth's shape must be held to he the cause. 124: _Use, if someone extended in thought a plane from every point on the Earth,'! there would not be snore, or less, of the heayens seen above the Earth, but an equal amount at an elevation as well as at ground level.

Of course the size of the heavenly bodies appears equal at an elevation as 1%ell as at sea lexrel. 127: But ifsorneone at this stage said that the half of the heavens above the Earth was not observed at ground and sea level, but only at extreme heights, their claim might have some rationale, since [in some cases] the heavens are certainly divided into two equal parts at extreme heights, but not at ground level, where instead less [than half] is visible above the Earth.'? But, in fact, it is irrelevant to our argument whether mo?-e [of See 11.3.71-7 j. 31. T h e arguments that follow were obviously created for dialectical purposes, not as the record of positions actually adopted. 3 2 Cf. FiLpre I or FiLgurej(a). 3 3. Both the language and logic of this sentence are awkward. T h e point seems to be that the contrast in the extent of horizons h e t w e n a plane and an elevated 30.

the heax ens] is observed abox e the Earth u hen our sight is elex ated, since this necessarily rewlts from the Earth's shape belng spherical. \That must therefore be offered is evidence that the Earth is not a point in relation to the whole cosmos-[that is], not as to whether it is possible to see more than half the heavens when our sight is elevated, but as to whether an equal amount of them is izot seen above the Earth [when viewed] from plane surface^,^^ given that the horizons at ground level are planar, while those seen from an elevated position are, and are called, conical.'( 140: There is the additional clairn (h) that different parts of the Earth would not be frigid, torrid, and temperate, unless the Earth maintained distances from the sphere of the Sun that were [obsenationally] yignificant; that instead, if the Earth were a point [in relation to that sphere], the Sun would not e>en be described as approaching us and as withdrawing again. Now here, as with (a), the response must be that the Earth's shape causes all these [phenomena] too: that is, some locations are torrid, frigid, or temperate depending on how the Sun's rays are sent down to the latitudes of the Earth.'"This is observed even in relativelv small subdivisions that are also a short distance from one another. Certainly, some [places] in Elis are parched, while the adjacent [part] of Achaea has no extreme heat at all.) So even if the Earth were of minuscule size, the result would be the same, in that the Sun's rays are not sent position may on occasion be such that a horizon of 180" can only be observed from a relatively elevated position. "Ground level" (ek toll khthumnl6n) here may therefore be a valley (cf. the example at I. j.yz-94) rather than the planar horizons envisaged later in the paragraph. However, the special conditions involved are not clearly identified. 34. For this to occur, the Earth aould either hare to be displaced from the center of the cosmos (cf. 1.6.33-35), or the cosn~oshemuch smaller, or the E k t h much larger. This is also a consequence of the theory refuted at 11.6.123-145 (see 11.6 11. 16), that more than 180" is seen from ground le\-el over the cumatures of the Earth. 3j. Strabo 1.1.20infers the Earth's sphericity from the enlarged horizon seen from an elerated location. 36. See 1.2.73-80.

T h e Heavens 1.8 / g j

down to all its latitudes in the same way, b ~ i in t a perpendicular and intense form in the case of some latitudes, while obliquely and in a diminished form in the case of others. Also, the Sun's approach to us and its subsequent withdrawal are identified with respect to its relation to our zenith, since the straight lines produced from the Earth to Cancer and Capricorn are equal to one an0ther.j-

157: That the Earth has in fact the ratio of a center [to the cosmos] is demonstrated by these and many other [arguments]. But having in our opening stated that the Sun sends out to us an appearance of being about I foot wide, despite its being much larger than the Earth, it is this very [clairn about its size] that we must demonstrate next by offering in suficient number for the present i~ltroduction[arprnents] derived horn a group of authors, including P o s i d ~ n i u s ,who ' ~ have written treatises exclusively on this subject. 3 7. T h a t is, the Sun at the summer and winter solstices is not at determinahl!different distances from the Earth, but is in a digerent reiation to the Earth considered as a sphere. 38. Lines 19-2 I above. 39. Posidonius reportedly demonstrated that the Sun was larger than the Earth in a hook of one of his treatises (FgEK; cf. Rolneo [1y;9] 14-1 j), h t Cleomedes' reference to other authors implies that not the whole of Crzrlt~stw11.1is d e r i d from Posidonius. Theiler nonetheless makes this chapter his Frgoa.

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Book Two of Cleomedes' The Heavens

OCTLISE

Book Tzo

Chapter I . T h e Sun is not the size it appears to be, as the Epicureans believe, but has a size calculable as far larger than that. Chapter

2.

T h e Sun is larger than the Earth.

Chapter 3. T h e Aloon, other planets, and stars are not the size they appeas to he. Chapter 4. T h e h1oon is illuminated neither by inherent light, nor by reflection, but by the mingling of the Sun's light with the AIoon's body Chapter j. T h e phases of the ,\loon are caused by its motion in relation to the Sun and the Earth. Chapter 6. Lunar eclipses are caused by the Aloon falling into the Earth's shadow. Data on the extrend latitudss of the planets, Chapter 7 . l-fppr~~rli.~: the maximum elongation of the inner planets, and the planetary periods; Conclusion.

CHAPTER ONE

Epicurus and most of his school1 claimed that the Sun was the size it appeared to be2 because they followed only the sense presentation caused 2:

bp sight: that is, the! made this presentation a criterion of its size.! 1ZTe can therefore see what follows from their claim: namel~;that if the Sun is the size it appears to be, it is quite clear that it will have in total more than one size, in that it appears larger as it rises and sets, but smaller as it culminates, while from the highest mountains it appears extremely large r. Since the Epicureans are mentioned collectivel~at lines 414-41j and 4x8-41y helow aithout any qualification, this phrase (like "most of the Socratic school" at I. 5.1;) must refer to the whole sect. 2. See Epicur. Pytk. 91, Lucr. j. j64- j73, Cic. Ac~rrl.2 . 8 2 , Philodem. De sig7 / 2 5 col. 9 (sect. 14 D e Lacy [1978]), and Demetr. Lacon (ed. Ronleo [ry7y])pnssiw. T h e latter two Epicureans both flourished close to the time of Posidonius. O n this theory see Sedley (1976) 48-j3, Ronleo (19:9), and Barnes (1989). 3. O n the principle underlying this claim, ziz.that all sense impressions are true, and on the criterion in Epicurean epistemology, see LS sects. 16-17; Cleometles ma!- have addressed this issue elsewhere (cf. line 408 with n. y j heloa-). (-it I.j.11-13 the belief in a flat Earth is similarly traced to exclusive reliance on visual appearance; cf. I.j n. h.) For a defense of the Epicureans against \vhat is obviously Cleornedes' pole~nicaloversimplification of their position see =Vgra (2000) 181-182.

M-henit rises.+ Kow either they will have to sajr that in total it has more than one size, or, if this is obviously atxui-d, it is absolutelj- necessary that they concede that it is not the size it appears to he.' I 3: Some [Epicureans] say that the Sun appears larger to us as it rises

(and sets)%ecause its fire is widened hy the air through the force of its rapid ascent.- But this in\-olves utter ignorance.The Earth, after all, is located at the exact center o f the cosmos, and has the ratio of a center to it; it is therefore equidistant from the sphere of the Sun in all directions," and so the Sun does not come near the air either at its rising and setting, or in any other part o f its course. In fact the Sun does not even rise ever!-where at the same time, but, given the Earth's spherical shape, it rises, sets, and culminates at different times in different places. So since it can be both rising and culminating at different places, it ivill be in total both larger and smaller: larger for those for whom it is rising, smaller for t i m e

4.At lines 47-48 helow the same location is associated n i t h an illusion of the Sun's greater distance. As Ross (2000) 868 notes, Cleomedes is mistaken here. since the Sun'i size is reduced v h e n \-ien-ccl from 3 height; 5he suggest5 that his estromission theor!- of the \.isual ra! (cf. n. r 5 belou) may ha\-e led him to assume that in such cases there \\ as p a t e r refraction through the atmosphere at the horizon. On the general issue of celestial illusions ant1 their interpretation see Ross and Plug (zooz). ;. If an object has conflicting appe:lrance$, then it is nut seen as it reall!- is; see Burn>eat (1979) on this principle in ancient epistemolog- and cf. n. 16 belO\$. 6 . T h e r e is no subsequent reference to the Sun's heing flattened by the pressure of setting. but that can perhaps be taken as implied. ;. On the possibilit!- of the Sun's being reconstituted h!. the confluence of firs\-particlessee Lucr. 5 . 6 6 0 - 6 6 ~ .n-ho does not refer to the air ha\-ing the causa! role assigned it here. Cleomedes p r o h ~ h l yhas in mind the theory of a diurnally rehndled Sun that is attLlcl;ed later: see lines 426-466 and n. 105 belo\\. 8. Epicusus was often charged uith "ignorance" Qptidczism); in addition to line 452 helon; see LS sect. 2-E-H and Pease ( 1 9 j j ) o n GC.De ,lilt. deor: 1 . 7 2 . 0 . T h i s only appears to he the case; in reality the Sun's orbit is eccentric in relation to the Earth. See 1.4.49-;I and 1I.j.103-132.

T h e Heal ens 1I.r

/

IOI

for whom it is culminating-at the same hour of daJi!" Nothing is more absurd than this. 26: These kinds of suggestions, then, are utterly meaningless and futile. The Sun appears larger to us as it rises and sets, and smaller at its culmination, because we see it at the horizon through air that is denser and damper (that is what the air closer to the Earth is like), while ire see it culminating through less adulterated air. So in the latter case the ralsent out toward it from the eyes is not refracted, whereas the ray sent out to the horizon \+heneverthe Sun rl\es or sets is necessarily refrdcted on encountering air that is denser and damp." h d i n this M a! the Smi appears larger to us (as, of course, objects in water also appear to us other than they are hecause they are not seen along a straight line)." Therefore all such states must be held to be cond~tlons'~ffectingour line of sight, not as properties associated mlth the object5 that are being \een (\$'hen the Sun is obsen ed trorn [\\ithln] deep n ells, at le'lst U here this 1s possible," ~t also reportedl! appears much larger because ~t is seen through alr wlthin the \\ell that is dmlper. L4ndin thls case the Sun cannot, of course, be said to be enlarged for those looking in its tiirection TO. See 11.1.430-43.; and +tX-qjz for analogous reasoning used q a i n s t the Epicurean explanation of the Sun's orbit as a dail!. extinction a n d rekindling a t sunrise and sunset. I I . O n such atmospheric conditions affecting the appearance of the Sun and its size see r\rist. J l c t e o ~37jb12-13, Srhol. in A.liat. x t . 419.6-420.2, Positi. F I 19.12-20 ET( (in M hich Posidonius questions this explanation), Sen. .\V 1.15.5, and Ptol. Ahn. 1.3, 13.3-9. For a discussion, with a translation, of II.r.z;-;5 in relation to the history of the analysis of the "solar illusion," i.e., the apparent enlargement of the Sun near the horizon, see Ross (2000). For a general explanation of m-hat is k n o ~ ~asnthe celestial illusion, and includes the lunar and solar illusions, see Plug and Ross (1994). I 2 . Such a case of refraction is a d y z e d at 11.6.178-1 87,though with reference to the visibilit!; not the enlargement, of the submerged object. 13. T h a t is, where these (vertical) ~vellsare located at latitudes on or lxnvecn the tropics, so that the Sun can be ohsen-ed at zenith from the base of the \wlls at ionie point durmg the )ear.

I02

/

C ~ P O ~ YT I Ph~e CHeavens S'

from [within] the well, but diminished in size for those doing so from above, but quite clearly the humid darkness of the air ~vithinthe well causes it to appear larger for the [former] observers.) 45: The Sun's distance [from the Earth] also appears larger and smaller to us: as it culminates it appears very close, but as it rises and sets it appears fiarther away, while from the highest mountains it appears at a still greater distance. And when it appears close bj-, it also appears very small; but the more distant it appears, the larger it also seems. T h e quality of the air causes all such [appearances]: that is, when seen through damp and denser air, the Sun appears larger to us and more distant, but when seen through clear air it appears smaller in size and closer in distance. (Thus Posidonius claims that ifit were possible for us to see through walls and other solid bodies, as L~nceuscould in the legend, then the Sun, when seen through these, would appear much larger to us and as reino~-edto a much greater distance.)14 57: TZ-hile the Sun appears larger and smaller to us, as similarly do the distances involving it, the [visual] cone that impinges in reality on it from the rays that flow out the eye1: is necessarily very large. But since the size and distance of the Sun are both contracted to what appears to be an extremely small quantity, we can conceive of two cones: one that impinges in reality on the Sun, the other that does so in appearance.'" 14. Lines j ~ - j 6= Posid. F I I ~ E Ksee ; Kidd Connm. 442-443. L!-nceus was a legendary figure with preternatural visual poxrers. I j. Hahni (1978) 6 j-69 (who ignores Cleomedes) doubts that the early Stoic theory of vision involved rays in the form of visual pneuma flowing out from the eye, as indicated here and at 11.6.181-18j (cf. 1.1.72-74) where our "line of sight" is like a conical "bead" of pneuma dram-n on an object. Note the verb epibnllein ("impinge") at lines j9, 62, and 234 below, and also 11.+1jo. For more on the visual cone see lines 2 j3-z j8 belo~r;and 11.j.110-112 (cf. 11.j.qc)- j4). 16. h "real" visual cone represents the conditions under which the Sun is seen without any conflicting appearances. See Burnyeat (1979) 73-7j on the implication that an object that is seen b!- different obsen-ers as having conflicting appearances must in principle be visible to all observers with the same appearance.

T h e Heavens 11.1 /

103

These will ha\-e a single vertex at the pupil of the eye, but m o bases: one in reality, the other in appearance. Therefore the real distance is to the apparent distance as the real size is to the apparent size. But the bases of the [two] cones are equal to the real and apparent diameters respectively.'Therefore the real distance is to the apparent distance as the real size is to the apparent size. But the real distance is almost immeasurablylVarger than the apparent one, since the Earth has the ratio of a point to the height of the Sun, and to the sphere conceived of from it. Therefore it is absolutely necessary that its real size be immeasurably larger than its apparent size. Therefore the Sun is not the size it appears to be. 76: Also, if the Sun is the size it appears to be, then if we in~agineit being double its size, each of its parts, when divided into two, will appear to be I foot wide.'"o if we also imagined it so enlarged as to extend over a distance of a r,ooo,ooo stades, each of its parts that is I foot wide would appear the size it is. If so, it follows that the Sun would in h c t appear the size that it is, although that is clearly impossible: human sight simply cannot attain such a degree of power that objects extended over ~,ooo,ooostades appear the size that they are in reality, since even

17. Here the Sun is treated like a Hat disk; see Figure I;. But at 1I.j.jr-j4, with the help of Eucl. O p t . prop. 2 j , it will be shown that less than half of the .\loon's sphere is seen by a terrestrial ohserver. 18. "1mnieasurabl~-larger" ((~peii.iivzrizin or ~pril-onregrtl~?~), literally "larger by an unlimited [amount]," often qualified by "almost" 6khetlon) (cf. 11.1.8j, 135, 241, 266, 360). presurnahly because attempts can be made to calculate the Sun's real size. 19. "I foot aide" (podiirios), this width being the approximate diameter (cf. the qualifications at 1.8.20 and I j9) of the flat disk that the Sun appears to be (see n. 17 "bole, and cf. lines 267-269 below); it is an informal measurement in contrast to more systematic procedures (see 11.3 n. 7). T h e term itself was prohahly inherited from Heraclitus by Epicurus (see Sedley 119761 j 2 - j3), and is frequent in descriptions of the Epicurean doctrine by secondary sources. As 4 g r a (2000) 18; notes, these distort a claim that may hare been intended as a polemical reaction to astronomers' claims ahout its distance and size. On Airistotleand the basis for this illusion see Schofield (1978) I 13-1 14.

the cosnlos itself, although of almost unlimited size, appears t o us to be ver) small."'

87: Now- since what follows from the Sun's being I foot wide is irnpossilde, it is impossihle for it to he

I

foot wide. For it cannot also be

claimed that, when the Sun is extended over such a great distance, some of its partsthat dre

I

foot \tide nil1 dppear the s u e that they are, mhile

others will not.!l T h a t is because the distances from the Earth t o all the parts of the Sun will be equal, since the Earth has the ratio of a center to the heliacal sphere. T h u s all of its parts that are

I

foot wide, n o t some

specific parts more than others, will have to appear the size that they are. So if all its parts that are

I

foot wide appear the size they are, the Sun it-

self, when extended that much, will appear in total the size that it is. Since thls is 0b.i i o u s l ~~mpossible,its parts that are appear to be the size they are-instead, So if the Sun itself is

I

I

foot v ~ d 14e 111 n o t ex en

they will not even appear at all!

foot wide, it will n o t e r e n appear. But it does ap-

pear. Therefore, it is n o t I foot wide. So it is clear from this, I think, that if the Sun were the size it appears to be, it u-ould n o t appear. But since it does appear, it is n o t t h e size that it appears to he. 102: If

the Sun is the size it appears t o be, and if the sense presenta-

tion derived from sight is itself the criterion for the size that belongs to it, it could be said to follow that this appearance would also be a criterion for the [other qualities] that appear t o belong to it.?' H e n c e if it is

2 0 . "COSITIOS" here must refer to the visible celestial hemisphere, \\.hicl1\ve imagine to be smaller by assi~nilatingthe sizes of heavenly bodies to familiar bodies at shorter distances. For an anal!-sis of this illusion see the passage translated from the -hahic as sect. ;of Ptolem!-'s Plmetici:,, IjypothesrxBookI. Part 2 at Goldstein (196;) 9. 2 I . Here \\-c hale an irnaginar!- opponent a-ho must haw accepted the a r p ment in the preceding paragraph, and is then trying to wriggle off the hook by claiming that the Sun is large in some places, but I foot wide in others. 2 2 . I hi3 wntence rnarks a return (until line 139) to arguments based (like those at lines j- jh above) on conflicting appearances. 7

.

T h e Heavens 11.1 /

105

the size that it appears to be, it also has the q ~ d i t i e sthat it appears to '~ this have. But it appears hollon; ,'\and f l a ~ h i n g , although coilfiguration does not helong to it; certainly at other times it is seen as smooth, Aloon-like, and not spinning." Yet is impossible for all these [qualities] to belong to it. Therefore the Sun's being I foot wide, of which the)- are 11 consequence, is also a falsehood. 110: Again, if the Sun is 21s large as it appears, and has the qualities it appears to have, then since it also appeals stationas!; it v-ould be unchai~ged in l'et it is not uimioved, and so is not unchanged in position. Hence it is also not the size that it appears to be. 114:T h e absurdity of their claim could also he p r o x d with the ut~nost 23. T h ~ wpplernent, s proposed h! R. Renehm 'it Cilclc,tlil ed. 'lodd 11.1.106, halances "not spinning" in the next sentence (see n. 2 5 1)elow). For such spinning bee h i s t . L)e cilelo zyoai2-18: it is an optical e f i c t that c m occur at hoth sunrise and sunset. 24. For hollo\vness and 1)rightness see Arclt. Philci~.818-830, m d for apparent hollowness caused by interposed clouds see Schol. in L4ii~t. w t . 410.8-1 3 anti 41 7 . 6 1 0 . Such a shape could he dark, and so mni-milji-ill ("flashiny") (line 10;) might he emended to / N P ~ I E ~ I I O ~ ~ I P(i'l~l;ickenecl"; I~OJ cf. Schol. 112 :lint. ;.LT. 411.8). 2 j . p^;i~ L I ~ O ~ ~ E(''not I , O Sspinning") (line 108):i.e.. the Sun's appearance at times other than sunrise and sunset. ( h e n the e\ idence at n. 23 nbore, there is no basis for emending it. either to I ~ ~ h ~ ("1)lackenetl") [ ~ ~ ( ~ (Theiler) ~ ~ t ~ (an ~ epithet x more appropriate in the preceding line: see n. 24 above), or pp6& n p o d p c v o s ("in no n-a>- ignited") (,\larcovich [rc)86] 117). .\larcovich finds support for his i d ; 132 belon), but h~p6219m p o ~ ~ pmust ~ ~ ~refer o ; to a n emenclation in m ~ ~ ( t ~ 7(line igneous constitution, not a f i e r ~appearance, and its true parallels are else\\ here: .;;vpd&p at l . j . 1 ~ 9(11, 7;dp~'osat 11.3.93, TI.j.4, and 11.6.104. 26. For this argument, supplied with its major premise ("e\-er!-thing that appears also is the case"), see the Epicurean Demetr. Lacon col. 20, with Romeo (1979) 16 and n. 41, ancl .Alga (2000) 185-186, who uses this text to defend the Epicureans, n-ho were well :111le to handle this widely recogni~edtype of illusion; . see Lucr. 4.391-396, and also Sen. Ep.88.26 and Ales. riphr. Dc ~ i l 77.1;-18 uith Ti)tltl(rqqj) 127 11.fi.For the generic case of distant objects appearing stationary although really ~ n o ~ i see n g S e x . Emp. PH 1.1 18.

106 /

Cho?~ledes'T h e Heavens

cognitive reliability on the basis of the follo~ving[arpment]. If the Sun is indeed the size that it appears to be, it is, I think, evident that the Moon too is the size it appears to be.'- And if it is so itself, then so too are its phases: so when it is crescent-shaped, the distance from horn to horn is also as large as it appears to be. This further implies that the distances [from the Earth] to the heavenly bodies near the 11oon are also as large as they appear to be, from which it further follows that all the distances of the heavenly bodies without exception are also as large as they appear to be. Hence the u-hole hemisphere of the heavens above the Earth is also as large as it appears to be.'" But this is not so. Therefore neither is the Sun the size that it appears to be. (Aso, if the JIoon along with its phases is the size it appears to he, then the black spots that appear in it are also the size that they appear to be. If so, the [JIoon's] "mountains" must also be the size they appear to t ~ e . But ' ~ this is not the case. Thus neither is the Sun the size it appears to be.) 129: Non- when the air is "pure" (that is, in a n a n d state), we cannot look back at the Sun. But when the condition of the air enables us to look at it, it appears differentl!- to us at difTerent times: sornetirnes n-hite, sometimes palish, occasionally tire-like, and is often to be seen as red ocher in color, or blood-red, or !,ellon., and occasionally even multicolored, or pale green.'" Also, n-e think that the pale cloud-like flecks that 2;. See Epicur. P y t h . y r mcl Lncr. j . j ; j-j84 for this as an Ep~cureanclaim. For more on the size of the JIoon see 11.3.1-33. 28. For Epicurean recognition that the Sun can appear closer than it really is see Lucr. 4.405-413. and Diog. Oen. Fr. 13 cols. 1.13-11.10 Smith (1993). Lucr. 4.397-399 (on distinct mountains appearing to coalesce in the distance) could presumably be applied to the distance between hearenly bodies, even if, for an Epicurean, they will still be the size that they appear to be. 29. Goulet 110 n. 237 argues that these mountains are terrestrial. Yet although the \loon, as he notes, is a rarefied body (1.2.3 7-39. 11.3.88-91 m"dI.4 pmsi?u), it could still appear mountainous as 21 result of its unevenly "turbid" appearance (we 11.3.89 and 11.j . 2 ) . 30. See -hat. Phneil. 832-879 on the Sun's rarying appearances, recorded there as weather signs; cf. "palish" (okbi-iciil,line 132) with Phnen. 8j1.

T h e Heavens 11.I

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107

often appear around the Sun belong to it," although they are at an almost imtneasurably vast distance from it. Again, often when setting or rising on a mountain peak, the Sun sends out to us the appearance of its touching the peak, although its distance from every part of the Earth is as vast as is to be expected when the Earth has the ratio of a point in relation to its height.j2 140: So surely it is utterly stupid-is it not?-to follow this kind of sense pesentation" instead of making something else a criterion, at least for things of such a great size,z4bearing in mind that being misled in these cases usually causes significant damage. 144:T h e utter inconceivability of the [Epicureans'] claim is also \-ery clearly proven on the basis of arguments constructed in the following way. Imagine a horse released to run along a plane in the time inten-a1 between the Sun's outer rim's emerging over the horizon and its complete en~ergence." X fairly obvious guess n-ould he that it would advance at 3 I. O n "flecks" (kn?kiilcs),pale spots produced hy a light cloud that lacks noi isture, see.4iattw 126.24-2 j. They probably created a halo; see Goulet 2 1 0 n. 238, \\l10 notes Sen. '\-Q 1.2.3. 32. [;or the same illusion see Lucr. 4.404-413. This passage is evidence that the Epicureans could handle the issue of the Sun's vast distance, as is Diog. Oen. FT;, 11.1-10, adduced h!, Agra (2000) 18j. For the constructive use of the illusion see lines 2 27-2 32 below. 33. One based just on sight (or \isual obsenations), that is; see lines 3-4 and 102-10 j abore. 34. T h e best definition of such an alternative criterion is given at l. j.2-6. Vsing its language, the Sun is not "fully displayed," and therefore implications about its size must he drawn from phenomena hy more elaborate h r l n s of reasoning, initially involving the comparison of difl'erent phenomena (lines 14j-2 24 below), arid later the use of calculations (lines 2 2 j-3 j 6 helou-). 3 j. :It Philodem. Dcsigzis cols. 10-11 (sect. I j De Lac>-[1y78])a Stoic, Diony.. sius of Cyrene, is reported as arguing that the Sun rnust be very large because it reappears slonly from behind an obstruction; the present argument is a rough attempt to lueasure the speed of this apparent motion. (On Dionysius and Posidonius, whose lives prohably overlapped, see Ronieo [1979] 14-16.) Cf. also 11.2.13-I 8 with 11.2 11. 6.

108 /

least

10 stades,

C'k07~?1.de.7'T h e Heavens

hereas a \ er) s~ ift h ~ r du o d d g o man! times farther

than t h e horse, and q a l n a inisslle n ~ t ah er!

S\\

ift m o m e n t u m v ould

g o m u c h farther than t h e bird, s o that In such a perlod of time i t n ould cox e r a t least jo stades.'" S o n o n the h! pothesis that t h e heavens tral el as fast as t h e horse, t h e diameter of t h e S u n \vould he determined as

10

stades; if as fast as a \-er!- swift bird, t h e n m u c h larger; b u t if as fast as t h e missile, i t u-ould be at least ;o stades. Given all this, t h e S u n will n o t b e I

foot wide, that is, n o t the size that i t appears t o be. I 55:

N o u \re could for i n t h e notlon that t h e heal ens

11101e

Inxnea-

s h e r than the misslle from the follon i n g procedures. sur'lhl! m a n y t ~ m e sn

156: ITllen t h e P e r s ~ a nK n g U as o n his expedition t o Greece, h e rep(jrtedly s t a t ~ o n e dpeople a t i n t e n als frorn Sousa as far a5 Athens, s o that hClth e acconlplished In Greece could be ~ n d i c a t e dorall! t o t h e Persians t h r o u g h people s t a t ~ o n e dat i n t e n als successn ely recelr ing oral messages f r o m o n e another. T h e oral message that progressed t h r o u g h t h e stdges of this relay reported! reached P e r s i , ~f r o m Greece In hi o i n t e n als of a nighttlme and a daytime. S o u if such a m o \ e m e n t (or "impact") of a~r,'although extremely swift, CO\-ereda minuscule portion of t h e E a r t h i n

m-o inten-als of a nighttinle and a da!.tiine, o n e can, I think, f o r m a n o tion of n-hat kind of speed t h e hea\ens have, and that it is i ~ n m e a s u r a b l y swifter than this, since in o n e interval of a nighttinle and a da!,time t h e heax ens g o t h r o u g h a distance imme'~surahl! man! times greater t h m Greece t o Persi,i." t h ~ from t

36. On missile thro\r s ;l5 units of ~ne:~surement see Lucr. 4.408-409. 'This missile. however. cannot depend on human propulsion, since 70 stades is seven times as hi-as a horse gallops in roughly 2 minutes. S o t e that at lines 150 and IS; \re h:ne emended the manuw-ipt reading zoo to 70. T h e minuscule letter used for zoo ( s i p a ) could hal-e been confused nith that for 70 (omicron), and 70 also makes more sense of the number5 at lines 166-168 (see 11. 39 belol\). 3;. Stoics (see SI.F 1.74 mcl 2.138 and 139) defined speech as an "impact" (plFg2) on :lir. 38. For the Persian relays see Hdt. 8.98 and S e n . C:,li: 7.6.17-18. This aryument is a "procedure" (cphoilo~),as \t e ha\ e defined it in the Introduction (cf.

T h e Heavens 11.1 /

rog

166: Aso, if \ r e imagined the missile going through the great circle

of the Earth, it would not even go through the z ~ O , O O Ostades [of the Earth's circumference] in three intervals of a nighttime and a da!-time!"' Yet the heavens go through the full extent of the cosmos, despite its being immeasurably larger than the Earth, in one interval of a nighttime and a daytime. Thus no notion of the speed-the rapid movelnent, that is-of the heavens can even he formed, and nothing like it can he interpreted in terms of a ratio. T h e Poet displays how great the speed of thc heavens' course is through the following [\wses]: T3e dinr cli.stmc thict il ?ilnn sees ~ i t his h eyes xhcn sitting o n n pl-omo~ztory.lookillg upon the zincblue avttt; is equii'nht to one stride of the gods' loud-n~i~ghi~~g h011(.~~.(..~~' But this is expressed in an exaggerated way and with strilung expansiveness. N o t o n l ~is, [Homer] pleased to use the farthest estent of sight to indin. 38), since it relies on an axiom that could he made explicit as folio\\ S: "Ift\r-o bodies, A and R, m o w in circles around the same center, and .-i mores along its circumference farther than B does along its circumference in the same time period, then A m o x s faster than B." N o t surprisingl!,, Cleometles does not spell this out. Similarl!; the argument that follows (lines 166-170) is an application of the axiom: "If IS$-o bodies, A and R. more in circles around the same center, and .-l mores the same distance along its circumference as R does along its circumference, hut in 3 shorter time period, then ,.2 mores faster than R." 39. Since this must he the missile introduced at lines rqg-I j3 above, it will ha1.e to cover zoo stades during sunrise if we retain the manuscript reading 21t I j o and I j3 ahore. Thus if the Sun's diameter is of its orhit (lines 18t-ic)r below), it will rise in '+.t'/-,, minutes (= 1.92 mins.), and the missile will corer 1jo.000 stades in a full day It v-ill thus orbit an Earth of 240,000 (or 2 jo,ooo) stades in less than z full days. But zoo can he plausihlp emended to 70 (see 11. 36 ahore), and in that case the missile will corer 5 2 , joo stades in a full (lay anti, in conformity with the text at lines 167-168 ("not elen in 3 days" being taken to mean "in [significantly] more than 3 days"), take over 4 days (specificall!- 4 clays, 18.3 hours) to orbit the Earth. 40. Homer Ilind -j.770-772. llilton kiirlndis-e 1,ost 8.38 is closer to Cleomedes in saying that the heavens have "Speed, to describe whose s~r-iftness number fails." Athough the Homeric verses identify only the sight line from the promontory to a distant horizon, Cleomedes adds additional u p ard and downward sight lines heca~lseof the comparison with celestial horses and the reference to the sea.

I 10

/

Clro7uede.r' T h e Heavens

cate the speed involved in the rapid movement of the heavens, but also adds to it an upper distance along with the [depth of] the sea below. Yet even this description falls short of properly indicating the swiftness of the heavens. T h e speed that the heavens employ in their rapid movement has no limit, and no notion of it can be formed. So surely it is stupid to believe that a part of them that is I foot wide could rise in such an interval of timeY' 184: T h e naii-et6 of this claim is also proved by water clocks, since these are a means of showing that, if the Sun is rfoot wide, then the greatest circle of the heal-ens will have to be 7jofpet! For when the Sun's size is measured out by means of water clocks, it is determined as ~/;,,th part of its own circle: that is, if, say I kuathosi2 of water flows out in the time it takes the Sun to rise completely above the horizon, then the water expelled in the whole daytime and nighttime is determined as 7 jo kztnthoi. Such a procedure was reportedly first conceived of by Egyptian~.~'

192: T h e [Epicurean] doctrine is also refuted by colonnades that face south, since the shadows of the columns are sent out in parallel lines.44 T h a t would not happen unless the Sun's rays were s e n t o u t t o each column in straight (i.e., perpendicular) lines4' And the rays would not be sent out perpendicularly in the direction of each column unless the diameter of the Sun were coextensix-ewith the whole coloni~ade.~" 41. In, that is, the inten-a1 determined in the three "guesstimates" (cf. stokkilz.esth~iat line 147)at lines 147-1j 3 above. 42. A krtnthos was '/h of a kotule, which was about ,/l of a liter, or about l/, of a modern pint. 43. O n ancient accounts of this rnethod see Goulet 2 1 0 11. 243 and K d d Contm. 4.49-4jo (add S a t . Emp. L.lAll j.7j to the critics). Cf. lines 197-299 below where this method is applied to the AIoon. T h e "water clock" (htdrologcioi~) ~ n u s have t been a type of clepsydra (see 1.1n. 18). 44. At the latitude of Greece, that is, the shadoa-s would always point in a northern direction. 45. See I.;. j j - j6 for this principle. 46. Cf. 11.3.23-33 for the a r g ~ ~ m e that n t the Sun and the ~10011must both hare diameters at least as large as the terrestrial shadow cast by the 110011 in a

T h e Heavens 11.I

/

111

197: Streets that throughout the inhabited world are arranged facing the equinoctial rising point also reportedly become shadowless when the Sun rises at the equinoxes, a result that is conditional on the Sun's size being coextensive with the whole inhabited world, specifically with its width. Again, at midday at the equinox all the streets in the inhabited world are illuminated on both sides, so that the Sun's size is coextensi-ve not only with the width, but also with the length, of the whole inhabited world. ( T h e length of the inhabited world extends east-west, whereas its width extends north-south.) Thus when the Sun rises on the day of equinox and renders the streets that face it shadowless, it has its diameter coextensive with the width of the inhabited world, whereas when it culminates and illuminates all the streets on both sides, it has its diameter coextensive with its length. (But the Sun is said not to culminate for everyone at the same time, but only for those who lire below the same meridian. So it must be stated that the preceding [argument] is expressed rather loo~ely.)~: 211: Also, when the Sun is in Cancer, bodies illuminated at Syene become shadowless at exactly midday over [a circular area] 300 stades in dia n ~ e t e rThis . ~ ~ clearly reveals that the Sun is not I foot wide. If it were I foot wide, none of this would happen. 216:~" That the Sun is not I foot wide is also indicated by shadows: for when the Sun displays its rim above the horizon, the shadows sent out are very long, but when it is above the horizon they are contracted

solar eclipse. Here the colonnade is analogous to the ,\loon, since it is the object n by the Sun. that creates a terrestrial shadow d ~ e illuminated 47. T h e caveat is needed, since the Sun rises and reaches culrnination at different times at successire meridians (cf. I.j.37-30). MTe are asked to extrapolate from the situation at a giren location to the whole of the i~lhahitedworld. +8. See 1.7.75-76, and lines 270-273 below. 49. Cf. 1.6.9-32, where the evidence of shadows is used in an elementary arp m e n t for the cosmocentrality of the Earth. Here shadows sen-e to indicate the Sun's distance from the Earth, and ro ipso the fact that its real size is greater than its apparent one.

II2

/

Cleonredes' T h e Heavens

to a much smaller size. This u-ould not happen unless the Sun's rays u-ere much higher than all terrestrial bodies, and that M-oddnot happen if the Sun were I foot wide. Therefore it has a diameter greater even than the highest mountains, since when it is completely visible above the horizon, it sends out rays higher than the peaks ofmountains (that is, froin a higher position). 2 2 5 : T h e following procedure, which goes forward on the basis of the phenomena alone, demonstrates not only that the Sun is not I foot wide, but also that it has a prodigious size.'" For u-hen the Sun rises or sets in alignment with the peak of a mountain, anyone at a significant distance away from the peak sees its rim, which is obsenable on each side of the peak. This would not occur unless the diameter of the Sun were larger than the peak causing the obstruction. So if this peak is I stade in diameter," the diameter of the Sun will have to be larger than I stade." (The preceding is said to be observed among the phenomena not just in the case of a mountain peak, but also in that of the largest islands. For u-hen our line of sight is at a significantly elevated position, and impinges on one of the largest islands from a considerable distance ava!; the island appears so small that here too the Sun's rim visibly protrudes on each side when it rises or sets in line with them. From this it is clear that the diameter of the Sun is also greater than the length of the largest islands.) 2 4 0 : IYith this taken [as true] on the basis of the phenomena alone, the nest stage is to demonstrate that it is necessary that the diameter of

jo. This procedure could be based on Eucl. Opt. prop. j (cf. 11.4.121-122 with 11.411. 3 2 ) : i.e., ~vhentwo objects are aligned relative to an observer, and the closer

one blocks (or, in this case, alnlost blocks) the more distant one, then the more distant object must he the larger of the two. j r . This is its one-dimensional appearance at such a distance; cf. IM?X'OS, "length," in line 238. 5 2 . This assumes that in the nest illustration there is no distance bemeen the Sun and the peak, or the Sun and the island; i.e., that the Sun is as close to these intervening objects as it appears. Distance m-ill be incorporated in the next stage of reasoning.

T h e Heavens II. I /

II3

the Sun be almost immeasurably greater than the diameters of the largest islands. This is established via the following procedure. (I) If an isosceles triangle has a base, say I stade in length, and if the sides are produced by an amount equal to those that enclose the base that is I stade long, the base of this [second] triangle will then be twice the base that is of I stade in length. Then (2) if we once more produce sides equal to the whole of the sides [of the second triangle], its base will be four times the base of the triangle [posited in (I)], and thereafter the same proportion will progress without limit.'3 Now assume (3) that we see one of the largest islands from a considerable distance when the Sun is rising or setting in line with it, with its rim visibly protruding on each side, and that the island is located between us and the Sun. Now (4) if our line of sight encompasses the island, the cone formed from the line of sight will have the diameter of the island as its base. So if its diameter is 1,000 stades, then the base of the cone will also be the same size. Now let us hypothesize (J) that the Sun is as distant from the island as the island is from us. So since [by (j)] the Sun's rim visibly protrudes on each side of the island, the rays that flow from our eyes to the Sun are [by (I), (2), and (J)] double [the length of] those that reach the island. Thus [by (I)] the base of this [second] triangle will also be double the diameter of the island.j4 If [by (4)] the latter is 1,000 stades, the diameter of the Sun will be 2 , 0 0 0 stades, since it is the base of the larger triangle. So since [by (J)] the Sun is as distant from the island as we too are on the opposite side of it, the diameter of the Sun will be 2,000 stades. But the distance [in each case] is not equal; instead, we are a short distance from the island, while the Sun is immeasurably many times farther away from us, and so the diameter of the Sun will [by (2)] also be almost immeasurably many times greater than the diameter of the island. How, then, could the Sun's size be I foot wide when it extends over such a great distance? j 3 . See Figure 18. 54.See Figure 19.

II3

/

C'leomeilt~s'T h e Heavens

269: T h e following kind of procedure reveals better than any other

the estimated value for the size of the Sun." [It assumes] (I) Syene is located below Cancer; thus when the Sun is located in this sign and stands precisely at culmination, objects illuminated by it are shadowless in this area up to a diameter of 300 s ~ a d e s .TT' ' ~ ith this as true anlong the phenomena, Posidonius hypothesized ( 2 ) that the heliacal circle is 10,000 times greater than the Earth's circumference." Starting out from this [premise], he demonstrated that the diameter of the Sun must he j,ooo,ooo stades. That is, if [by (2)] one circle is ro,ooo times greater than the other, then the section of the heliacal circle that the Sun's size occupies must be ~ o , o o otimes greater than the section of the Earth that the Sun renders shadodess when located overhead. So since [by (I)] this section extends to a diameter of 300 stades, the section of its own circle this is that the Sun occupies at any time must be 3,000,000 stades.'"ut taken [as true] on the basis of the aforementioned hypothesis. _ h dwhile it is plausible that the heliacal circle be no less than ~ o , o o otimes greater than the Earth's circumference (given that the Earth has the ratio of a

j j. O n this calculation see L J d Co7itm. 443-44; ad deugebauer (197;) 6 j j-6 j6. O n problerns involved in reconciling it with other reports of Posidonius' determination of the size and distance of heavenl!- hodies see kjdd Chntm. 4 j t - l j 6 and 464-466 on F116 and F110 Elth part of its own circle.) Therefore, in accordance with the preceding assumptions, (16) the Sun's -, diameter is determined as 520,000 stades. '

66. See lines 184-191 above. 6;. This follon.~,if the diameter of a circle is I/; of the circumference; see ( 2 0 ) below, and cf. I . ; . I I ~ - I ~ (with o I.; n. 2-1). If the Earth is not "a point" in relation to the orbit of the JIoon (cf. 1.8.100-112 and 11.3.71-80). then (8) is a h!-pothesis, albeit less radical tha11 ( 1 2 ) . 68. That is, 7 jo / 6 = I 2 j . This also assumes that the lunar circle is concentric n-ith the circumference of the Earth. 61) For this value see Apollonius of Perge at Hippolytus Rcfkiltio 4.8.6 (1o1.31). It can also be reached from (S) show (i.e., ;jo s 40,000/6); it is, in other words, '/h of the lunar circle. 70. This hypothesis (cf. lines 334-338 belon-) is used to explain anon~alous planetary motion at Gem. I.iog. 1.19. 7'he speed in question is not angular hut linear; it is the rate at which a planet runs through the circumference of its circular course. ;I. These are their sidereal periods given earlier: 1.2.zH-:y (S~in),and 1.2.41-42 (cf. 11.3.97-98) ( A h o n ) . 7 2 . T h e cornputation here is approximate. Cleornedes is considering only the v-hole number of times the )-ear is chided h!- 27'/; 73. This calculation is again (cf. n. 58 abo\-e)implicitl>-based on an identity between ratios: specificall5 I : I ~:: AIoon's diameter:Suii's diameter :: +o,ooo: jZO.000.

T h e Heavens U.I /

II7

312: Since (17) the heliacal circle (just like the zodiacal circle) is divided into 12 parts, then (18) each of its twelfth-parts will [by (16)] comprise 32,500,000 stades,;' and (19) the distance from the Earth to the Sun is [by (8)] 2 twelfth-parts. ( A r a t ~ also s ~ ~states this with reference to the zodiacal circle as follows: Six times the length of the rayfi-om an observer's eye-glance would subtend this tide, and each sixth, measured equal, emompasses76two comtellations. Here he has called z d6dekatemoria of the zodiacal circle "constellations" (astra), and in the verses quoted reveals that the distance from the Earth to the Sun is '/h of the whole ~ i r c l e . ) ~In' other words, while [by (8)] (20) the whole diameter is I/, of that circle, then (21) the distance from every part of the Earth to the Sun is '/6 [of that circle; i.e., 65,000,ooo stades] (since that circle has as its center the Earth, which is located at its exact center).j8 So since the heliacal circle is determined by this procedure [cf. (7) and (16)] as 3go,ooo,ooo stades, each ofits twelfth-parts, as we said [at (18)], is 32,~OO,OOO stades. So if the latter too are divided into 30 degrees, just like the d6dekatemol*iaof the zodiacal circle, each degree will be 1,083,33314stades. There will be 720 half-degrees in the whole circle, but the Sun will [by (7)] be of it, and hence less than I/, degree. Thus since degree is j41,666'/, stades, the Sun itself is with probability determined [by (16)] as having a 74. T h a t is, 7j o X ~ ~ O , O O 12 O = /32, joo,ooo (see lines 324-32 j below). Here, in (19) and at line 326 below, d6dekatimoria can be translated as "twelfth-parts," since it is not being used in its technical sense to designate the zodiacal signs (cf. 1.4 n. 17 and lines 319 and 328 below) which are each I/,, of the zodiacal circle. 7j. Phaen, j41- 543, translated by D. Kidd (1997) I 13, with minor changes. ~ 76. At Phaez. 543 the best manuscripts of Aratus have T E ~ L T & V E T ~("inc ~ a i See tercepts") for the verb in Cleomedes' text, ~ ~ p i ~ i A h ("encompasses"). D. Kidd (1997) 113. 77. T h e radius of the zodiacal circle is thus taken as '16 of its circumference; see Hipparch. In Ayat. et Eudox. Phaez. 1.9.12 (94.16-17) and Schol. in Amt, vet. 320.13-1 j. A scholiast in the latter collection (321.4-6), however, notes that the radius is equal to one side of a regular hexagon inscribed in the circle (cf. Eucl. El. 4 prop. 15 porism). 78. This is how it appears; for the reality see I.q.j7-71.

II8

/

C'leorwedes' T h e Heavens

diameter of j zo,ooo stades, in accordance with the assumptions as we have made them. 334: Yet it is certainly held to be i~nplausible(12) that the planets move at an equal speed in accordance with the course based on choice. Rather, the course of the more distant planets, composed as they are of a more tenuous fire, is much swifter. For how is it possible for the hloon, whose own body is mixed with air, to have its course based on choice equal in speed to those [planets] that subsist from fire, which is tenuous (i.e., estrernely light)?-' 339: So while different claims have been made regarding the size of the Sun, none of the natural philosophers and astronomers has claimed that it has a diameter less than that given above. (Hipparchus, they say, demonstrated that it was 1 , O j O times the size of the Earth!)")So how could it be I foot wide when it is determined as being of i~nrneasurable size by every method of reasoning that adopts an essentially systematic procedure? 345: Yow since [by (7) and ( 2 1 ) ] there have to be 12 j solar magnitudes between the Sun and the Earth, then if the Sun is I foot wide (i.e., the size that it appears to be), the Earth's distance from it will have to be 1 2 j feetlY1 (That means that the Sun will be located well below the highest mountains, since some of then1 have a vertical height exceeding even 79. If the varying density of the planets' aethereal mediums causes them to move at different speeds, then their apparent speeds n-ill also necessarily differ, as they xvould anyway because of their rarying distances from the observer (cf. 11.j.102-10;), even if their real speeds m-ere equal (cf. Eucl. Opt. prop. jq, which proves that "when objects move at an equal speed, those more remote seem [dokt,i] to move more slowly," tr. Burton [19qjj). 80. O n Hipparchus see Toomer ( I y+;; j) 140. 81. Diog. Oen. Fr. 13 col. 11.j-8 Smith (199 3) argued that the Sun's distance was greater than it appeared: otherwise, it would ignite the Earth. Cleomedes could respond that it would then also have to be larger than it appeared. Furley (1996) 1 2 j argues that the Epicureans are conxnitted to a cosmos in which heayenly bodies are not disproportionately distant from an Earth to which they are proportionate in size.

T h e Heavens 11.r

/

I 19

10 stades.)x'Thus,

on Epicurus' doctrine, the Sun's height (in relation to which the Earth is a point, despite [by (q)] being 2 jo,ooo stades [in circumference]), is determined as being 12 j feet from the Earth. That is what is implied by the doctrine of "the sacred soul who alone discovered the truth"lR' 353: -4s for the height of the ,Moon, what could one even say? For if the Sun is I 2 j feet distant from us, and far lower than mountains, houfar distant from the Earth must the Moon be when [by (14)] its circuit is, by the minimum calculation, of the solar circuit?81 357: But even if Epicurus could pay no attention to these [calcul/,,

lations], nor uncover them in an inquiry that was beyond a fellow who valued pleasure, he should at least have paid attention to the actual power of the Sun, and to have reflected [on the following]: (a) that the Sun illuminates the whole sky, which is almost immeasurably large; (b) that it heats the Earth so that some parts of it are uninhabitable because of extreme heat;8' (c) that through its considerable power it provides an Earth that is alivex%o that it produces crops and sustains animal life; and that it alone causes animals to subsist, and also crops to be nourished, grow, and come to fruition; (d) that it alone is what causes not only the daytimes and nighttimes, but also summer, winter, and the other seasons; (e) that it alone is the cause of people being black, white, and yellou; and 82. At I.;.rzj-rzq a maxi~numheight of I j stades is given for mountains. 83. Epicurus was frequently lauded in extravagant terms by memhers of his school; see further Goulet 2 I j n. 286 and Pease (19jj) on Cic. De m t . (11~07: 1.43 and 72, and also lines 461-462, 467 and 487-488 below. 84. Cleomedes could have argued that if the Earth is a point in relation to the hloon (implied by [#] above; cf. n. 67 above), and if the hloon is I foot wide (its apparent size), then for the Epicureans it should also be at the sirme distance from the Earth as the Sun. 8j. Cleo~nedesaccepted that the torrid zone was uninhabitable (see 1.1.88-89, 210-211, 266-267; and 1.2.73-;6), and criticized Posidonius' arguments for its habitability (1.4.90-131). 86. rnrpi~ons:literally "endowed with pneuma," i.e., with the force that is, in effect. the soul of the cosmos.

I zo

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Cleomedes' T h e Heavens

differing in other visible aspects, depending on hou- it sends out its rays to the latitudes of the Earth; ( j ] that the power of the Sun, and it alone, renders sorne places on the Earth well-watered and teeming with rivers, others dry or lacking in water; some barren, others adequate for crop production; sorne acrid and foul-smelling (like those of the Fish-Eaters),&others fragrant and aromatic (like places in Arabia); and different places capable of producing different kinds of crops.

376: T h e Sun is, in general, the cause ofvirtually all the variety found among things on the Earth, since the Earth s h o w considerable contrast at some latitudes. TSTecan, for example, learn of the variety of things reported in Libya, in the territory of Scythia, and in Lake l l a i o t i ~ , ~ % v h e r e the crops, anirnals and, in a word, everything are subject to major transformations, including the temperatures of the air, and its varying states. Then there are the differences observed throughout the whole of Asia and Europe" in springs, crops, animals, metals, and hot springs, and in every type of air-very cold, very torrid, temperate, light, dense, moist, dry-as finally in all the other differences and peculiarities observed at each latitude. O f all these the power of the Sun is the cause. 387: T h e Sun, furthermore, has such a great superfluity of power that the AIoon too receives its light from it,"o and so has this as the exclusive cause of all its power in its different phases, since the A1oon not old!- fashions enormous changes in the air by controlling it and thereby fashioning innumerable purposeful results, but is also the cause of the flowing and ebbing of the Ocean."' 393: T h e Sun's power has also a further observable property: that X;. T h e "Fish Eaters" (Ikhtbuopbngoi) are often associated with the Arabian Gulf; see Hdt. 3.19 and Straho 1 6 . 4 . t 88. This is the ancient natne for the Sea of AZ~T-. See Straho 2 . j . 2 3 , and also 2.1.16 on its climate. 89. Asia, Europe, and L i h y (see lines 378-379 h o v e ) were the continents of the inhabited world known to the ancients; see, for example, Htlt. 4.4: and 198. go. For the details see 11.4.21-32. y r . O n lunar power see also 11.3.61-6;.

T h e Heavens II.I /

I2 I

while fire cannot be extracted by reflection from ordinary fire, we contrive to extract fire by reflection from the rays of the Sun, despite its being such a vast distance away from the Earth. 396: Also, as it goes through the zodiacal circle (that is, as it effects this type of course), the Sun by itself harmonizes the cosmos, and so, by being the exclusive cause of continuing stability in the comprehensive ordering of the whole cosmos, it provides the whole cosmos with an administration that is fully concordant.'? And if the Sun changes its position, either by abandoning its own place, or by disappearing completely, not a single thing will then be born or grow-in fact nothing will "subsist" at all, but everything that exists and is visible will be dissolved together and so be de~troyed!'~ 404:Epicurus, then, should have attended to all this, and reflected on whether a fire that was I foot wide could have a power that was so extensive, so great, and so prodigious.94But in astronomy, in the area of sense presentations, and in every investigation generally, he was the same as in his treatment of the first principles of the cosmos, the theory of the goal of life, and in ethics generally9'-a man far blinder than a bat!96No wonder, since pleasure-loving fellows certainly cannot uncover the truth 92. Despite the "administrative" activity of the Sun, it is the heavens in their totality that play this role; see 1.2.1-4. An earlier Stoic, Cleanthes (ca. 331-230 B.c.), had represented the Sun as the "controlling organ" (h?gemo?zikon)of the cosmos ( S W 1.499), but Posidonius did not follow him; see Kidd Comm. 14j. y 3. See also Cic. De nat. deor. 2.9 I for this argument. 94. Lucr. j. jgz-613 argues that a Sun of extremely small size can cause major terrestrial effects, but concedes the Stoic point by envisaging (at 610-613) an adjacent band of invisible heat that augments solar power. g j. For Epicurus' treatise on the goal of life see Usener Epicur: I 19.13-12 3.17 and Diog. Laert. 10.27, and for that on sense presentations Diog. Laert. 10.28. T h e areas of philosophy identified here could also correspond to the categories of Cleomedes' own program of teaching. 96. T h e English idiom is used here. T h e Greek refers to spalakes (blind rats or moles), which were thought to have eyes under their skin; see Arist. De an. 42 ja~o-11.

I22

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C'1~o~11ede.c' T h e Heavens

in mhat exists. That is for w ~ e nu h o are natural11 d~sposedto xirtue and L alue nothing ahead of it, not for lox ers of a "tranquil cond~tionof flesh" and the "confident expectation regarding it.""414:In an earlier generation they drummed the Epicureans and their scriptures out of communities in the belief that doctrines that had reached such a lex el of blind pen ersion offered people offeiise and corby contrast, because people are, I think, undone by r u p t ~ o n . Today, "~ effeminate luxur); they esteem the members of the sect and their actual treatises so highly thdt they seem to ha1 e a stronger desire for Epicurus and the members of his school to speak the truth than for the gods and Providence to exist in the cosmos. In fact some would even pray for Proridence to be destroyed rather than have Epicurus convicted of false statements.""That is the uretched state that they are in-so reduced by pleasure that they relere its advocate above everything in life! 426: In addition to all the absurdities mentioned, the Epicureans also claimed that heavenly bodies were kindled on rising, and extinguished on setting.lO"Thatis just like someone saying that people exist while they are being seen, but die when they are not seen-or his applying like reasoning to every other visible thing! So Epicurus was such a clever and inspired man that it did not e~-enoccur to him that, because the Earth has a spherical shape, each [heavenlJ-body] sets and rises at different times in different [regions], and so by his doctrine would have to he extinguished g.;. Both expressions were used in Epicurus' "On the Goal of Life" (Pu-i telol,.~); see Usener E ~ ~ C II 2I II.34-I :

22.3

98. For corroborator!- e\idence see Goulet 214 11. 2;;. 99. O n alleged Epicurean impiety see, for example, S '?: 2.111j-I I 16, Posid. F r zki-bEK, and Usener Epiilri: 146.20-148.2 3. 100. This was in fact just one of a set of multiple explanations for the alternation of daytimes and nighttirnes, as Algra (2000) I X3 notes; see Epicur. Pytb. 91, and Lucr. j.6jo-h62 and 758-;61. Ptol. -462. 1.3, 11.24-12.18 refuted it, as did the earlier Platonist Derc)-llides (see 1.2 n. y), according to Theon E.~pos. I 99.2 1-1 2. Posidonius dismisses the audible quenching of the setting Sun at Fr1g.3-6 EK. O n the illogic of rnultiple explanations see 12jsserstein (1978) 490-49

1.

T h e Heavens 11.I

/

I2 3

and hndled sim~~ltaneously. At every alteration in horizons, that is, there ~ r o u l dhave to be, in repeated progressions, incalculably numerous cases of the destruction of bodies-bodies that were both destroyed and rekindled, since this v-ould happen at every alteration in horizon.lO' 438: IZTecan learn about the alterations in horizons from countless other [phenomena], but preeminently from reports of [the lengths of] daytimes and nighttimes at the solstices among different races.I0' Thus the [lengths of] nighttime at the summer solstice are reported [as follows for these places]: hours

Aleroe in Ethiopia

II

Alexandria

10 hours

T h e Hellespont

9 hours

Rome

under 9 hours

Alarseilles

811.hours

Among the Celts

8 hours

Lake Jlalotis

j hours

Britain

6 hours

It is obvious from these [reports] that the Sun sets and rises at different times in different [regions]. This happens also for people below the same parallel circles (that is, with identical seasons), whether they are located hrther east and encounter the Sun's onset sooner, or in the west and do so later.'"' So if there are countless alterations in horizons (there being a different one at every latitude of the Earth), heavenly bodies will have to be extinguished and kindled incalculably Inany times. Anything more 101. If the Epicureans thought that the Earth was flat (cf. 1.j 11. 6), then horizons would / l o t alter (I.j.j0-44), hut their theory would still have other problems. 1 0 2 . On Ptol. Alrv. 2.6, the rliajor ancient evidence on variations in lengths of daytimes, see Neugebauer (19jj) 44. For more ele~nentaryaccounts see Gem. Isi/g. 6.7-8, AIart. Cap. 8.8 jj(cf. 6. jg j), Plin. ,VH 2.186, and Straho 2.5.38-42. 1 0 3 . These are theperioikoi: see 1.1.236-2 j1 and cf. I. j.3;-39.

I 24

/

C'1eonze~le.s' T h e Heavens

unthinkable in its display of every kind of reckless ignorance could not be even conceived! 452: Certainly not even the illunlinations of the AIoon, despite being very vivid, restrain the Epicureans from such ridiculous clai~ns."'~ I mean, how could the 31oon be illuminated and shine throughout the night, if the Sun is extinguished on setting? O r horn-is the _\.looneclipsed on falling into the shadox- of the Earth, if it is not even illuminated at all? O r how does it exit from the shadoxv and become illurninated again when there is no Sun below the Earth? O r how does the Sun itself, if it is extinguished, reach its point of rising again? Epicurus, in het, believed in an old wives' tale, like the Iberians' report that the Sun on falling into the Ocean makes a noise when it is extinguished like red-hot iron in water. That is how "the first and only man to discover the truth" arrived at this doctrine! And he did not even understand that every part of the heavens is at an equal distance frorn the Earth, but believed instead that the Sun sank into the sea and rose arain from the eastern sea-landled by water in the east, but extinguished by it in the west! 467: That is what the "sacred \visdomn of Epicurus discovered! But, by Zeus, it occurs to me to compare him to Homer's Thersites. For Thersites was the worst man in the Achaean army, as indeed the Poet himself says and portrays Odysseus as saying. His own words are "He m-as the ugliest man to come to Troy" and so on, while he depicts Od!.sseus saying to Thersites: "There is no other mortal man, I vou; bvorse than

""

v o u . " l O B ~despite t being like this, he still did not keep his peace, but

104. T h e option of lunar illun~inationh! the Sun is in fact included in Epicurean multiple explanations; see Epicur. &h. g j-96 and LLIC~. j.~0j-714. Ioj. T h e r e is n o evidence of the Epicureans causall!. linking solar landling and extinction ivith a circurnarnbient ocean. (Ptol. .-llm. 1.3, 11.24-fi jiust refers to the Sun falling "to the Earth.") Cleomedes did not mention this additional 21)surdity earlier, but (cf. lines 13-19 and n. ;aboi-e) onll- a less bizarre theor!- of solar reconstruction ("kindling") through interaction with the air. 106. I h d 2.216 and 248-249. On the general topic of the Stoic reading of H o m e r see Long (rygz).

T h e Heavens 11.r

/

I zj

first wrangled boastfully with the kings as though he too had status, then dared rank himself among even the leaders by mentioning "[the women] whonl W-eAchaeans give jrou first whenever we take a stronghold . . . [the man] whom I or another Llchaeanmight bring in in chains."10;In this vein Epicurus too boasts of being important, given that he tries to include himself among the philosophers, and not just that, but also affirms the right to take first prize, and thereby reveals himself as more thirstily ambitious than even Thersites. T h e latter, after all, boasts only of being a prince and an equal to the kings, but does not also assign himself first prize, whereas Epicurus clainls that he alone has found the truth through his vast wisdom and knowledge, and so thinks it right that he should also take first prize.

489: T h a t is why I would believe it to be quite wrong for someone to say to him: "Babbling Thersites, clear orator though you are, hold offf'!""'Vor I would not also call thi.~Thersites "clear," as Odysseus does the Homeric one, when on top of everything else his mode of expression is also elaborately corrupt.10"H e speaks of "tranquil conditions of flesh" and "the confident expectations regarding it," and describes a tear as a "glistening of the eyes," and speaks of "sacred ululations" and "titillation~of the body" and "debaucheries" and other such dreadful horrors. Some of these expressions might be said to have brothels as their source, others to resemble the language of women celebrating the rites of Derneter at the Thesmophoria, still others to come from the heart of the synJew talk, far lower than the reptiles! 503: But despite being like this in discourse and doctrines, he still does

agogue and its suppliants-debased

not blush to rank himself with Pythagoras, Heraclitus, and Socrates,'I0 even asserting the right to occupy the first place among them, just like 10;. Iliild 2.22 7-228 and 2 3 I . 108. I l u d 2 . 2 4 6 - 2 4 7 . 100. For ancient attacks on Epicurus' style, and especially his use of neologisms, see Usener Epirtii: 88-90, and Pease (19j j) on Cic. 13e nnt. deoi: 1.86. I 10. Posidonius respected Pythagoras ( T ~and I Tq jEK); for Heraclitus see 1.8.96-97; on Socrates, the early Stoics, and the Epicureans see Imng (1988).

I2 6

/

C'1eo~~1ede.s' T h e Heavens

temple robbers trying to rank themselves with priests and hierophants by asserting the right to hold first place arnong them! Or imagine Sardanapalus trying to square off against Hercules in an endurance test, and grabbing Hercules' club and lion skin and telling him "I have more right to these!"" ' 511: JTill you not be off, e\ 11 degenerate, to our saffron-robed whores, a i t h U horn you will dally on couches, u hether combing purple v ool, or wreathed in crouns, or ulth ).our eyes painted, or even entertamed bp the N Z I I Oin S ~excessi~e ~? and unseemly drunkenness, and then coming to the final act like a worm \vallowing in utterly vile and excremental slime? So will you not be off, "most brazen and shan~elesssoul," routed from Philosophy, to Leontion, Philainis, and the other whores, and to your "sacred ululations" with Alindyrides, Sardanapalus and all your boon

companion^?"^ Do you not see that Philosophy summons Hercules and Herculean men, certainly not perverts and their pleasures? Indeed, it is evident, I think, to cultivated people that Epicurus has nothing to do with astronomy, let alone with philosophy."+ I I I.

T h e contrast between this hedonistic Assyrian monarch (seventh cent.

R.c.)and Hercules was standard; see, for example, Jurenal 10.361-362. O n Hercules' club and skin as s p b o l s of strength see Cornut. Thrul. 63.12-21 (at S I T

1.514). This was a reed instrument and the principal wind instrument of Greek music; see Alichaelides (1978) 42-46. I 13. Leontion was an associate of Epicurus; see Csrner Epzrlri: 41 I and Pease (19 j j) on Cic. DE17nt.deo~:1.93. T h e other narnes are conventional symbols of hedonism; see SCIF 3, pp. 198-200, and Goulet 2 16 nn. 298 and 299. 114. Astronomy, this sentence implies (see Goulet 39 n. 31 on its con(see struction), is subordinate to philosoph!; as claimed by Posidonius F I ~ E K Appendix). I 12.

CHAPTER TWO

I: \Ye

have demonstrated that the Sun is not I foot wide, and so certainly not the size that it appears to be. Next we shall try and establish that it is larger than the Earth. This has already been in effect demonstrated, yet something else was being primarily established in the earlier discussion.' Here, however, we shall speak directly about this [thesis], starting out from the phenomena alone.!

7: In the first lecture course we demonstrated that the Earth, through having the ratio of a point [to the size of the cosmos], conceals none of the [celestial sphere's] 360 degrees, indeed not even a small fraction of a degree, since, as is demonstrated by the equinoxes, precisely 180 degrees always show above the Earth, along with the 6 zodiacal signs, and half of the equinoctial circle.' So since the Earth does not conceal even a snlall fraction of a degree, whereas the Sun occupies a magnitude of almost I/? degrees,+the Sun is larger than the Earth. I . 111 the calculations of the siz,e of the Sun at 11.1.286-312 the relative size of the Earth n-as mentioned only at 11.I . 2 94-2 y 6 in connection with Eratosthenes'

measurement.

For reasoning siinilarly based "directly" on the phenomena see also 1.j.104-113. 3. Cf. 1.8.37-43 w ~ t h1.8 n. 11 4. See 11.1.329-330. 2.

13: Now if we also hypothesize something equal in size to the Earth rising or setting [like the Sun], it will not spend an>-time at the horizon.' That is because just as the Earth, given its position in the exact center [of the cosmos], does not conceal even a small fi-action of I degree, so too something equal in size to the Earth will not spend any time at the horizon when it rises or sets. Yet the Sun both rises and sets over an extended i n t e l ~ a of l time. It is therefore larger than the Earth." 19:-=Use, when one spherical body is illuminated by another, then if they are equal [in size] to one another, the shadow of the illuminated body is sent out in a c!-lindrical form. But where the illuminated hody is the larger, the shadow is funnel-like,xwith its [outer] ends being continually further widened and its fom-art1 progress being without h i t . But if the bodv that causes illumination is larger, it is necessary that the shadow of the body that is illuminated be configured in the shape of a cone. S o w since both the Sun and the Earth are spherical bodies, and the former causes illumination while the latter is illurninated, it is necessary that the shadow of the Earth he sent out with a shape that is either funnel-like, cl-lindrical, or conical. But it is neither cylindrical, nor funnel-like.

j. Tiking the ratio of the E;irth's diameter t o that of the Sun as approximately 80,000: jro,ooo st;ides (or 1:6.j) (cf. II.1.2yj-zy6 and 3 1 I-3rz), then, adapting the example at 11.1.14j-148, in which a horse ran 10 stades nhile the Sun rose, , a t the same tiistance from the the Earth (or a hody of equivdent s i ~ e )located Earth as the Sun, \vould appear t o rise for a terrestrial obsen-er in the time taken by such a horse to run just over I.; stades. 6. For a more elaborate version of this a r p m e n t ]l!- the Stoic Dionj-sius of C y e n e (a near contemporary of Posidonius; cf. 11.1 n. 26) see Philodem. Dc sig 711S cols. 10-11 (sect. I j D e Lac!- [I~;H]).and Barnes (ryqo) 2661-2662. 7 . See Figure 2 I for the shapes proposed in this paragraph. 8. T h e adjectil-e so translated (knlictlwi&.$ literall!- means "basket-like," n-here the container (knlicthos) has 3 base signiticantl!- mrron-er than its opening; i.e., it is shaped somewhat like a modern tilter funnel, or, in relation t o the present -\. 2.51 calls a t ~ r l d on~ctlrs(an upcontest, like a n inverted cone, or u hat Plin!- H right spinning-top).

The Heavens II.2

/

I zg

Therefore it is conical," and, if that is so, the Earth has as the cause of its illumination something larger than it-the S u i ~ . In ~ "the discussion concerning the 1Zloo11'~ n e shall demonstrate that the Edrth's shadon 1s neither fimnel-like, nor cylindrical. That, then, is enough on the size of the Sun. 9. 'This argument (also at Heraclit. .4lley/: 46. I'lin. Y H

I .j I,

and *Pheon

Ii.~po.~.195.j-I 97.7) implicitly relies on the Stoic "fifth untlenmnstrated argument" (see I.j.20-2y and 1.6.1-X), in nhich all but one of a set ofdisjuncts are eliininated. 10. Posidonius (FyEK) :irpes thlit the Sun is larger than the Earth 11ec;luse the Earth's shadou is conical in a lunar eclipse. I I . At 11.6.;9-108.

CHAPTER THREE

I: T h e notion that the 11oon too is not the size that it appears to be can also be formed from what was said above about the Sun (that is, most of a-hatwas said there can also be applied to the JIoon),' but it is the eclipse

of the Sun that primarily demonstrates this. That is because the Sun is eclipsed only when the l l o o n passes under it, and obstructs our line of sight; a solar eclipse, in other words, is a condition affecting not the Sun, hut our line of sight.' So whenever the ,\Ioon passes under the Sun such that it is in conjunctio~lwith the Sun, and at that conjunction is located on the circle through the middle [of the zodiacal band],' it necessarily sends out to the Earth a conical shadow, reportedly extending over more than 4,000 stades (the 11oon's shadow equals the total area in M-hichthe Sun is invisible when the JIoon moves below it). So if its conical shape is extended over this much of the Earth, or even more still, the base of the cone (also equal to its diameter)4 is clearl!- many times larger.

S. On the apparent size of the 1Ioon see 11.1.114-128 (with 11.1 n. 2; on the Epicureans). 2. For this definition see SLT 2.6 j o and Posid. F I jEK. ~ See also 11.4.127-131. 3. That is, it is located on the zodiacal circle. 4. See also 11.1.67.

T h e Heavens 11.3 /

I 3I

IS: Also, an obsen-ation of the follo\ving land occmred at a solar

eclipse.' On an occasion when the Sun was totall!. eclipsed at the Hellespont, it was obsen-ed at AAlexandriaas eclipsed beyond of its on-n diameter," which is just ores 2 digits in appearance. (The apparent size of the Sun, that is, and similarly of the Moon, is held to be 12 digits.)- So from this it is clear that the d i g i t appearance of the size of the ;\loon I/;

and Sun is coextensive with a distance on the Earth equivalent to that between AAlesandriaand the Hellespont, both ofwhich are located below the same meridian."^ if by hypothesis the [conditions] of this eclipse remain fixed, then for people initiating a journey from Alexandria to the Hellespont the 2-digit appearance" of the Sun seen at -Alexandria would become proportionately less. As there are 5,000 spades from Alexandria to Rhodes, and another 5,000 from there to the Hellespont, the appear-

j. 7'he eclipse is that of Jlarch 14, 189 B.c.; see Neugebauer (19: j) 316 n. 9. It u as recorded by Hipparchus; see Pappus I71 Ptol. j.1 I (68.j-g), and cf. Pr6aux (1973) 2 j 5-2 56. 6. In other ords, the Sun u-as obscured to +/, of its diameter. 7. Cf. 1I.t.1I j , and sec Figure 2 2 . By Ptolerny's time (cf. Alr~r.h.j), itwas the practice to define the maximum obscuration or magnitude of an eclipse in terms of digits, where I digit ( d f ~ k t ~ d oiss )'l,? of the diameter of the eclipsed body. T h e eclipse in question thus had a magnitude of 1 2 digits in the Hellespont and almost I O digits in .Alexandria. Such digits are not the same as those digits of angular measure which are found in Bahylonian astronomical texts, and amount to j ' of arc each (cf. Toorner [1gX4] 3 2 2 n. j). Kor are they the digits, or finger'sof a hanti's span (.cpithnn@). breadths, that m-ere ' / , h of a foot (poli.9, or 8. There is in Fact no such coextension (or alignment). As Neugebauer ( [ ~ q j] ; 964) notes, the "obscuration of one sphere by another does not ,-ar!- linearly with the displacement of an ohsewer on a third sphere." q. pbnsis: the term translated "appearance" here is being used, as it often is, as a synonym for the commoner term for appearance,phm?ztnsi~~; cf. line 2 0 above for "the d i g i t appearance (pbn7ltizsin)." In astronomy, howe\.er, it acquires the more technical sense of "appearance at a significant confi_pration with the Sun" (cf. Toorner I19841 2 2 ) . Thus the fixeti stars and planets are said to have phases, e.g., the first visibilityofa fixed star at sunset, and at 11.j.70-71 Cleoniedes refers to "the phase of [lunar] illumination."

ance of the Sun seen at Rhodes will necessari1~-he I digit."' T h e n as they go from Rhodes to the Hellespont, this appearance too \\-ill be proportionately diminished, and will finally be out of sight when they reach the Hellespont. So clearly, if the 2-digit appearance of the size of the \loon and Sun is coextensive with so great a quantitj- of the Earth, it is necessary that their whole bodies be coextensiw with 6 times such a quantity of the Earth." 34: From this procedure the notion can be formed that the [remaining] heal-enly bodies too are of enormous size (but certainly not the size they appear!), and particularly the fixed stars, n-hich are the fiarthest

aria!:" For while the difference in their sizes is ohsen-ed to be large, none appears less than I digit. Tenus in h c t sends out the appearance of 2 digits, making its diameter

of the Sun's diameter, assunling that they are

the same distance from the Earth, hut othenvise in proportion [to their true distances].l-' T h e size of the bodies that appear I digit in diameter is I/,: of the Sun's diameter, if they are assumed to be at the same height as the Sun, but since the!- are at a greater height, the proportion of their [true] distance will he taken into a ~ c o u n t . ' ~

10. Straho 2 . j.40 gix-es the approximate clistmce from Alexandria to Rhodes as 3,600 st-acles, and that from Rhodes to ;Ucxandria in the 'Troad as 3.400. 11. H e r e again (cf. I.; m . 9 and 21. and 11.1 m. j8 and 73) a calculation is i~nplicitlybased the principle that nr-o ratios (or spatial coextensions) are the same: i.e.. z digits:~o,ooostacies :: r z digits:60.000 stacies. T h e implicit conclusion. then, is that the Sun must hare n dixneter of at least 60,000 stacie,, sufficient t o show, a i a preliminary "notion" (cf. i.i~i~oiziii at ljne 34 M O \ \ ,and 1.1 11. qo), that the Sun is not the size it appears to bc. 1 2 . For the Epicurean claim that the tixed stars are as large as they appear see Epicur. q,'tb. g I , and Lucr. 5.58 j-, y I . I 3. AI supralunar>-h a \ enly bodies are %er> " in proportion to their distance into the fire-sphere ofthe acther (11.1.33j-336; cf. II.i.q),yet inherent luminance is not a factor in this anal!+, or in that otl-ered in the nest paragraph. 14. Here this formula is used to admit that a celestial distance uincorrect, just because it is a pure hypothesis. (If. 1.7.46-47 (nit11 I.; n. 11) where it is a safep a r d a p i n s t the plausible measurement of a terrestrial distance being incorrect.

T h e Heal ens 11.3 /

133

43: Thus the question of whether some heavenly bodies are also equal to the Sun's size, or even exceed it in size, should not he abandoned. If, for example, one of them were elevated so far that the Sun, if also imagined elevated just as far, will be seen possessing the size of a star, then it will be equal [in size] to the Sun. But if elevated farther, it v-ill be larger in proportion to its height. So since the fixed stars at the outermost circumference of the healms are very distant, though none is less than I digit in appearance, the!- will all be larger than the Sun. l' (Furthermore,'" the Earth, being a point in relation to the height of the Sun, would either not be seen at all by a human being when seen from the height of the Sun, or else would be seen to have the size of an extremely small star, whereas from the sphere of the fised stars it would not even be seen at all, .'-) It is evident, then, that all the stars seen at this height from the Earth are larger than the Earth, as of course is the Sun itself too, to m-hich many fixed stars are also probahly equal in size, or even exceed it in size. That, then, is our discussion concerning this topic. 61: As for the size of the Jloon (specifically its not being I foot wide) evidence can also be derived from its power, since it not only illuminates the whole sky, fashions major changes in the air, and has many things on the Earth in sympathy u-ith it, but is also the exclusive cause of the ebbing and flowing of the Ocean.'" 65: T h e preceding [discussion] is an adequate argument that neither the Sun, the JIoon, nor any other h e a ~ m l ybody, is the size it appears to be. 1 j. This t-isibility is caused by a luminance that increases in proportion to the distance from the Earth; see 11. 13 above. 16. This parenthesis (lines 51- j j ) repeats 1.8.2 1-2 6 , where the radius of the Earth is shown to he negligible in most celestial ohsen ations. 17. T h e clause in angle brackets is at lines 52-53 in the manuscrilm, where it disrupts the reasoning; here it parallels the argument at 1.8.2 j-26. 18. On the \Ioon's "power" see 11.1.387-392 0 1 7 the causation of tides see Posid. Fr38EK. anti cf. Fro6EK.

I

3 4 / Cleomedes' T h e Heavens

68: Now while none of the other heavenly bodies (at least those visible to us) is held to be smaller than the Earth, astronomers claim that the Moon is smaller than the Earth,' offering as their primary evidence the fact that its diameter measures out the Earth's shadow twice.?O Again, at solar eclipses, as we have already said,?' the Sun has been observed partially eclipsed at Alexandria during a total eclipse at the Hellespont. This would not happen unless the Earth had a significant size relative to the Moon:12 in other words, if there is this much difference over a distance of ~ o , o o ostades, the Moon evidently does not cast a shadow on much of the Earth. But if the Moon were equal to, or larger than, the Earth, it would cast a shadow on a considerable area of it during its courses below the Sun. But in fact there will even be areas of the Earth where the Sun is totally visible, while it is being totally eclipsed elsewhere. 81: T h e Moon does appear large, in fact equal in size to the Earth, and larger than the other heavenly bodies, when in reality it is smaller than they, since it is closest to the Earth of all the heavenly bodies, and thought to be located right at the junction of the air and the aether.23 That it is the closest of all [the heavenly bodies] to the Earth is demonstrated from [the following considerations].*' (R) For those who view the 19. T h e Stoics ( S W 2.666) and Posidonius ( F I ~ z E Kare ) both reported as claiming that the Moon was larger than the Earth. Theiler (2.179) and Kidd (Comm. 472) are reluctant to attribute this view to Posidonius, and argue that he agreed with Aristarchus that the diameter of the Moon is half that of the Earth (cf. 11.1.286-2 88). See also Pease (195 j) on Cic. De nut. deor. 2.103. 20. See 11.1.286-288 on this being determined at total lunar eclipses. 2 I. At lines 15-33 above. 2 2. I.e., if it was not observationally insignificant (or "a point") in relation to the Moon; see 1.8.106-112 and cf. 1.8 n. 2. 23. See also 1.2.37-38. 24. Statements (a)-(e) all record observations. T h e physical theory introduced in (b) is not essential to the argument from observation. Thus the lMoon's proximity to the Earth, like the cause of its eclipses (see 11.6.35-36; cf. 11.6.56 and 194-196), is directly demonstrable from the phenomena.

T h e Heavens 11.3 / 135 Moon with special care it is demonstrated by sight alone,25since no other heavenly body goes under it, whereas it is seen to pass under all the planets. From this it is demonstrated that they are more distant than it. (b) Its own body is mixed with air, and is rather murky [in a p p e a r a n ~ e ]be,~~ cause it is not in the unadulterated [part] of the aether, like the rest of the planets, but, as we have said, at the junction of the two elements [the air and the aether]. (c) T h e Moon alone falls into the Earth's shadow, but none of the other heavenly bodies do; otherwise they would at different times appear brighter and fainter, since every body that is composed of fire appears brighter in a shadow, but fainter under the rays of the Sun." (d) In contrast with the other heavenly bodies the Moon has a unique sympathy with bodies on the Earth, just because of its greater proximity to the Earth.28(e) It goes through its own circuit in 2 7 % days,29whereas no other planet has a period of less than I year. 100:It is evident from these [phenomena] that the moon is the closest to the Earth of all the heavenly bodies. 2 j. "Sight alone" would not, of course, be an adequate criterion for establishing the nature of something unobservable; cf. 1.5.1-9. 26. See1I.j.1-4,andII.jn.3. 27. See 11.6.101-105, and cf. Sext. Emp. PH 1.119. Also cf. 11.4 n.10 below on the special case of the Moon. 28. See lines 61-67 above. 29. See 1.2.41-42.

CHAPTER FOUR

I:

T h e r e h a e been sex era1 t h e m e \ c o n c e r m n g t h e d l u ~ n ~ n a t ~ofo tnh e

\ l o o n . ' Berossus ~ ~ t u a l cl l)m n e d that t h e J l o o n n as "half fire," and that it moved with a pluralit>- of motions.? First is t h e o n e i n longitude;' seco n d the o n e in latitude (that is, i n height a n d d e p t h [relative t o t h e zodiacal circle]), which is also seen occurring in t h e case of t h e five planets; I . For the three theories considered in this chapter see :Ipuleius D e i k Sotratis 117-119, nith Donini ancl -Berossus' first motion as the ,\loon's diurnal notion, nhich is not longitudinal, M-hereasits longitudinal motion is sidereal, i.e., in rhc opposite direction to the cosmos (as identified collectively for the planets at the 1.2.8-I I). In this n-a>-M-eaddress the p o l ~ l e r nof the omi,sion of sidereal motion raised hy Goulet zro n. 336. ITTe

and third is the one around its own center. Berossus belie~esthat the A\Ioonwaxes and wanes as it rotates with this third motion, that is, as it turns difierent parts of itself toward us at ditierent times, and that this rotation occurs in a time equal to its reaching conjunction XI-iththe Sun. 10: IIis doctrine is easily refuted. First, since the Aloon exists in the aether, it cannot be "half fire" rather than being completely the same in its substance like the rest of the heavenly b o d i e ~Second, .~ what happens in an eclipse also conspicuously disconfirms this theory Berossus, that is, cannot demonstrate hon; when the I\loon falls into the Earth's shadow, its light, all of which is facing in our direction at that time, disappears from sight.' Tf the Aloon n ere constituted as he ~tv ould h a e to - ~ on f d l ~ n gInto the Earth's shadom- rather than become n ~ o l lum~nous disappear horn sight' 18: Others sal that n111le the \loon ir ~ l l u n ~ ~ i i ah) t e dthe Sun, ~tillum i ~ ~ l tthe e s a ~h)r reflection, as 15 seen happen~ng&o with rnmors, bright silver objects, and the like. 2 1 : A third option claims that the ,\loon's light is mixed both from its own %alld from the Sun's light, m d that such a [state] comes ~ l x ) u t regal-(1 the test at 11.4.2-3 as having been contaminated by the reference to the motion that "occurs together with the cos~nos,"which %as prohabl!. original1~-a gloss that \$-a\ ~nisrakenlyinserted into the text. For planetary latitudinal motion at lines 4-5 see 1.2.64-69. 4. T h e AIoon, that is, callnot h a w two radically distinct parts, if it is locatcd in the aether, sincc while the aether may he less dense at greater distances from the Earth (cf. II.1.336), it must he equall!- dense at any specitic distance. On the other hand. it may be difficult to Jifi%rentiatethe AIoon if it shares in all the phys; 'Ibdd (2001). ical properties of its m e d i u ~ n see j. See lines 82-94 helon- for an account of how lunar eclipses occur h! the theory advocated in this chapter. 6. T h a t is, if it were inherently luminous by heing "half fire." .; For this principle see 11.3.c)~-952nd 11.6.103-103; also Plut. D~'j2c.93 jL). 8. T h i s supplement, confirmed by lincs 80-81 helon-, rules out the interpretation of this third theor!- as i n r o l ~ i n gthe admixture of two kinds of light: solar light and an inherent lunar light. Goulet 2 2 1 11. 346 rightly rejects this proposal, made h!- Cllerniss (rgj;) 123 n. c. \{-h0 is followxi by &dd Con?)lt.474-47j. If

I38

/

C'li.ov~edrs'T h e Heavens

through its not remaining unaffected. That is, unlike solid bodies that give off light, it does not hare solar rays rebounding from it and illuminating the air by reflection in a process of reception that involves its reciprocating the ra>-Sand thereby sending them back in our direction. Instead, the A1oon is altered by the light of the Sun, and through such a blending possesses its own light not intrinsicall!; but derivativelyy(just as fully heated iron possesses light derivatively), since it is not unaffected, but is transformed by the Sun. This option is sounder than the one claiming that the Aloon causes illunlinatlon by reflection because rays rebound from it, as is seen happening where bodies that are solid give off light. 33: T h e inqmssibility of the AIoon sending out light by reflection might be best summarized by the following [argusnents]. 34: ("l) It is not impossible for reflection to occur from relatively solid bodies (reflections are also seen occurring from water, since even water is to some extent compact), but it is impossible for reflection to occur from rarefied bodies. After all, how could reflection occur from air or fire,l0when such bodies are i~lturnllydispo5ed to absorb light rais, > e t are not illurnlnated h! them just on the surface, but fully absorb

nothing else, inherent lunar light is excluded by the criticis~nof Berossus' theory above. rUso, pnce f i d d C'o~zm.476, this theor!- of ad~nisedlunar light could he Posidonian (cf. n. 19 below). T h e h c t that at Posid. Fr2;EK the AIoon is called "luminous and fiery," and at F1 2 2 . 1 - 2 EK is ,aid to be mixed from air and fire, does not mean that it also has an inherent and risible lunar light. ,hi!. such luminance can be totally lost (see lines 82-94). W-hileany inherent light is risible only under special circumstances (see n. 10 below). 9. kntir metokhin: literally. "h? participation." 10. Air and fire nlingle at the point of their coniunction (1.2.37-38; 11.3.83-84) in the lower part of the aether, where the ,\loon is located (see line 1I). T h e 1Ioon is therefore ''mixed u-ith air" (11.3.88; 11.j.2 and 6), hut too loa- in the aetherial fire-sphere to be inherentlj- luminous. Hence its igneous component furnishes a "murky" appearance, clearly risible onl!- n-hen the Lloon is darkened during a lunar eclipse; see 1.2.38,11.3.89, and 11.j.2-4 with 11.j n. 3.

T h e Heavens 11.4 /

I 3y

anything that impinges 011 them, just as sponges invariably absorb water?'" 42: (17) T h e light from bodies that illuminate by reflection is sent out a short distance, but the hloon not only sends out its luminance as far as the Earth, but also illuminates the whole sky. Yet bodies that illuminate by reflection do not send out luminance even 2 stades, as can be seen with mirrors as well as with every single body that illuminates

h>-reflection. 48: (c) If anyone suggests that in illuminating by reflection the Moon sends its light farther than the [solid] bodies just n~entionedbecause it is extremely large, we shall respond that both sinall and very large bodies that illuminate by reflection are subject to the same proportional progression:" that is, a larger area will be illuminated by large bodies in respect of length, yet light will certainly not he sent out a greater distance forward. Instead, whether the body that illuminates by reflection is I foot or I stade wide, it will send out its light over a distance that is equal in respect of its depth. 56: ((l) It is in addition quite evident that if the Aloon caused illumination by reflection, it m-ould not illuminate the Earth at either the crescent or the quarter.'3 That is because objects that illunlinate by reflection send out their light at right angles, and so, since the A10on is spherical, its light would be sent out to the west in the phases just men-

I I. O n lunar density see the prohlerns and solutions at lines 81-94 and g j-10 j helou.. Since the AIoon's "sponginess" does not allow it to he totally permeated l)! its ahsorhed light (lines 101-102 h e h ) : dz'huli71 (line 40 here) must he translated "fully" rather than "totally." See also 11. 24 below. I 2 . T h a t is, the larger the reflecting surface, the larger the volume of air illuminated tn.0-tiimensionally ("in respect of length"). 13. For this argument see also Plut. De f2c. 92gF-930rl. T h e ancient Greeks used dik/~otonzo.i(literally "cut in half ") to describe the ,\loon X-lienthe Sun's light illurni~iatesesactly half of its face. This happens at what we call the first anti last quarters.

140 / Cleomeder' T h e Heaven5 tioned, and thus straight toward the Sun.I4 Indeed, not even when full would it cause illumination with the whole of its circle. It would do so if its shape a-ere flat,'! but since it is a sphere and tlms has the extremities of the circle that is visible to us sloping round,"' illumination from these sloping [extremities] 11111 be sent out at equal and right angles, n ith the result that oldJ the \er! iniddle of the JIoon \\111 illu~mnatethe Earth, not its u hole c~rcleIn other ords, the llght from the er! nucldle of the AIoon c m he sent to\\ ard the Earth ~t right angles, but the l ~ g h from t ~ t sloplng s [ e ~ t r e n i ~ t ~ eU shlch ] , do not f x e the Earth, cannot. So ~t the \loon caused illurn~nation,!I reflection, ~ t Us hole c~rcle I\ ould not illuminate the Earth. But ~t 15 e\ ]dent tlut the Earth 1 5 illuminated from its whole circle.'- In fact, as soon as its outer rim rises above the horizon, it illuininates the Earth, although its parts t h ~slope t round fice the hear ens, certainly not the Earth. So since the 11oon illu~ninates not oidy nith its middle, which faces the Earth, but also with its sloping [extremities], which do not face the Earth, clearl!- it does not send out its light by reflection.'~nstead,it is because it is illuminated through14, T h e argument here is compressed. Cleomedes posits that spherical ~ n i r rors send out their light at right angles to their surfaces, i.e.. raclially (cf. Goulet 2 1 1 11. 3 j 0 ) . His point is that the \loon. \ \ h a 1 it is at die crescent or quarter, uould thus not reflect an!- light to the Earth. See Figure 23. Stephen Alenu has raised in a private communication the intriguing possibility that Cleomedes has girbled a somewhat t~ettera r p m e n t , originally framed in terms of ref ection at f,yu~zlangles, h!- casting it as one a l ~ o u reflection t at riyht angles. I j. Cf. 1I.j.j;-40 n h e r e a LIoon n i t h a flat shape is also said t o he incapahle of undergoing phases. I 6. T h e adjectivepi,i-iklii~?.i,("sloping round"), used frequently in this contest. refers to the bulhous nature of a hemispherical h d ! . I t is used, for example, of the dome of a building. I;. Cf. Plut. Detii. 9 3 0 E on l u n x illumination geometrically demonstrated as occurring by reflection from a cu~?-et1surface. 18.T h i s conclusion is reached trithout taking into account the size of the \Loon, and its distance from the source of its illuminntion. \ T l e n noted at lines 102-103 Ixlou; they are used to defend the 1-iea-that the \hen cannot be totdl!. penetrated h! the Sun's light.

out by the rays of the Sun (that is, has its light in a blended form) that it illuminates the air. 79:'' Since the AIoon causes illumination in this way rather than 11y reflection, obviously its light is blended both from its own hody and froin the rays of the Sun. Yet there are thought to be the follorving prohlems [with this theor!,].

82: Hoz: does the L110072S: light dis~~ppear as soo~as it jdls iuto the shador of'the E a r t h Conversely: Ho-;. is the same [light] i'isible i77 it as soo~z~ . sit I e a i ~[thnt shadoi:]? But there is no need to raise this problem and puzzle over it when something similar is seen ~vhenthe N ~ I is . illu~ninated.~~'

If, for example, a light is brought into a darkened room, the internal air is immediately illuminated; and if the light that illuminates it is extinguished, the air is darkened at exactly the same time as the e ~ t i n c t i o n . ~ ' This is also seen occurring in the case of the Sun when at its rising the air is immediately illuminated, u-liile it is darkened at the same time as the Sun is concealed by the horizon." (Even if by hypothesis the Sun is extinguished by falling into the Ocean,?! not only would the air he dark-

19. T h e three problems that follon- (lines 70-126) are sufficiently interconnected to have had a common source, which m-as probably Positlonius, a e n though he is only mentioned (line 9 8 ) in connection with the seconcl. ('l'heiler Fzgr stops, without good reason, at line 107.) K~dd'shesitation on this point (Chmm. 47 j-476) is based on his interpretation of the earlier theory of lunar illumination as the hlend of lunar and solar light. But, as we haye seen (n. 8 alwve), that theory is one of admixed light, to which Posidonius could have subscribed; in that case, he could have defended it by all three of the arguments presenteci here. 2 0 . Since the \loon is a separate hody, and not just any random volume of air, the analogy here is loose. 21. Xex, riphr. DE aiz li111:7 I I N i I f . 139.17-19 argues that light cannot be suddenly extinguished in a confined space, if it is, as his Stoic opponents claim, a body 2 2 . But the "northern lights" (1.4.196-zo;), and refractively caused solar illumination (11.6.168-177 and 18;-I~I),can both occur after sunset. 2 3 . This is the Epicurean theorl; criticized at 1I.r.qjg-466.

142 /

Cleomedes' T h e Heavens

ened when this happened, but it would also get dark at exactly the same time as the extinction.) It is not, I think, at all puzzling to have a similar result in the case of the Aloon, too, whenever it falls into the shadow of the Earth. Such is the nature of bodies that are rarefied 95: Another problem raised in this area is: U%y in solar eclipses do the m y of the Szm not rend orlt lzght by (ovzpletelype1zet1atl71gthe l loon, a! the)! do clo~ds,whzch are denser than the .Zloon? Posidon~usduly responds that not onlj 1s the surface of the l l o o n illurnlnated b) the Sun (as In the case

of sohd bodies that haxe o n l ~their surface illummated), but that the l l o o n , as a rarefied bod!, has rays from the Sun penetrating ~tto a Lery great distance, yet not totally.'i T h e reason 1s that the Aloon has a considerable volume because of its very large diameter, and because the Sun is no small distance from it. Cloudy air," by contrast, inasmuch as it has no ~ o l u r n e , takes ' ~ in ray? that easily penetrate it. (It may be relevant to mentlon that the hloon's compactness, through a hich the rays of the Sun cannot escape, also has a unique physical qua11ty.)~108: ,A further problem raised is: Hoi: does the Atloon,ac the smn1le1-[of ITS thole bod): that IS,by bezng coexthc t z o ] , C O ~ C ~ M / ' *the Szrn 611 ol~~tmit171g tensi~eztith its d o l e dlamctel-.i S o w some predecessors believed that in 24. Since the AIoon is like a sponge, though not one fully permeated b!.water (see n. I r above), lunar illumination does not directly exemplify the "total blending" involved in Stoic cosmoloq, M here pneuma pervades the cosmos totally; cf. 1.1.72-73, and see Todd (1976) 29-73, zj. That is, raretied air. For clouds dense and voluminous enough to reflect sunlight see 11.6.171-173, with 11.6 n. 22. 2 6. "lhlurne" here, and in the preceding sentence, translates bathos. Cherniss (195;) 103 n. c argues that, as at Plut. Defitc. qzqD, this term refers to density. But the reference to the Sun's distance implies that when its rays reach the Aloon they are weak enough for the latter's volume to block them. Density is introduced as an afterthought; see nest note. 2 7. K d d Chn~m. q j 7 and 478 is probably right to see this parenthesis as Cleomedes' own conlment. It certain1~-conveys some reservations about volume alone being able to explain the LIoon's absorption of solar rays. 28. "Conceal" translates the verb rpakotrin. although it literally means "cast darkness on," a sense applicable to lunar eclipses (see line 133 below-).

T h e Heavens 11.4 /

143

total [solar] eclipses when the centers of the deities are in a straight line, the rim of the Sun is observed encircling the hloon by protruding in all directions.'%ut this is not part of what we detect; if it were, then, since the Sun is much larger than the Aloon, the protrusions would be seen by us as extremely bright rather than as revealing a minimal extension. So it must be said that although the Xloon is smaller than the Sun, nothing prevents its concealing the whole of the Sun, since it is equal, at least in appearance, to the Sun."' That it is equal in appearance is also el-ident just from a [solar] eclipse, but is best proven from the following procedure:" when a body is positioned at an appropriate distance, and conceals the whole diameter of the hloon by being coextended with its total size, it also conceals the Sun. And, in general, there is nothing to prevent larger bodies being concealed by smaller ones, and this can be caused in several ways. After all, even in our ordinary experience extremely small bodies conceal n~ountainsand whole seas, and at all events whatever conceals something does not have to be either larger than m-hat is concealed, or even equal to it.'?

29. Cleotnedes is efkctively reporting the view that all total solar eclipses are annular; cf. P. Par. I col. 19.16-17, a papyrus document dating from the second century B . C . 30. This equality can be calculated bp water clocks (11.1.184-191 and 2 9 7 zgq), or expressed through "digital" measurement (11.3.1j-43). Cleo~nedes ~vouldappear to be siding with Ptolemy here in the view that there are no annular eclipses of the Sun, i.e., that all total eclipses of the Sun entail complete obscuration. According to Ptol. Ahn. j.14, 417.1-1 I , while the apparent diarneter of the Sun is constant, the apparent diameter of the A1oon is the same as that of the Sun onlpu-hen the Moon is at apogee, i.e., at its farthest, and hence smallest; see hTeugebauer (197 j) 106. 31. It is a "procedure" (ephorlos) because an axiomatic principle derived from optical theory (see 11. 32 belou) is applied to obsen.ations. 32. T h e principle involved here (cf. also 11.1 n. jo) can be seen as a corollary and extension of Eucl. Opt. prop. j (8.6-7) ("objects of equal size unequally distant appear unequal," tr. Rurton [19+j] 338). Thus two objects of unequal size (the ,\loon and Sun) are unequally distant, yet appear equal when they are aligned

I 44

/

Cleornedes' T h e Heavens

I 27: The

Sun, then, is eclipsed through being obstructed by the Moon; certainly this happens only at their c o n j ~ n c t i o nAlso, . ~ ~ a solar eclipse is a condition affecting not the deity itself, but our line of sight: that is, when the Moon comes between us and the Sun, our line of sight, since it is obstructed by the Moon, cannot impinge on the Sun. A lunar eclipse, by contrast, is a condition affecting the deity itself, since the Moon, whenever it falls into the Earth's shadow, is deprived of the Sun's light and plunged into darkness. This happens whenever the Sun, the Earth, and the Moon are in a straight line. That the Moon is eclipsed only by falling into the shadow of the Earth will be demonstrated once we conduct our discussion concerning the wanings and waxings of the Moon.34 at "an appropriate distance" (summetrondiastima, line I 19)so that the nearer and smaller object obscures the more distant and larger one. 33. Knowledge of solar, as well as lunar, eclipses was assumed earlier at I.j.39-44,I.8.106-11z,II.1.4j 5-457,11.3.4-33,and lines 12-17above. 34. That is, in 11.6.

CHAPTER FIVE

I:' T h e Aloon, as has heen denm~strated,~ exists in closest proximity to

the Earth of all the heavenly bodies. It therefore has its body mixed with air and somewhat murky, and this becomes particularly striking in its total eclipses.' Now just as the Sun also naturally illuminates every other body that is not totally composed of fire, so too it casts its rays on, and illun~inates,the A10011, which is both compact and mixed with air. Accordingl!; the part of the hIoon that is turned to the Sun is illuminated. 8: Non- if the Moon always maintained the same relation to the Sun, then a single part of it would always be illuminated. But since, in accordance with its motion based on choice, it approaches the Sun at one time and m ithdraws fronl it at another, as it goes from conjunction to full ,\loon and from fill1 l l o o n to conjunction, the light from the Sun therefore goes Cf. the account of lunar phases g i \ m up to line 40 below with Gem. hug. 9. :it 11.3.81-99. 3. Since the ,\loon has no inherent light (see 11.4 n. g), the murkiness eoident in total eclipses can only result from its inherent, but relatively limited, heat. T h a t is, it is located at the edge of a fire-sphere, the aether (11.4.11),hut acquires part of its substance from the adjacent element air (1.2.37-38; II.3.8384; lines 2 and 6 here). Its heat is then notahlyvisible in the darkness of an eclipse, since hotlies composed of fire are always more lurninous under such conditions I. 2.

(114.93-94).

146 /

Clronrrdes' T h e Heal-ens

round the whole Moon in its circuit of it.l By moving relative to its illumination from the Sun, the Jloon is, in other m-ords, affected in just the same way as is the Earth through being stationary T h e Earth, that is, always has an equal amount of light from the Sun, yet, in the course of the Sun's period, has different parts illuminated by it at different times. This is because both the Sun's luminance and the Earth's shadow complete a circular course along m-ith' the Sun, and the tip of the Earth's shadow is directly opposite the center of the Sun. In this way the 1~1oontoo always has the same [amount of] light from the Sun (it is certainly not illuminated in differing [amounts] at different times!), yet different parts of it get illuminated at different times, as it approaches the Sun and again nithdrams from it, and in this m y it has the light from the Sun encircling the whole of its body.

24: Thus at conjunction it is the hemisphere of the 11oon facing the heavens that is illuminated, since that is the part of it facing the Sun at that time. But as it passes beyond the Sun, and in proportion to its withdrav~alturns its hemisphere that is facing the Earth toward the Sun, it first causes a crescent shape on being illuminated from the side, then a half shape%s it increasingly revolves toward the Sun, then a gibbous shape, and after that a fill1 shape when it is in opposition to the Sun. So in the course of reaching opposition from conjunction, the Sun's light goes down from the hemisphere of the JIoon facing the heavens to the one fixing us, and in this way the IIoon is said "to wax" up until full Moon. But when, after being in opposition, it passes beyond opposition, it, by contrast, wanes as the light is carried round from the hemisphere of the A1oon facing us to the one that is facing the heavens, right up until conjunction. So if the ,\loon's shape were flat, it would be full as soon as it

4. In effect, then, the Aloon makes one revolution on its axis in a synodic month; cf. 11.4.5-9. j. s~rri~pe~-i~zostein; see 1.8 n. 2 0 . 6. dikhotonros: i.e., the shape of the AIoon a t the first quarter (cf. 11.4 n. 13). See also lines 7 3 . 88 and go belon-.

T h e Heavens 11.j

/

147

passed by the Sun after conjunction, and would remain h l l until [the next] conjunction. But since it in fact has its shape in the form of a sphere, it produces the types of its shapes in the way described.

41: T h e cause of the Aloon's having differences in its shapes could be more effectively summarized if we used the following procedure to learn what happens to it.- Tu-o circles are conceived of in the ,\loon: A, the one by which its dark part is separated from its illuminated part; B, the one by which the part visible to us is separated from the part that is invisible. Each of these circles is smaller than C, the circle that can divide the Aloon into two equal parts, that is, its great circle. Because the Sun is larger than the ,\loon, it illuminates more than half of it, and thus A (the circle that separates the dark from the illuminated part) is smaller than C' (the great circle of the Aloon). B (the circle in our line of sight) is, by the same token, necessarily smaller than C' (its great circle), since we see less than half of the A1oon. T h e reason is that when a spherical body is seen by two eyes, and the distance between them is less than the diatneter of the [sphere] that is being seen, the part [of the sphere] that is seen is less than h a l f . 9 0 since B divides the AIoon not into equal, but into unequal, parts, it too is smaller than C, the great circle.

56: RothLland B, however, appear as great circles relative to our perception, and while they always have the same size, they still do not maintain the same fixed position, but cause nunlerous interchanges and configurations relative to one another as at different times they coincide with one another, or slope to intersection at an oblique angle.' A1ost such intersections are mini~nalinterchmges, but, as is the case with a genus, all are of two lunds: a right-angled [intersection], and one in \vhich they .; Lmes 44-64 ~nxol\ea "procedure" (ephodos,see Introduction n. 38), since thelr reason~ngrelles o n ~ndependently~dentifiahlegeoinetr~caland opt~cal principles. 8. This is a verhatim statement of Eucl. Opt. prop. 2 7 (44.I 4-1 5); cf. also Plut. Dejic. g31C. 9. See Fipre 24 for the cycle of the phases of the ,\3oon and their correlation ~viththe nvo circles described in lines j6-80.

I 48

/

Cleom-edes' T h e Heavens

intersect obliquely with one another."' There are also only two coincidences: when they coincide at conjunction, and at full A10011.

65: Now when the 31oon passes by the Sun after conjunction, circles A and B distance themselves from one another, and slope to intersection at an oblique angle, so that all that is left illuminated, at least in relation to us, is the small [area] between the circumferences of both. This type of transition, from the coincidence of the circles to their intersection, completes the Moon's crescent shape, since as the circles continually move toward intersecting one another at right angles, they also increase the phase ofillumination, since the [area] between the intersection of the circles is always illuminated in such a progression.

72: Lf'hen the figure of intersection reaches right angles, the hloon is seen at the [first] quarter. But when the circles proceed from this figure to obtuse angles, they cause the deity's gibbous shape, while they cause full AIoon by again being fully coincident at opposition. Then by proceeding again from this coincidence to yet another, and by completing the same shapes as they wane, they proceed to the point at which all the luminance disappears when the circles A and B exactly coincide with the part of the Moon that faces the heavens. That is essentially our discussion concerning the waxings and wanings of the Aloon.ll 81: T h e earliest natural philosophers and astronomers also realized that the Moon acquires its light from the Sun, as is clear just from the etymology of the word-the name of the Moon (sel8n8) is derived from its always-having-new-light (selirsaei~1eo~2)~~-as also from the passing on

10. T h e text of this final part of the sentence is uncertain, and the translation follows a Byzantine paraphrase (see C~elestiired. Todd at 11.j.61-62.) n hich maintains the required meaning. I I . This account of the phases ofthe Moon completed here ignores the effect of the JIoon's motion in latitude, as well as the subtleties introduced at lines 41- j6 above. 12. For this etymology see PI. Cmt. 40gb12. O n Posidonius' interest in etymology, m-hich continued an earlier Stoic tradition, see K ~ d dComr?~.77: and 699.

The Heavens 11.j

/

149

of torches to people entering the festival of Artemis (symbolic of the Moon acquiring its light e~ternally).'~ 87: Earlier [thinkers] claimed that the Afoon had three shapes: the crescent, the quarter, and the h11 (hence the custom of making Artemis also three-faced).l4 Afore recent ones added to this trio the shape now called "gibbous," larger than the quarter, but smaller than the full, Aloon. 92: >JI?nis applied in four significations." (a) The [lunar] goddess is called .\fin when she is crescent-shaped," as is (b) the actual condition of the air between conjunctions (as we regularly say: "the month @?n) has been humid or temperate"). Also called men are (c) the interval of time between conjunctions, and, finally, (d) the interval of 30 days (as in our saying that we have been out of town, or in town, "for a month," without meaning in any way "from conjunction to conjunction," but just the sum total of 3 0 days). T h e first two [entities]'; (the crescent-shaped goddess, and the condition of the air) are bodies, whereas the next two are incorporeal, since time itself is also incorp~real.'~ 13. On Artemis and the hIoon see S W 2.748, and the further references at Goulet 223 n. 369. I 4. For these three shapes linked with Hecate see Cornut. Theol. 72 .7-I 3 and cf. Plut. Dr.jirr. 937F. For the four confiprations see Posid. Frz2EK with Kidd Comm. 473. I j. For (g) and (L) see SVF 2.677, p. 199.30-34 For (12, the only astronornically significant sense (as lines 102-141 here show) see Gem. Isng. 8.1. For supplementary semantics see lines 148-149 below. 16. .IIt'n was originally a rrlale h a t o l i a n deity (Marines), represented with a crescent AI0011 behind his shoulders. Similarity to - p , ~ v ,the root of the word for "month" seems to have led to the form nzi% being applied to a temporal period. 17. In Stoic nletaphysics they are termed "somethings" (ti77N); see, for example, S I T 2.331. 18. .l"signification" (siruraimn~e~o71)) for the Stoics is by definition the incorporeal meaning (the lekton; cf. 1.1 n. 48), in contrast with a corporeal speech-act or the object spoken about; see S W 2.166. It is being used in an extended fashion here to identify the reference of the word nr?77 in (R) and (h)), as well as the

I jo

/

Cleovzedes' T h e Heavens

102: T h e

conjunctions of the AIoon with the Sun do not always maintain an equal time internal for the follom-ing reason.'Vhe Sun, as already stated,?' gets both closer to the Earth and higher in accordance with its course based on choice. So when it is lower, it necessarily goes through the zodiacal sign more quicklj-, but when higher does so more S I O W ~For ~ ~ when . ? ~ it is lower it goes through a shorter arc, but through a longer one when higher. 107: lTTemight learn this too from what happens with respect to the sections of cones:!! that those near the bases are wider, those closer to the vertex narrower. Now the cones flowing out from the eye to the heavens have the [point] right at the pupils as their vertex, and have the object of vision on which they impinge as their base, and since the Earth is the center [of the cosmos], the bases of the cones flowing out from it to all the zodiacal signs will be equal. 114: Now if it so happened that the Sun moved at neither a greater nor a lesser height, but always kept the same height from the Earth, then it would go through the zodiacal signs in equal periods of time,

meanings in (c) and (ri). .llthough the time inten-als identified in (c) and ((1) are called bodies in one Chrysippean quotation (SlrF' 2.66j), the incorporeality of time can transfer to the time inten-als as intends, without reference to the bod) T h e point made ies that determine their character; see Brunschwig ( 1 ~ 8 8106. in this text also applies to the instances of time inten-als at 11.1.1j o - I ~ I and 182-183, and 1I.z.r:-18. It shows the extent to which astronomy is being approached from the perspective of Stoic philosophy. 19. T h e analysis that follom is a commentary on sense (c) from the preceding paragraph; it also elaborates the brief reference to the lunar month at 1.2.42. 20. At I.4.j~-71.See Figure ;. 2 I . T h e varying speeds attributed to the Sun here, and then later to the Aloon and the other planets, are all apparent (see Theon E.~pos.13j.6-I I). T h e issue of their real motion, which is a function of their density (cf. 11.1.334-338 and 11.1 n. 79), is ignored in this contest. z 2 . T h e three propositions introduced in this paragraph are the assumptions for an ephodos at lines 114-141.

T h e Heavens 11.5

/

I jI

and in that way its conjunctions with the ,\loon would also maintain an equal interval of time.?' But since this is not the case, but the Sun is instead observed moving at its greatest height in Gemini, and at its lowest in Sagittarius, then in Gemini it will go more slowly through the section of the visual cone2+(a wider one because it is closer to the base), whereas it will go through the section in Sagittarius more quickly, since here, by contrast, the section of the cone is narrower (that is, closer to the vertex)." I 23:" So when conjunction occurs at the start of Gemini, the month will necessarily be abbreviated, since the Moon is moving closer to the

Earth there, while the Sun is at its greatest height. That is because the Aloon will overtake the Sun while the Sun is still in Gemini, a sign through which it goes in 3 2 days. But if conjunction occurs near the start of Sagittarius, the hIoon will not catch up to the Sun while the Sun is still in this sign, since the Sun takes 28 days to go through it." This month will, therefore, be the longest of all, since the A1oon passes through Sagittarius more slo\vly, and the Sun does so quickly, and so the Moon catches up with it slowly. T h e result will be proportionate in the intervening signs.'" 133: In the same way it is also proven that all the planets have high 23. This would be true only if the Moon's circuit was also concentric about the Earth. 24. Literally "the cone that forms the line of sight" (kinos t?s opse6s). That is, every line ofsight hasvisual pneuina in such a shape; see 11.1.j7-6 j and 2 j z - 2 j j, and cf. 11.6 n. 27. 2 j. Cf. 1.4.62-71. 26. O n the duration of lunar eclipses see 11.6.68-78, which presupposes the present analysis, as would any account of the duration of solar eclipses. Cherniss (1957) 126 n is, however, wrong to claim that the present text applies to solar eclipses. 27. Geminus in his calendar has the Sun taking 3 2 days to traverse Gemini (108.1 Xujac [197j]),but 29 (rather than 28) to traverse Sagittarius (103.3). 2 8. Cleornedes seems to suggest here that the Moon's circle has a fixed perigee and apogee (see Figure zj), hut this would not be correct.

Ij 2

/

Cleo/-nedes'T h e Heavens

points and low points [relative to the Earth]?"in each of the zodiacal signs. For given that all the zodiacal signs are divided into 30 degrees, then when planets go through some of then1 more quickly, and others more slowl!; they obviously go more quickly through the sections of the [visual] cones that they encounter when lower, whereas when the sections of the [visual] cones are wider, their passage is slower because of their height. Since all the planets are heightened and lowered, all of their circuits are comparably eccentric, since because of the variation in their heights they are not equidistant from the Earth in every direction.

141: So since the Aloon's [circuit] is also like this, it is spread belou the zodiacal band at an oblique angle to the whole of it. Specifically, it touches the northern [circle of the zodiacal band]jOto the extent that the A'Ioon itself invariably approaches the northern [regions], and [touches] the southern [circle] in the same way." So, given this, it necessarily intersects with the circle through the middle [of the zodiacal constellations] at two points,'2which are variously termed "points of contact" (szi7zaplphni) or "nodes" (sundennol). 29. T h e terms that describe these dista~lces,hzlpsos and tnpeim%na (literally "highness" and "lowness"), are also used analogously in astrology to identify degrees of planetary influence; see 1.2 n. 2 2 . At 1.2.64-69 they refer only to positioning in the zodiac. jo. Like Goulet 223 n. 373, \ye reject the suggestion in Neugebauer (197 j) 962 that the circles approached by the l l o o n are the arctic and antarctic circles. On the inclination of the JIoon's orbit to the ecliptic cf. 11.7.1-2. 31. Cleomedes does not conunit himself here to identifying the northernmost circles of the zodiacal band with the northernmost and southernmost parallel circles reached by the hloon. 32. Mre have follo\ved most critics in deleting a relative clause at lines 14j-146 that glosses the phrase describing this circle as "that which is called 'heliacal' and 'ecliptic' (eklriptikos)." This clause is a~vb~vardly positioned in the sentence relative to its antecedent, and so is probably a marginal comment added to the text later, giren also that the term ekleiptikos (sc. kuklos) ("ecliptic circle") is attested in only two sources for the period to which Cleomedes' treatise is datable: P. Osy. 4138a ii.121 (second century A.D. in Jones [rggg]) and Ach. Isay. j3.y -10 (midsecond to rnld-thud centurr i . ~ . ,see AIdnsfeld and Runia [1997] 300)

T h e Heavens 11.j

/

I jj

148:Just as "the Sun" is used in two senses-both in the sense of itself and that of its light-so we also standardlTruse "the Al0011" in the same two senses." 150: \ZTe shall next conduct our discussion concerning the eclipse of the J10on, our object being to avoid sharing with old hags the belief that at eclipses witches drag the hloon 3 3 This srntence may have been displaced from a more logical location after line X6 above. , (1973). and Bicknell (1984). 34. On this folk belief see Jlugler ( ~ g j g )Hill Cf. 11.1.4jq-461 for a similar ridicule of folk astronomy

CHAPTER SIX

T h e Moon is eclipsed by falling1into the shadow of the Earth whenever the three bodies-Sun, Earth, and Moon-are in a single straight line, with the Earth in the middle. This can happen only at full ~ V o o n . ~ And the Moon falls into the Earth's shadow in the following way. T h e , ~ its own circuit located below the cirSun moves, as already ~ t a t e dwith cle that is exactly at the middle of the zodiacal band. Accordingly, the Earth, when illuminated by the Sun, necessarily sends out a shadow, as do all other solid bodies that are illuminated. Now since this shadow has a conical shape, it does not occupy the whole zodiacal band, and so is not aligned with its total breadth, since it terminates in a vertex. But this shadow, since it is necessarily directly opposite the center of the Sun right at the exact center of its vertex, is itself also located below the exact middle of the zodiacal band. Now this shadow far exceeds the distance of the I:

I. "Falling" here and elsewhere translates a compound verb (peri-piprein), the prefix of which refers to the Moon's circular orbit "around" (peri) the Earth. 2. For this as a Stoic definition see S W 2.678 (also Posid. F I ~ ~ E KFor ) . other elementary accounts of lunar eclipses see Gem. Isag. 11, and Theon Expos. 193.23-198.8. 3. At 1.2.53-59 and 1.4.52-53.

T h e Heavens II. 6 /

ISj

Moon, though without going up as far as the remaining heavenly bodies. So when the Moon is detected as being in opposition to the Sun, and either to the right (that is, north) of the zodiacal circle, or on the opposite side, it evades the shadow of the Earth, and for this reason the Moon is not eclipsed at every full Moon. But when in opposition to the Sun the Moon is detected as being so situated that a single straight line can be extended through the centers of the Sun, Earth, and Moon, then, by falling right into the shadow of the Earth, it is fully eclipsed. T h e shadow of the Earth, in other words, moves in direct opposition to the Sun, and is, as it were, "dragged" by it, just as Homer says: The shining light of the Sun fell in the Ocean, dnzgging black night ouey the feltile land.' 24: Since the shadow moves along with the Sun in this way, and at its very tip is directly opposite the Sun's center, then the Moon, as it proceeds in accordance with its motion based on choice, meets the shadow moving from east to west as it itself moves west to east.' And by falling into the [Earth's shadow] in this way, [the Moon] is deprived of rays from the Sun (just as we too are when someone stands in our way when we are in sunlight). But it is not always the case that the iMoon as a whole is darkened by the Earth (that is, totally concealed by its shadow), but on occasion [the Moon is darkened] just partially. This hap4. Iliad 8.485-486. j . Cf. lines 38-42 below, and Plut. Defnc. 932F-933A. T h e Earth's shadow and the Sun both have a proper motion eastward, that is, in the direction opposite to the daily rotation, while the Moon similarly has a proper motion eastward, although a much faster one. This means that the Moon overtakes the Earth's shadow each month from the west, with an eclipse occurring if it enters this shadow. Cleomedes misleads the reader when he states (in lines 26-27) that the ,Moon, while moving east, meets the Earth's shadow as this shadow is moving only westward (cf. lines 41-42) For, while it is true that both the ,Moon and the Earth's shadow, because of the difference in their proper motions eastward, share to different degrees in the diurnal motion from east to west, it is wrong to say that the Moon and the Earth's shadow meet because they are moving in opposite directions.

I

56 / Cleomedes' T h e Heavens

pens when through being in opposition to the Sun it touches the [circle] through the middle [of the zodiacal constellations], yet is not detected as having its center at the exact ~niddle[of the zodiacal band]; for this is how a specific part, but not the whole, of it falls into the [Earth's] shadow. 35: That the hloon is eclipsed by falling into the Earth's shado.l\; and only in that way, can be seen from the phenomena alone."(n) It is eclipsed only at full hloon (the only time in fact that it can fall into the Earth's shadow while in opposition to the Sun). (h) In any total eclipse the parts of the Moon facing the east are seen to be the first to disappear, because as it sets out for the east in a notion opposite to the heavens, it meets the Earth's shadow, which always moves from east to west. But when it starts to emerge after the eclipse, it has those of its [parts] that face the east emerging first. That is, it is absolutely necessary that as the hIoo11 meets the shadow, the first of its parts to encounter the Earth's shadow and be concealed are again the first to emerge after being concealed. (4JTlenever the hloon is partlall) echpsed, and is affected in this n a! as it goes down from north to south, then the parts of ~tthat face south necessarily d~sappear,slnce in the donnxt ard course the! take the lead in falling into the shadow and are in this way concealed, whereas the parts that face north escape the shadow. But when the Moon goes up from the south to the north and effects a partial eclipse by being in opposition to the Sun with its center not yet at the exact middle of the zodiacal band (that is, in line with the center of the Sun), then the parts of it facing north are eclipsed, since they take the lead in falling into the Earth's shadow, whereas the parts facing south are visible. 56: So all these [obsen-ations] establish for us by essentially visual means that the sole cause for the JIoon's eclipse is the process by which on falling into the shadow of the Earth (that is, being darkened by it) it 6. Since "the phenomena alone" iirlctir til phnii~ormizn)here represent "clear" visual evidence (cf. lines j 6 and 19j), they can serve as a criterion (cf. 1.5.4, and 11.3 nn. 24 and 2 j). 7. For lunar motion in relation to the zodiacal circle see 11.5.141-147.

T h e Heavens 11.6

/

I jj

is deprived of the irnpact derived from the rays of the Sun that illuminate the part of the hloon that is always turned toward the Sun. 60: Furthermore, the segments of the Aloon that are illuminated at an eclipse are seen to be curved.KThis too happens of necessity since the Aloon, which is spherical, falls into the conical shape of the Earth's shadom-, and so its illuminated segments are also seen to be curved. In other words: U'hen a spherical shape encounters a conical shape and has the part that is in contact with the conical shape always disappearing from sight, necessarily the remaining part, which has not yet disappeared from sight, has its shape curved along the segment (that is, is crescent-~haped).~

68: T h e following too has been observed in the case of the lunar eclipse: the Moon effects a total eclipse at a very great height, when very close to the Earth, and at an intermediary distance.'" m'hen eclipsed at a very great height it emerges more rapidly, but does so slowlywhen very low, and when in between it also has an intermediary duration for its eclipse in between the [extremes] mentioned. This [variation] clearly reveals that the h'loon is eclipsed in no other way than by falling into the shadow of the Earth. That is, when it is eclipsed at a very great height, it emerges more rapidly through encountering the narrower part of the shadow; but when very close to the Earth, it has to go through a wider extent of the shadow, and thus the duration of its eclipse is greater. But when on occupying an intermediary height there is a proportionate outcome, it also has an intermediary duration for its eclipse.

79: This [evidence ofvarying eclipses] proves that the Earth's shadow also has a conical shape; in fact, these [phenomena], given the way they 8. Because of the general principle introduced at lines 64-67 (cf. also Arist. De c~~zelo 297bz 5-30 and Plut. D e j k 932E-F), this proof is an ephodos (see Introduction n. 38). On a traditionally related claim, that the curved shadows appearing on the JIoon during lunar eclipses demonstrate the Earth's sphericit); see Neugeh e r (197j) 1093-1094, who describes it as "mathernatically inconclusive." 9 . 'This curve is in three dimensions, not two. 10. At 1I.j.1oz-132 the Aloon's eccentric orbit was analyzed with reference to the case of conjunction.

Ij8

/

Cltwwdes' T h e Heavens

are, are proven by one another. That is, a lunar eclipse is demonstrated to occur only by the _\1oon's falling into the shadow of the Earth; conversely, variations in eclipses of the AIoon demonstrate that the Earth's shadom- is conical, since the .\loon spends a longer time in eclipses that are closer to the Earth, yet emerges more rapidly in eclipses that are at a greater distance from the Earth, whereas in eclipses at intermediary distances the duration of the eclipse is also intermediary. Partial eclipses too show that the Earth's shadow is conical, since the Jloon then has segments illuminated in such a way that its shape becomes crescent. This would not occur unless it fell into a shadow with a conical shape. 90: But it is from the following [argument] that the conical shape of the Earth's shadow-might be most effectively demonstrated.'' If its shadow were in fact cylindrical or funnel-like (that is, if the body that illuminates it-the Sun-were equal to, or snlaller than, the Earth), then the shadow that was funnel-like would occupy most of the heavens by terminating in a broad span, with the result that not only would the ,\loo11 be eclipsed every month, but it would also remain in the [Earth's] shadow all through the night. But if the shadow were cylindrical, it would occupy the whole breadth of the zodiacal band, since it would not terminate in a vertex, and the AIoon would be duly eclipsed each month hy falling into the shadow. But because the Earth's shadow is actually conical, and so tern~inatesin a narrow vertex, the 11oon evades it when it is detected occupying the northern or southern parts of the zodiacal band at full Moon. (If the shadouwere cylindrical or funnel-like, it would also advance as far as the [fixed] stars. As a result the stars W-ouldat different times have a brighter or fainter appearance: brighter when in shadow, since every body that is composed of fire is brighter in the darkness of a shadow; but fainter when in the rays of the Sun.'?)h none of this is observed among the phenomena, it is clear

I I At 11.2.1y -30 t h ~ argument s a as used to demonstrate that the Sun n as larger than the Earth. See Figure 21. On the trans1'1tion "funnel-hke" see 11.2 n. 8. 12. Cf. 11.3.91-9j.

T h e Heavens 11.6 /

I jg

that the Earth's shadow-is necessarily ~ o n i c a l .If' ~so, it is evident that the body that illuminates it-the Sun-is larger than it.'+ 109: Lunar eclipses are such as we have demonstrated. But statements made about paradoxical eclipses seem to contradict the theory that establishes that the Moon is eclipsed by falling into the shadow of the Earth. For some say that a lunar eclipse occurs even when both lurninaries are observed above the horizon," and that this indicates that the 11oon is not eclipsed by falling into the Earth's shadow, but in some other way. For if an eclipse does occur when both the Sun and the Moon are seen above the horizon, the Moon cannot at that time be eclipsed by Mling into the Earth's shadow. Furthermore, if both [Sun and Aloon] are visible above the horizon, and if the Earth's shadow can no longer be at the place where the Jloon is seen to be eclipsed, then the place where the Illoon is located is illuminated by the Sun! If this [theory] is correct, we shall have to lay clai~nto a different cause for the Aloon's eclipse. 1 2 2 : Earlier scientists confronted with such statements tried to solve this problem as follows. They said that the Aloon could Call into the Earth's shadow (that is, be precisely opposite the Sun), even though both the luminaries were above the horizon. This could not happen if the Earth's shape were flat (i.e., a plane), but, because its shape is spherical, both divinities' bodies could be observed above the horizon directly opposite one another. To explain. Because of the protrusions of the Earth's curnatures the [two divinities] will not actually face one another in direct opposition. Even so, those who are standing on the Earth could not he prevented from seeing both [divinities] because it is the Earth's curvatures on which they are standing. These curvatures do not i n 13. T h e logical necessity here is again (cf. 1I.z.1g-30, with 11.2 n. g) implicitl!. based on the Stoic fifth undemonstrated argument. 14. Cf. 11.2.27-28. I j. For such an eclipse reportedly observed in the west b!, Hipparchus see Plin. AVH2.57.

I

60

/

Cleon~erdes'T h e Heavens

pede people standing on them from seeing both the bodies above the horizon, although they will obstruct the divinities when they are in direct opposition to one another. Thus W-hile[the Sun and Moon] will not face one another, i:e will not be prevented from seeing both of them because we are standing on the Earth's curvature^.'^ T h e latter obstruct those bodies that are in low areas at the horizon, whereas the cuwatures on which we are stationed are more elevated.'139:That was how earlier scientists solved the problem adduced here, hut their position may not be sound. This is because while our line of sight might be affected in this way at an elention, since the horizon becomes conical when we are elevated into the air far above the Earth,'" this is no longer the case when we are located on the Earth. For despite the existence of curvatures on which we are located, our line of sight is eliminated by the size of the Earth.I9 So it must not be stated, or believed to be at all possible, that a lunar eclipse occurs when both [Sun and A'Ioon] are observed above the horizon by us while vie are standing on the Earth.

149: Instead, we must confront [proponents of paradoxical eclipses] initiallj- by clainling that this theory is 'iabricated b>-certain people who wish to impose a problem on the astrononlers and philosophers who are engaged with these matters. For numerous lunar eclipses have occurred, both total and partial, and have all been recorded, yet nobody is reported I 6. Such a siyht line \vould mean an Earth n o longer discountable ("a point") in relation to the distance of the Sun (as argued in 1.8). Either the cosmos would he smaller, or the Earth larger. See 1.8 n. 34. I;. This observer is a t ground level, but has a "conical" horizon (line I ~ z ) , i.e., one of more than I 80". T h e Sun and ,\loon are thus in the "low areas" heneath this enlmged horizon, and the Earth affects ohsen-ation as though it \rere a mound over W-hichwe look at bodies on either side of it. 18. Cun-atures are inherent to a spherical Earth ( I . I . z and ~ ~ 2 jo; 1.3.1; and 30: I. j.116 and IZO),but visible only from an elewteci position (1.8.138-139) due to the Earth's size. 19. For a ground-level obsen-er the sight line literally "disappears into" ( i ~ i ~ ~ p h a i z i z ~the t o idistance, ) and the Earth appears to be flat (see I.j.11-13); i.e., we have a horizon of 180°, tven though the Earth is spherical.

T h e Heavens 11.6

/

I 61

as having recorded this type of eclipse, at least up to our lifetime-no Chaldean, Egyptian, o r other scientist o r philosopher. T h e claim is just a Fabrication. Second, if the ,\loon were eclipsed in any other

\\-a)-

than

by falling into the shadow of the Earth, it could also be eclipsed when izot

at full AIoon, that is, when i t advances a large o r small distance away

from the Sun, and eclipsed again after fill1 h10011when it approaches the Sun and is waning. But in fact, although it undergoes numerous eclipses (eclipses heing frequent enough), it has never been eclipsed except at full J I o o n , that is, when in opposition to the Sun-in

fact only when it is

possible for it to encounter the shadow of the Earth. Certainly all its eclipses are predicted by people who construct astronomical tables, because they knou- that, whenever coincidence occurs, it is at full J l o o n that the AIoon is detected either totally o r partially below the exact middle of the zodiacal band, and that in this map it eEects either partial o r total eclipses. I t is therefore impossible for a lunar eclipse to occur when

both luminaries are seen above the horizon. 168: Since there are by nature a wide variety of conditions that affect the m, ~t mould not be i~npossihlefor us to encounter an lnlage of the

sun?"1' s not yet ha\ ing set after it had already set (that is, after ~tW A S be-

loll the horizon). T h e cause" could be a rather dense cloud present in the ue4t that is ~llununatedby the rajs of the Sun and sends out a11 iindge of the Sun to us." O r

it

could he the occurrence of a counter-Sun,

20. This "image" (phmtilsiir) is a genuine illusion, unlike cases of visible objects projecting illusory appearances (e.g., 1.8.21 and rjy-rho), or the cases of the Sun's appearance cited in 11.1. , may he Posidonian, are in21. The multiple explanations that f o l l o ~M-hich co~npatible~ i t one h another, like some sets of explanations in Epicurean physics (see \\ksserstein [r9;8]). Cf. 1.4.90-109 where, by contrast, Posidonius is reported as entertaining multiple, though coniplementary, explanations. 2 2 . On this phenomenon (knon-n as parhelion, or ~rlock Sun) see Kidd C'omnr. 467-470 (on Posid. F I ~ I E Kand ) D. K d d (1997) 476-477 (on h a t . t'hneu. 881). Clouds can be permeated by the Sun's rays (11.4.9j-97 and 103-IO~),hut also acquire ~noisturefrom the atmosphere at the horizon (line r; j helo\v; cf. 11.1.zy-jo), ancl so can reflect light (see 11.4.3j-36).

I 62

/

Cleon~edes'T h e Heavens

since many things like that appear in the air, and particularly around Pont u s . ? B u t the ray that flows out from the eyes could also be refracted on encountering air that is damp and moist, and encounter the Sun after it is already concealed below the h o r i z ~ n . ' ~

178: Something similar to the latter is also observed happening in our ordinary experience. For example," if a gold ring is placed in a cup, or in some other vessel, then if the vessel is empty the object placed within is not visible at an appropriate distance'" because the visual pneuma runs unimpeded down from the brim of the vessel in a straight line. But when the vessel is filled with enough water to become level with the brim, then from the same distance the ring lying within the vessel is visible. This is because the visual pneuma no longer runs [straight] down from the brim, but comes into contact W-iththe W-aterthat has filled [the vessel],'' and is thus refracted, goes to the bottom of the vessel, and encounters the ring.'s Something similar could, then, occur with damp and sodden air too, so that when the ray from the eye is refracted and bends below the horizon, 23. For a counter-Sun (anthelion), sometimes confused with parhelion, occurring in the eastern sL?, in the area of Pontus, see Alnaxagorasat DK j9.186. 24. O n atmospheric conditions affecting astronomical obsen-ations, with reference to this passage. see Lloyd ( I 982) I 34-1 3:) and cf. Ptol. Opt. 5.2 3-2 6 (tr. Smith [19y6] 238-240). Cf. also 11.1n. I I . 2 j. For this example see also Archim. at OI!-mp. I 1 2 N I P ~ C 211.18-23 OI: (= Archim. Fr. 18; cf. Fr. I 7), Sen. .\'Q r .6.j, Ptol. Opt. 5. j (tr. Smith [19y6] 2 30-2 3I), and Damian. Opt. 14.3-6 (ed. Schiine (18y;j). Cf. Eucl. Crrtopti: 286.1~-1y for the general principle involved. 26. This distance is "appropriate" (~cmn~et~.oil; cf. 11.4 n. 32) in the sense that eye and object are at a distance and angle that ensures the object's risibility. For this same general sense see Alex. -1phr. De m. 41.17-1y, Sex. Emp. A.117.188 and 438, and cf. Sedley (19 76) 49 with n. go. 2 7 . "[Level] to the brim" ( ~ a A 4 X t ~ h r iline , 18j) is the manuscript reading printed in Todd's edition. It is omitted here as a gratuitous iteration of the same phrase in the preceding line. Since the wssel is already said to be full to the brim (lines 182-183), no additional reference to this fact is needed. 28. T h e risual cone (see 11.1.~;-;o and 11.j.107-I~I), also relevant to refraction, is not mentioned.

T h e Heavens 11.6 /

I 63

it encounters a Sun that has already set, so that an image of it is engendered as still being above the horizon. Perhaps something else much like this could also on occasion produce an image in us of the two [hea~-enly] bodies being above the horizon after the Sun has already set. Still, that the Moon is eclipsed orrh by falling into the shadow of the Earth is a cognitively reliable2" [conclusion] derived from the phenomena. That, then, is enough on the eclipse [of the Moon]. 29. eml-ges: that is, not just 'i.isua1lj hut cognitirely reliable, and applied to a process of reasoning. See Introduction 10, and 11.1n. 61.

T h e AIoon is said to moke a greater distance than do the other planets tovard each [side] of the c~rclethrough the middle of the zodiacal constellations, next in order is Tenus, u hich goes j degrees to each [side] I:

in its chosen motion, then llercurp (up to L+ degrees),' Alars and Jupiter (up to zl/,degrees), [and] Saturn (up to r degree on each side).' 5 : \lercur) and ITenusdo not 1110~e to e\ er) [angular] distance from the Sun, but AIercur) [n-~oles] 2 0 degrees at most, Venus jo degrees at most, the remaining three, just like the Aloon, mole to ever) [angular] distance from the Sun 8 llercury eftects [superior] conjunction 15 ith the Sun in I I 6 da! S,

I . Since this chapter offers no rationale for the data presented, and since lines 11-14 could follow 11.6 n-ithout an!- interruption in thought, lines 1-10 may he an interpolation. r . In the list of planets at 1.2 .zo-42, .lIercury, not Venus, is located just al~ove the 1Ioon. another reason perhaps (see preceding note) for regarding this material as interpolated. 3. Neugebauer (197 j) 1or;r-1016 anal~zesthe evidence in Ptolemy's H n i z ~ ~ ~ '73les for estremal latitudes, and compares it to the values given in the Almngest. 4.Neugehauer (197 j) 804-80 j catalogues ancient evidence on the masirnum elongation of the inner planets.

T h e Heavens II. 7 /

I 6j

when the latter comes in befiveen it [and the Earth]; \%nus resumes the same position in relation to the Sun in 584 days, hlars in 780 days, Jupiter in 398, Saturn in 378.' 11: That will be as far as our discussion of these [matters] will go, at least for the present.These [two]lecture courses- do not comprise the writer's actual doctrines, but have been amassed from certain treatises, earlier as well as more recent ones, with most of the statements taken from Posidonius' [works].' j. T h e interval in which a planet returns to the same position in relation to the Sun (e.g., conjunction) is known as its synodic period. Neugebauer (1975) 782-78 j catalogues ancient evidence on planetary periods, and notes ('785) that "beyond the Babylonian parameters only the synodic periods listed in Cleornedes 11.7 are astronomically rneaningfi~l."See also Neugehauer (197 j) 96 j. 6. For evidence of a forthcoming course see 1.1.94-9 j, 173-174 and I 91-1 92. 7. T h e "lecture courses" (skhol~zz)are the sets of lectures that seem to have comprised the n w books of the (;i~eli~tii~; cf. 11.2.; where "the tirst of the skbolzkn" refers to the whole of Book I. 8. This typical disclaimer (cf. also 1.8.161-162 above; see illnittaker [1987] 1 0 2 with n. 77) should not be deleted as a gloss; see Crrelestin ed. Todd Pizrqf xviii.

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FigU,lfes

Legend

0 ob\er\ er N north tene\trial pole NCP north ~ e l e , t ~ npole l

T

z

4

A

1

center ot the E a t h obqer\ er'\ zenlth

Figure I T h e ( e ? ~ ) k l ~(n6~)uof the north celestial pole for an obsener In the northern hem~sphere ( I 1 176)

9 is equal to angle ZOQ which is in turn equal to angle OTE. the ob>en.er', latitude.

NCP

-horizon plane

[hqwl

0

obsener nolth terre5t11,tl pole N C P north i e l e ~ t ~pole ~il S w u t h ter~ejtlldlpole SCP south celestul pole Z obcel\er', m n t h

N

SCP

( a )Latltude ( 6 ) = 90°N Arctic circle and horizon circle coincide

(b) 4 = 70"N

(C)

$ = 4O"N

Figure 2(a)-(c). The variation of the arctic circle with the observer's latitude (1.1.193-101)

horizon plane

0 N NCP S SCP

z

ob-sical theory underlying eclipses. 26. E! interpreting the subject of the rerh here, which is in the singular, 11s the class of astronomers, or "any astronomer" (see n. I I, above). Lve avoid hat-ing Posidonius claim that a given astronomer will adopt more than one h>pothesis. as I. G. Kicid (see n. ;above) would ha\-e him do. 11.1.310-31 I and 332-333 siniilar language is used in con27. -It C~z~lestiir nection with premises in a calculation of the size of the Sun, though there the

202

/ Appendix

3 2 : For e.;an~ple:~'11hy do the Sun, the \10011, and the planets appear to move unsmoothly?' After all, whether we h!pothesize that their circuits are eccentric, or that the heavenly bodies go round along epicycles,"' the apparent unsrnoothness of their motion will be saved.:' And [we] n-ill have to go through nll the modes according to which these phenomena" can be caused, so that our systematic treatment of the planets will resemble a theory of causes [set out] according to each possible mode [of explanation]."

hvpotheses are assumpt~onsn l d e ~r thin the larger arLpmentrather than the kind of foundational hypothem thdt concerns Pos~tlon~us here. 28. See the preface to this Appendix, and 11. 12 above, on the relation of this iection to the rest of the passage. 2 9. ai1ovtnl8.r: on this t e r m i n o l o ~ see B o w n (I 999) 2 89 -2 96. 30. Hipparchus seems to hat-e evaluated both the epicyclic and eccentric theories purely as hypotheses (Theon E.~pos. 166.4-IO), and was criticized (Theon E.~pos. 188.1-j-24), in t e r m consistent n-ith Posid. Fr8EK, for "not being supplied 'for the road' (eph8iliirsthiri) from natural philosophy (pbr/siologiu)." T h a t is. he did not adopt a "procedure" (t.pbodos) grounded in physical theory 31. T h e eccentric and epicyclic hypotheses are treated here as independent rather than equivalent, since Stoic philosophers (the "W-e"of this passage; cf. nn. ;and I I above) are concerned uith their physical consequences. Also. no tvriter of the first centuries B . C . and A D . mentions this equivalence, and those that do address the issue of the planetar!- motions choose one hypothesis or the other, and not both. (On the project of saving the phenomena of the planetary motions before Ptolemy, see Boxr-en [zoor].) Ptolernh- actually suggests the possible equiralence of the nvo hypotheses at.i/i~r.3.3 (cf. Too~ner[1984] 144 n. 32), but does not discuss it until Alnr. I 2.1. O n the strength of the latter text some modern ) suppose that the proof of this equi~-scholars (e.g., Seugebauer [ I g j j] and [ ~ cjy]) alence goes back to Apollonius of Perge (third century B.c.). But this overlooks the fact that the single denior~strationPtolemy gixes in .-2lm. 12.1 of the planetary stationary points is his own, and that, according to Ptolemy his predecessors made their cases for each hypothesis separately; see Boaen (zoor). 3 2 . T h e phenomena that are "sal-ed" are identical, whichever hypothesis is adopted. OV V 8 ) is hest taken in this dis33. T h e phrase ~ a 7 6~1 ' ~dV S E ~ ~ ~T E~ L~ ~~ OT(37-3 tributive sense. T h e translation "the possihle neth hod" at I h y d (1978) 213 and a d d Comnt. 133 is ,.ague and question-begging, and for K ~ d d"possible" is also a synonym for "hypothetical"; see 11. ;abore.

39: T h a t is why a certain Heraclides of Pontus actuall!- came forward to say that the apparent unsmooth motion of the Sun can he saved" even if the Earth so~nehowmoves, while the Sun somehow remains stationary" 42: For in general astronomers do not l ~ a - kno~vledge e of what is 1)y nature at rest and what sort of things are ~noved." Instead, by introducing hypotheses of some things being stationar!; others in motion, they investigate which hypotheses will follow from the phenonlena in the heavens. 46:'- But astronomers have to take as first principles from natural philosophers that the motions of the heavenly bodies are simple, smooth, and orderly, and through these [principles] they will demonstrate that the choral

34. In fact the Earth's motion and the Sun's inmo'nilit) U-ould not explain this apparent unsmooth rnotion (manifested, for example, in the inequalit!- of the seasons) without some additional assumption, such as that the Earth moves on an eccentric circle. 3 j . On this text as evidence for Heraclides' cosmology see Gottschalk (1980) 62-69. l: (deroptory use of "a certain" (71s) and "somehow" (7ws) would nlake Posidonius' whole report r a p e and dismissive, and therefore not worth pursuing in any detail in the present context. Heraclides is chosen probably because the sirlgle possible explanation that he gave from the multiplicity arailable was so unusual, and, for the Stoic Posidonius, so exceptionally counterintuitive. 36. T h e Stoic natural philosopher \\ill know this, and what causes it, on the basis of the theor!- of the centripetal motion of the elements, whereby Earth, as the densest element, is stable at the center of the cosmos; see on Cntdestzn 1.6 at n. 14, and also 1.1 n. j j . Derc!&ks (early first cenhlry A.D.; see on Cmlestin at 1.2 n. g), cited at Theon Ev~pos.200.4-12, argues?much like Posidonius, that astrononlers must adopt this theory from the natural philosophers. His position ma!- reflect Posidonian ideas; see 1. G. Kidd (I y 78a) I I and Cbvm. I 3j. 37. Contrast the present paragraph, and lines 30-39 above, nith Simplic. 171 ile cnelo 488.3-2 j. Here Sirnplicius similarly recognizes the existence ofa true account of planetary rnotion that is based on physical theory yet denie5 that this account, n-haterer form it tna!- take, is the basis for definitively selecting the true astronon~icalaccount from a set of divergent theories. Instead, he sees astronomers 3s accounting for the phenomena of planetary rnotion on the basis of a few unexanlined h!-potheses about that motion. He does not claim that their divergent accounts must be reconciled with the single true physical (i.e., philosophical) account. His tolerance contrasts sharply with the position adopted in Fr8EK. Cf. also n. 10 above.

tiance3\of all [those hociies] is circular, n-it11 some revolving in parallel circles, others in oblique circles. 50: T h ~ l t then, , is how G e ~ n i n u s(or rather Posidonius [cited] in Geminus) transmits the distinction 1)enveen natural philosophy and astronomy anti he takes his starting points from .kistotle.

3 8. kboi-tin:Kidd Cbnrm. 13 j cornpares PI. Tim. 4 o c 3 T h e point about a choral d m c e is that it in\-olves intersecting circles.

GLOSSARY OF SELECTED TERMS

AETHER:

AIR:

~ifhi7.

a??.

m7fipode.r phnizesthai, phantazesthni A P P E A R A N C E : phnntasia A R C : penphewin A S S E M E : h~lpotithesthui ASSUXIPTIOS: hupothe~is B O D Y : sOmi/ C A U s E ( N .) : nitia, nitioa C E N T E R : kentmn, ~ r m o n ----, E X A C T : mcsaitnton C I R C L E (N.): kllkL0~ ----, A N T A R C T I C : mrtai-ktikos ---, A R C T I C : nrktikos ---, E Q U I N O C T I A L : i,.?nle~.im.r ----, G R E A T : wtegistns ----, H E L I A C A L : belinkos -, X O R T H E R N : 170wio.c ---, S O U T H E R h-: notios ----, T R O P I C A L : tmpikm C I R ~ ~ ~( OI FT P L A N E T A R Y A ~ O T I O N ) : kzlklos C I R C U M F E R E N C E : pei-iokh? ANTIPODES:

APPEAR (B E SEEN):

CIRCV~lHABITANTS:

pet-iolkoi

C O E X T E N S I V E TVI TH, B E :

~~lr'ipi~~~ekteit~esthiii

ephm-nrog-e epimein

COISCIDENCE: CONCEIVE OF:

C O N C E I T - I N G , P R O C E S S OF: CONJuXCTIOs:

CONTRAHABITANTS: COSMOS

----,

rpir~oin

.WHO~OS

nntoikoi

V N I T T E R S E ) : ~ O S / H O S(see

(=

W'H 0 L E :

C O U R S E ( O F P L A X E T A R Y MOTIOS): CRITERION:

"heavens")

fa h 0 h pov-ein

kv-itirion

CL'LZIIl\iATE:

?I?~SOI~~~~IIIP~~?

kz~i-tOvtn D A Y , D A Y T I M E : hemem D E M O N S T R A T E : deikmmni, epideiknunni D E M O N S T R A T I O X : npodeixis CCRYATURE:

DETECT, DETERVINE

(BY OBSERVATION OR CALCCLATION):

diffmetv-OS D I S A P P E A R : nphnnizesthni (see "sight, out of ") D I S T A N C E : npostnsis, d i n s t i m D O C T R I N E : d0.m EAST: nniztol? E C L I P S E : ekleipsii E C L I P S E D , B E : ekleipein, ekleip~ii~ poic.icthni E F F E C T ( A M O T I O N ) : poieisthni jk~n?.iin) E X C L O S E: pel-iekhein, pei&wrlm~zeii~ E Q V I S O X : i.Gne& E S T A B L I S H (A T H E S I S ) : kntn.ikr~ua;eiii,pnristnuni DI.4.LIETER:

FIRE:

pill-

pocJini0.r oikFsis B O D I E S : nstin

( I ) FOOT W I D E : HABITATION: HEAVENLY

H EA T-ENS: ~ O S T I I O S .O N ~ ~ I O S

~U/~LPSOS h?ki~k0~ H O L D I N G - P O W E R : he.~is H O L D T O G E T H E R : s~ii~ekhein H O R I Z O N : hot.iz6n HEIGHT:

HELIACAL:

hezi~.iikein

Glossary /

207

hupothesis hupotithesthai I L L U M I N A T E : lamprunein,photizein I L L U M I N A T I O N : ph6tismos I M A G I N E : epinoein I N C O R P O R E A L : a~omat0~ I N D E F I N I T E L Y : eis apeiron HYPOTHESIS:

HYPOTHESIZE:

I N T E R V A L (OF A N I G H T T I M E A N D A D A Y T I M E ) :

diastt'ma LATITUDE: k1ima;para (with the dative case) L E N G T H E N I N G : auxisis L I G H T : ph6~ LIMITED: peperasmenos L I N E , STRAIGHT: eutheia (grammt') L I N E O F S I G H T : opsis L U M I N A N C E : lampid% M E R I D IAN: mesimbrinos (kuklos) M O N T H : min M O O N : selini M O T I O N : kinisis -, based on choice: proairetikt' kinisis M O V E (INTRANS.): kineisthai, pheresthai NATURE: phusis NIGHT, NIGHTTIME: nux NORTH: b0r~a~ NORTHERN: boreios NOTION: ennoia N O T I O N , F O R M A: ennoein O B L I Q U E : 10x0~ o BS E RVE: theorein, tirein, horjn O C C U P Y : katekhein, katalambanein O P P O S I T I O N , B E I N : diametrein O P P O S I T I O N , I N : kata diametron P E R C E P T I O N : aidisis P E R I O D : periodos P H A S E (OF M O O N ) : phasis, skht'ma P H E N O M E N A , THE: taphainomena PLA CE: O t POS I N T E R V A L (OF SPACE O R T I M E ) :

nukhthimeron

epipedon planitai, planiimena P O 1 x 7 : kentron simeion P O I N T E R : gi~imiin PLANE:

P L A N ET S :

POLE: P

POWER:

O

~

dunamis

aporia, npowiz ephodos P R O T R U S I O N : exokhi P R O V E : elenkhein P R O V I D E : pawkhesthai P R O V I D E N C E : p~onoin RAY: aktii R E C E I V E : dekhesthai R E F R A C T E D , B E : kataklnsthni, periklasthai R E F R A C T I O N : anaklmis R I S E: aizatehiiz, anedhesthni, anirkhein, anaphe?*esthai R I S E (N.): anatoli S E A S O N : hil-22 S E C T I O N (OF A CIRCLE): t n z e m ~ S E E : hol-an S E N D O U T ( L I G H T , S H A D O W ) : apopempein S E N S E P R E S E N T A T I O K : phantasia S ET: kataduein, kataduesthni, duesthai SETTING: dzuis S H A D O W : Skin S H O R T E N I N G : meiiisis S I G H T : opsis S I G H T , O U T O F : aphnn?.~(see "disappear") S I G N ( Z O D I A C A L ) : ziiidion S I G N I F I C A T I O N : simni~zomeno~z S I Z E : megethos P R O B L E M ( R A I S E A): PROCEDURE:

S O L S T I C E : i'70Pt? S o UTH :

nmirnbria

SOUTHERN: ? Z O ~ ~ O S

SPHERE:

sphaira sphai~ikos rtndion. stndios

SPHERICAL: STAD E:

Glossary /

STAR: STARS:

-, ----, ---,

nSft?l;f l S t i v i 1 asttv

a L w A r s VISIBLE:

FI XED :

neiphaize

aplnz?

aphalze s UB s r s T: huphictnsthni S U B S I S T I N G , S T A T E O F : hz4po.sta.ri.r S C B S T A N C E : ousta S U N : hdios S I N DIAL : h#7.o/ogion S U R F - ~ C E : epiphnnrin T R O P I C : tropikos ---, S U M M E R : therinos -, W I X T E R : kbejv~e~inos U N L I S I I T E D : flPell.0~ V E R T E X : ko?-qhi V I S I B L E , .4LTVAYS: nciphn~zes V O I D : kmon T-O LL-ME: ol7ko.s vr.4 K E : meioztsthai W A N I N G : meiOsis \VAT E R C LOC K: hz~drolo~jo?~ WX: nuxestbai W A X I N G : nuxisis W E S T : dlt.Tk Y E A R : etzinutos Z E N I T H : kol-[LP& z o D r . k c , Z O D I A C A L B A N D : c6idiako.s Z O N E : z~T/? -, C O N T R A T E M P E R A T E : nuteukultos -, F R I G I D : kntepsupenP OI'T

OF SIGHT:

-,

TEST P E R A T E : P U ~ W Z T O S

-,

TORRID:

ilinkeknumene

209

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BIBLIOGRAPHY

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I. PRI,ZZ1RI7 S O U R C E S These are identified either in the List of Abbreviations at pp. xv-x~iabove, or in headings in the I?likvLocoum at pp. 0-0. For studies that contain texts and translatjons see Part I1 of this bibliography under Aujac (Geminus), Burton (Euclid, Opticil),Cherniss (Plurarch), D C1,aq (Philodemus), Goldstein (PtolemS; Plirnct~~i~~~liypotheses). Goulet (Cleo~nedes),Heath (Alristarchus),KeEer ( W e n ) , AIaass (Achilles, and .?~ntizn),Pease (Cicero, L)L' ~ t z ileorz~n~), m R o ~ n e o(Demetrius of Laconia), Rosernan (Pytheas), Schone (Damianus), -4.AI. Smith (Ptolern!; Opticc), AI. E: Smith (Diogenes of Oenoanda), and Toorner (Ptolemy, Lil/~~ngest). Basic infor~nationon the primary sources used in this study can be conveniently obtained from D. J. Zeyl, ed., Ei~z)dopedinof'(2'li~ssii-dPhilosop~y(\f>stport, Conn., 1997).

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Review of Theiler. Gnomon 58: I 1 0 - 1 2 0 .

Ed. JInistir.: Classical, Byzantine and Renaissaizce Stzldies $7Robeit B1.0rni7zg.(Byzantina Australiensia j). Canberra. Ed. Collecting Frngnie?~t.rFi-ngmente sammeh. (Aporemata Gottingen.

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"Sur l'origine et le sens de l'expression ~ a 8 a c ~ cT$V i v och$v7v." Reccw rles itudcs tcsnnciennes 6 I: 48- j 6.

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"Cleomedes and the Meridian of Lysimachia." Amei-icn7zJoz~rnnl of Philologq, 62: 344-347. ":lpollonius' Planetary Theory" Communications on Pzu-e and L4pplzed,21athemntics8: 641-648; repr. in Neugehauer (1983): 311-318 "The Equivalence of Eccentric and Epicyclic Motion according to Apollonius." Ssi-ipta Mathematicn 24: j-21; repr. in Neugebauer (1983): 33 j-351. Histo~yOf'Ancient ;Ili~thematicalAstronomy. 3 vols. Berlin. .4sti-o?1onqand Hzstovy: Selected Essays. New York and Berlin.

R. R. (1 9 80)

"The Sources of Eratosthenes' AIeasurement of the Earth." Qzra~tel-!\~Jo~~i~i~ilrrl oftile RojalA4.st~-or~on~icnlSociet~ 2 I : 379-38;.

Pease, -1. S. (1955)

Etl. LIIm-i Xdli Cicemlis De AY~t~li.n Deoixrn. Cambridge, Alass.

Pedersen, 0.

A Sri-zey oj-the .?lvrngest. Odense. (1971) Petruccioli, S. (2oo1)Ed. Stol-iir dellil siiema: I. LN scieiiza gi.eco-i.ot~~n~~n. Rome. Plug, C., and H. F,. Ross. "The Satural Lloon Illus~on 1Alultlfdctor Angular ;\ccount." Pei.ceptloi/ 2 3 32 1-3 3 3 Ln lune d m s lil pens& gwcque ( I c ~ i d h l royale e de Belgique: Alemoires de la classe ties lettres. Ser. 2 , 614). Brussels. "On Empirically Equiralent Systems of the \Thrld." Erkemt71;s9: 313-328. Q1rii1ditie.s.Cambridge, ,\lass. "Eratosthenes' Geodesy Unraveled: 11%~ There a HighAccuracy Hellenistic .1stronomy?'' I'ix 73: 2 jg-26 j. "The Eratosthenes-Strabo Nile JIap: Is It the Earliest Surviving Instance of Spherical Cartography? Did I t Supply the jooo Stades A k cfor Eratosthenes' Experiment?" ;I1-chixfir Histoq o f E . ~ m tSciences 2 6: 2 I 1-2 I 9.

Poseidor~ios.Munich. Kosmos m d Synzpntl~ie.AIunich. "Posidonius von Aparnea." Real-Ei~iylopiiilie22:1: 5 j8-826. "Demetrio 1,acone sulla grandezza del sole (P. Herc. I O I ~ ) . " C t - o n ~ ~Er~.olai~exi hr 9: I 1-3 j . Roseman, C. H ('991) Rosen, E. (1981)

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h~cholausCopernicus and Giorgio i:alla." Phyk 23: 449-4 j7. T'

Koss, H. E. (2000)

"Cleornedes (1st century A.D.) on the Celestial Illusion, Atmospheric Enlargement, and Size-Distance Invariance." Perreptioil 29: 863-871. Ross. H. E., and C. Plug. The . l l ~ s t e i qf'the : ~ 12Ioor~Illzaio~~. Oxford. (2002) Santlbach, F. H. Ariitotlr nnd the Stoics. (Cambridge Philological Society Suppl. (1985) ITol. 10). Cambridge. Schnabel. P. B~rossosI I I die ~ E~~l~yIot~i.ici.rlle~~i.ctti,-i.c Lite~ntz~r: Leipzig. (1923) Schofield, AI. (1978) Schiine, R.

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Sorabji, R (1988)

Mzttel; Spare, a d .\lotion: Theol-irs in A n t i p i t y irnd Thrii Sequel. London. Ed. ill-istotle Z.an$o~-med:The .4ncirlzt Con~mri~tato~s m d Their Ii~jlz~erzce. London.

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PASSAGES FROM CLEOMEDES IK COLLECTIONS OF TEXTS

BOOK ONE 1.1.3-7: SC7:z.j~g;3-16: F276 Th(ei1er);7-17: SI/Fz.jj+;20-38: SI'F2.j37 (summar>);43-48: S W 2.jj7; 43-54: F277 Th.; 64-67: SCF 2.j41; 68-74: S W 2 . j46; 68-80 F2 78 Th.; 81-82,89-103: F278 Th.; 96-103: S W 2.540; 113-149: SVF 2 . j38 (summary); I 50-152: SW 2 . j j j (selections); I 53-166: S I T 2.j j j , 159-192: F279 Th. 1.2.1-19: F280 Th.; 36-40: F281 Th 1.4.30-43: F282 Th.;90-131: F2roEK;go-131: F283 'Th., 132-146: F284 Th.; 197-213: F28 j d Th. 1.5.114-145: F286 Th.; 128-134: SV'F 2.45 j 1.7.1-49: F287 Th.; I- 50: F2o2EK; 121-1.8.18: F288 Th. ; Th. 1.8.79-99: F289 Th.; SVF 2 . j 7 2 ; 158-162: F I ~ E KF274

11.1.2-524: Fzgoa Th.; 51-56: F I I ~ E K269-286: ; FIIjEK 11.3.61-11.4.107: Fry1 Th. 11.4.95-107: FI 23EK 11.5.1-7: ~ 2 9 2~ h . 11.6.168-191: F293 Th. 11.7.1-4: F294 Th.; 11-14: F27j Th.; Tj;EK

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GENER-4L INDEX

.Achaca (in l'eloponnere), 9 4 .Acliacans (sc. Homeric Greeks), 124-2 j riene~idilnus.I 0; air: adjacent to acther, 40, 134; bounded 11y aether and water, 9: displaced from cont-diners, 23-24; partial constinlent of the \2oon. I 18, 13j, 1 4 j ; sphericity of, 73 ,l~thei (= ,lether: sul~stanceof the heavens), 291143, 31nj1, jllnr, 731136: epdations of densit! in, 118; guarantor of'sphericity of cosmos. 73; located hemeen air and volil, 29 ilitioiog~ic(theor! of causes), 196, zo111z3 Alesander of .iphl-odisias: and Cleornedes' date, In+, 261131; on illumi~~ation in the \oici, 261126; source for Posidonius, 1991113 Ugra, K., 2114. 41113, jn16, 61120, 221110, r 3 n 1 j , 2 4 1 ~ 0 99113, , 1031119, 10jnz6, ro;njz, rzznlo analogies. Sce Stoicis~n nnuprph?.~(without physical contact), z 2111 I mzirnnl& ( u n s n ~ o o t h l ~of) :planetary notion, zoznzy ;mthelim (counter-Sun). 1621123 N ~ O ~ C I S(de~nonstration), ~ Y ~znjg .ipollonius of Perse, r16nf;c), zorn;I k a t u i , 46, r r ; .Iristarchus, I r jn(i2, 134nry

.lristotle: follotxrs' denial of cxtracosrnic void refuted, 24-2 j, 26-28; source for distinction het\veen astrononl!- and natural philosophy, rygnrj, 204 ~ ~ k l l i l physical z: first principles at basis for astronorn!. 198-99, 203-4 Arternis: festival of, 149; and ,\lou11. '49"'i iutln: as term for h e ~ m l bodies, y jRn1 astronomers: Chaldean, 161; distinpuishcd from natural philosophers, 193-204; Egyptian, 161; and hypotheses, I9j96, ry6n6, zorn31 atrnospherc: cause of refraction at horizon, 102-3; cause of Sun't enlargernc~it,101-2 :iujac. G., 39ny, 4ong. j1n3, ~ j n 1 6 . 1~3"' L~II/~s. 1261111 2 Bake, J., 1yyn16 Rarnes,j.. 1 g ; n ~ / J N ~ ~ (UY. YO ~ U I I128116, ~ ~ ~ ) , 142Il26 Berossus. I 36112 body: dctinirion of, 2 jnz4; not e s t w cosmic, 29; not unlimited, 28, jo: in pl;~ce,2 2 . See ulso incorporedity and Stoicism Brunschwip, J., 2 yn++, I jonrii Burnyeat, 1I.F.. 921128, ~ o o n j ior1116 ,

Celts: latitude of, r 2 3 Cherniss. H., yznz;, 1 3 7 8 , r j r n z h chiasmus (of s h a d o w cast by Sun), F I ~I .2. 761110 Chrysippus, jn16 circles: arctic and antarctic, 33-34, 34nj9. 6 2 ; of celestial latitude. Fig... 2 ( ~ i - ( J h 33-34; equinoctial, 46-47> 62-66; heliacal, 41, j3-j4; tropics. 33, 43%62; variations at different latin~des.F;-?. z o , 34. 62-66; zodiacal, 41nn1;-18, 53, 62 Cleanthes, 1z1n92 Cleomedes: anti-Semitism in, 1 2 j: and Chrysippus, 51116; dare, 2-4, 891116; division of chapters in treatise, >on. 331158, . + I n I j , 4911~0, j o n i ; lectures and teaching, 2nj. 1211195, 16snn7.8: order of exposition. jn;; relation to h a t u s , 3119; reliance on Positloniui, 15-17, 165118; Stoicism of. 66n9; title of treatise, rnr; treatment of void, 2 21110; use of Eratosthenes' calculation of Earth's circumference, 84n23: use O of Homer. .3nq. , See L ~ S Stoicism cleps!-dra, 241118, 26n2; constellations: Arpo, 80; Draco, 46, 68: Helice. 46: H ~ l d e s 89 , cosmos: administered hy ATanlre, 2 2 ; directions in, 31-32; sense used of, 21: size reduced if the Earth is Hat, FIR.1 1 . 69nnz1-22, 6y -70; sphericity of, 32-33, 64-65, 72-73, see ~itht?: See also kosliros criterion (k~ittriou):and demonstrative procedures, 11-1 j ; of truth tor Stoics, y -I I; m d unohsei~ahles.64113, 64-6 j; and x-isual obsen-ations. 11jn61, 1341124, r j j n z j , I 56116. 163n29. See alsophniztnsia driktidor (digit; unit of celestial tueasurement), 131n; day: length of. 41112, 541116, j q - j j daytime: defined, 361168; monthly increase at Hellespont. j I n j ; x-ariation at different latitudes, 123n102 Derneter: rites of, at Thesmophoria. 1 2 j Dernocritus, 6 jn;

iliitkosmisir (stratification of elements). 21112, 38111 diameter: as 1/6 of circumference. 841124. 116-17 tiikhotomo~(half-shape o f l l o o n at the quarter). 1391115 146116 Dionysius of Cyrcne, 107113j, 128116 riiciekritt.~~~oriuil (twelfth part of the zodiacal circle), ,41113. jjn17, 88, 1I;nj;t IIUIZNW~IS (poa-er): inherent in bodies in the Stoic cosmos, 281137; o f l l o o n , r r 313I 8: poii'tiki (causatix-e pox$-er), 48n1;, zo11123 Earth: cosmoccntricit!: 74-77; cun-amres. I 60111 8; distance from AIoon, I 19; distance from Sun, I 16-19; eshalations from. 721133:flat for Epicureans. 6 j n 6 , r z j n I o I ; inhabitants. 34-37: shadou cast hy Sun, 11j , 128-29; sire, 78-84; size tliscountahle relative to cosmos. 86-90. 100, to heliacal sphere, 86, 90-91, 104, and to Aloon, 92-93, I 161167; source of nutritious e.halations to heaxens, yrn24; sphericity of; 3 2 - 3 3 , 64-72 84-8 j;sphericity and x-iea-from higher elevations, 93-94; Sun's distancc from. I 181181; surface conditions and sphericity, 84nz j, 84-87: zones, 34 eclipses: annular, l q n n z g , 30; and Earth's sphericit!; 671112; lunar, I j4-79; parai jg-63; solar, F i b 2 2 . d o ~ c a lunar. l 42, 137, 131%142-44 Kdelstein. L.. 193111 eklc+tikos (ecliptic circle), 411118, I j211jz ekplrriszs (cosmic conflagration): and esistence of separate void. 24 cleinents: centripetal motion of in Stmc tlyainics. 2116, 71123. 2 71132, 33n5;, 7311 j8, zoInz4; stratitication of, 29n43 Eiis, y 4 (endowed with pi7eltnm), I 19n86 r!i~pr~oi~~ i.phor1o.r (procedure in deinonstrative reasoning), 111138.11-rj, 1081138, r 4 j n j r . 147117, 1ion", I j;n8, 20on2o Epicureans: degeneracy of, I 2 6; fanaticism of, 122; impiety of, rzzngg; o n size of cosmos, 1181181; o n size of Sun, 99-

121; on Sun's diurnal extinction and rekindl~np,122-24 Epicurus: comprehensive ignorance due to hedonism. 1 2 1-22; dogrnatism, 125; literar>-st!.le. 1 2 j ; unjustified lrmensiions, I 24-2 6 equator (terrestrial): distance from tropics, 5in2y; hahitability of, 56-j8; temperatures at, j 8 equinoxes: explained. 4 8 - j ~ ;and shadows, m

-

/>>l11

Eratosthenes: measurement of the size of the Earth. Flgr. 14-1 j.691123, 81-84, 11,

Ethiopians, j6nz3, 6; Euclid, I Izn jo, 147118

Geminus of Rhodes, 61122, 194111, 196116.

hilpsm (height): of celestial bud!- relatire to of celestial the Earth, j+nr+, ISZIILY; hody's position in the zodiacal hand, 4'"" hypotheses, 131144. 58, 128, 131-33. See phi~~omi~i~n Therians: proximity to circumambient Ocean. 124; at n-estern extren~ity of known ivorld, 6;. ;c Ikhth~ruphngoi(Fish Eaters), 120118 7 illusions: of celestial imniohilit); rojnz6; of proximity of heavens, 106nr8; solar and lunar, rornri incorporeality: of lc~kton,14gn18; of place, 22; of surfaces, zyn44; of time, I jcn18; of void, z j inhabitants (of the Earth), Fig ; antipodes, i j ; nntoikol (contrahabitants), 3j ; mtinroi, j jn64; defined h!- shadows, Figs. y @)-(L?; perioikoi (circurnhabi?ants), 34. 12311103

[;oillet, K., ~ n n - 2 ,jny. jnn16, 17, 601142,

137118, IqynI;, I 521130 Granr ick, -1.. j8nn1-2 Great Sea: located in torrid zone, j 8 Hahn1, D., 27132, 10211102 tIearh, 'T., 1141157, ryjnI Hecate: and lloon's shapes, 1491114 Herispilw.os (Daun Bringer): epithet for Ttnus, 40 lIer,lcles: contrasted with Epicurus, 126 Heraclides of Pontus, 71123, 194, 2o3n3j Heraclitus of Ephesus, 92, 103n19, 1 2j He~pcros(Evening Star; also Phivpho~m): epithets for Venus, 40 hesis (hoidinp power in Stoic cosnioloa), 27""34, 35 Hipparchus, j3nr I , 118n80, 131nj, r j y n 5. ~ 2021130 hurm2 (in~penlsof Stoic cosmos), 281138, ~ 1 I l j I

h~~pnl.kbeil~, z 31112 brq~ostns~s (state of subsistence; i.e., suhsrant~alexistence), 231112

kulat/!oeirlis ((funnel like: shape of Earth's shadow), 128118, I 58111I khim (space), 22n10, 391116 k l ! u r e ~(dance, ~ sc. movement of planets), 2041138 Kidd, D., .+6n9,117nn;j-76, 161nzz K d d , I.G., 61119, 11, I jn48. 161149, r;njz, 22, j b n ~ j 57, , j7n29, 60, 621146, 64113, 79114, 80118. Xrnrr, 102~114,I 101143, r 14nn.j j,T rjn60, 1211192, I ~ ~ I I13;n8, I ~ , I+rnIg, 1421127, 148n14, I ~ ~ I I161nnz1, I ~ , r y j n r , 196117, 1y8nn10, zoon18, 2011123, zo1nz6, 2021133. 1031136, 2o4n38 kii~Esisp~.uniretik? (motion or course of planets based on choice), jtinj, jo, I 16, 118, I j j ; pini~oetikr(providential), 38n3 k i i i n ~(latitude), Figs. 1-2; concept of, 32n.j.5, 3jn63 Lwek~de.r - . . (flecks in lower atmosphere distorting ohsenations),

1071131

kiiiwios: used in sense of the heavens, j r n $1. 200n17. Sec cos~nos kiirrtho.~(liquid measure): defined, I 101142 latitudes of the Earth: Uesandria. 788 4 %123; Britain, 61, 123: effect on oljien-ation o f cclesticll l,ltihdes. Figr. zjii)-(f), j. 34%44-4;: Ethiopia, 56, 6;; Greece, 60; Hcllespont. jrn;. 123, 130-3" AIeroe (in Etlliopia), 1 2 3: Rhodes. 78-81: Rome, 123: Syene. 56, 6;. 81-84; Thule. 621146 Icktoii: not estracos~nic.jon48; as a signification, 1491118; Leontlon (associate of Epicurus). 126 Libya, rzo Ih!-d. G . E . R . . 1621124, 197118, 207.1133 Long. $. \., 1 2 ~ n 1 0 6l,2 j l l I I O Long. -1. A. and 11. S.Sedley ( L S ) , 91129, I 51148,99113. 100118 longitude: of Iberians and Persians. 66-6; L!-nceus. 1ozn14 .\Iaiotis. Lake, 1 2 0 , 123 \Im&ld,J., jny JIansfeld. J. and D.T. Runia. \ \ , I j l n j 2 sidereal period of, I\Iars ( P I I ~ ~ I J164-65: ). +C"" .lI?v. meanings of. 149 J l e n n . S.. 1401114 \Tercur!- (Stdl~in),40. 164 .\Iilton, John, r o g n j o mixture: of Sun's light with .\loon to c'luse illumination, 138-39, 13y n n 140-41.

siderei period, 41. 116, 135; size relati\e to the Earth, Fig. 2 0 , I I jn63, 134n19 multiple esplanation~,56112j,122n10, r24n10.+, 161nz1 natural philosophers: tlistinguishcd from astronomer,. 126~1114,193-204 N'lture: a5 basis for cosmic finitutle, 21, for terrestrial habitahilit!; 37 i\'eugeh,luer, 0..1112, 4, j n I 4 , 32115 j. 52118. 6 7 1 2 , 681116, 821120, 891116. 13Illj. 14jlljo. 152n30, 15jn8, 1 6 . ~ 3$. , nighttime: defined, 361168; lengths at ditferent latin~dei.123 Ri\-er. j;, 86 notion (ir~iioin):formation of, 87, 108-9. 130: as preliminary concept, 281140 (period of night anti day). i771ki~i.?n1einn 361168 Ocean: di\-iding zones of northern hemisphere, 3; Odl-sscus, i 24

Panaetius, j y j o parallax: absence of in celestial o1mn.ar i m s from Earth, Fig, 16. 8 7 8 ; lunar, 92112; pni-rk/icsth/ii(pro\-ide), z 1119, 48n r7 parhelion (mock Sun), 1611122 Persians: at eastern cxtremit>-of h o u n world, 66-67. 70; use of relays on expedition to Greece. 108 tnontlis, sknodic: xariation in lenprhs. Fig (phenomena): insufficient to phil~iio/~rtwn - 150-j2 -). establish physical theor!; 8, 194-99, ,\loon: coniunctions with Sun at m r ) inp 201-3; and lunar eclipses, I j 6 ; suffiinten-als, I 50-52; densit! of. 139111 I , cient to demonstrate the Earth's 142; distance from Earth, 110; eclipses spherlcit); 9, 71-72. Sce criterion of. I jt-63: et!mology ofsr1i;iii;. 148n12: pP/iiiti~.vcr: P ~ N I I ~ N . S ~kiltill2ptlkE II (Stoic criillumination by admixture not rcflecterion of truth), 8-9: presentations tion, Fig. 23. 40-41. 136-41; at ~UTICin peneral, 91128, I 5114;; as ~ i s u a l tion of air and aether. 291143, 40. I 34; ~llusion,161nzo.S E Ccriterion length of orbit, 41; motion relative to phnsi~.(appearance), r 3 In? the zociiacal circle. I j r , 1x611;: 1ilurL3Philoponus, John. 23111 j appearance, 145; p h z e s . Fig. 24. 14splace: defined in relation to void. 2 2-2 3. 49; p m e r of, 120, 133; proxi~tiityto See also topos Earth. 40, 134-35; senses of. 153; planets: apparent irregular motion, 9

Genel-nl Index /

latitudes, 164; ~naximumelongation. 165; motion in zodiacal hatid, Fig. 4. 38-39; n u ~ n h c of, r 39119; sidereal periods. 3yn9, 40-41, I 16; rynodic periods, 164-6 j, 16j n j ; velocity in relation to density, I I 18 pnetrmiz: in Stoic c o s ~ n o l o p73n3 , j, 731138: in Stoic theory of vision. 261116,

poiliirios (I foot wide; epithet of Sun's appearance), 18, 103n19 poi~in(to cause). 481117 Pontus, 162 Posidonius: cited by nanie, 56-57. 78-80, y j , 102,114. 142,165; and Cleomedes' treatise, zn;; on distinction hetlveen natural philosophy and astronomy, 6-7, 193-204; on habitahlity of the torrid zone, 56- 58; lullar illunlination explained hy admixture of Sun's rays, 1411119; measurement of the size of the Earth. Fig. 13, 78-81; measurement of the size of the Sun, 114-15; source for Cleomedes, 15-17; treatise on Sun's size, 9 jn39; use of hypotheses, ;gn+ 811111, ~ q q - y g , 201-3; use of proportional ratios, 16. 6 9 n z z , 1 1 p j 8 , 1161173, r j z n ~ r See . also ~zitiulo,yii~ Ptolem!; 75117, 104n20, zozn31; and equation of time, 4nnI1, 1 2 Pythagoras, r 2 j Pytheas of \Iarseilles, 62

refraction in visual obsewation, IoInr I , 162 Reinhardt. K., j n l + r;n jz, 194112 Renehan, R., roj1123 Sandbach, F. H.. 199111j Sardanapalus, I 2 6111 Saturn (Phizi~&~), 40, 164-6 j Schumacher, it:, 31110 Scyrhia, r 2 0 seasons: annual variation in lengths, Fzg. ,(a), 44-47, j j ; caused by Sun's

229

motion relative to zodiacal circle, Fi,y. -(/l), 53; rariation in lengths at different latitudes, 59-6; Sedley, D.h-., 99113, 1621126 simnmonrcnoi7 (signification), 1491118 s?nteiotz (evidentiary sign), grnz8: ( peometrical point), 88n1o shadow: c:iused by spherical bodies of . 128, r 58; detesdifferent sizes, F I ~21. ruinant of Earth's cosmocentsicity. y j76, of Sun's size. 110-12, of Sun's si7c relative to the Earth, 128, I j8. of terrestrial habitations, Figx 9 (ii)-@), 58j c ) . Stae i h o chiasmus. kaluthot,id?~. Sharples, K. L\:, 2114, r jnzr Simplicius: and hypotheses. zo3nj;; as a source for Posidonius, I rqnr 3 skheseis (directions in cosmos), 311150 sklolc' (lecture course), 2115, 16jn; Socrates, 1 2 jn11o stade. -8112 stars: -\ldebran, 8yni j ; Antasec, 8gn1i; Canohus, 80; fixed, 38-39; nu~nher of, 39n8; Sirius. 8onX Stoicis~n:analogical reasoning from 101, ro7-8, 138, 139, I l I n z o , 143, I j j , 162; argument forms, 661110, 7111z8, ~ z y n yI, j y n r j ; concept of See also ekpiii-isii. hesi~.,incorporealit!. lekton, phi~i~titsiir. place, su7nnpatiwciz. tfJ7lfJ.i. void Straho, 561124 .xmpnthein (sympathy in Stoic continuum), 22, 2 j .;ii~~pi~i~zurfeiiz (complete a circular course). 901120, 146nj 5un: apparent enlargement near horizon, Iornr I ; apparent irregular motion, 195, 1981112, 2021129. sec mOmii/ij.~ cause of climatic differences, 43, y t y j ; distance from Earth, 118-19. ~ . < o 52; eclipses, 134; f i g ~ r a t i i econtact U-ith da!--circles, 481116; larger than Earth, 12;-29; notion in the zodiac, 48-51; not as large as it appears. 99 103; not I foot wide, 103-1;; sidercal period, 40. I 16; power of, 58, I 10-1 I :

Sun j i o n t i n u t d ) senws of, 153; size calculated through hypotheses by Posidonius, 114-1 j ; size more securely calculated, I I j-I 8; size relative to AIoon, 116 smiienimi (nodes), I jz sun dials: used hy Eratosthenes to determine Earth's size, 82-84; used to prove Earth's discountability in celestial observations, go surface (of a body): incorporeal, z g n + + 'l'heiler. IT:, 17njz. j8n33, 9jn39, lOjIl25, 134LlIg Thersites, 124-2 j Thorp,J.. z y q j thought experiments: circumnavigation of Earth, 33; dirplacernent of cosmos. 21; enlargement of the Sun, 10;; missile circling the Earth, 109; planets supposed to Itlove at an equal speed. 116; stationar)- eclipse. I 3 I: viev ing of the Earth from the Sun. 8; tides: caused by lloon's power, 133 time: equation of. qnIz, j4-jg; not extracosmic, 301148 to17o.i (tension as property of Stoic cosmos), 26, 73n35 Toomer, G., 1181186, 13111;. 131119 topns (place): in Stoic physics, z z n ~ o39n6 , Venus, 40. 164-65 vision: aEected by atmospheric conditions

1621124: diminishes vast disrances, 103-4; via extromitted visual cone, Fzg>,.I--19. 102-3, ~ j o - j z , 1j1n24 void: existence of, 22-ZS; inactive, 28; nonexistent within finite continuum, 2 3-26; occupiable, 2 j; space for cosmic expansion, 24, 2 8 ; unlimited and extracosmic. 29-3 I; ~moccupied, 231113 ITBsserstein. A., I 61112 r water clocks: used in estimating Sun's size, 110, 116 IThitraker. J.. 165118 IThlff, AI.. 33115; 73n38 !-ear: length computed from seasons, ,31111: relation to total nighttime and daytime. 63 zodiac: hand in contrast with zodiacal (i.e., heliacal) circle, Fig.j(il), 41nn1;,18; extent, 41; motion of planets in, 41-13; relation to heliacal circle, 5;-j1: signs of: Cancer, 61-62, 68, g;, I I I , 111; Capricorn, 95; Gemini, j4, I 51; Sagittarius, jq, I j i ; Scorpio. 89; Taurus. 89 zijui~on(zodiacal constellation or sign), 54"'3 zones (of the Earth), 31-36; mid-torrid, 4411;; torrid zone's uninhabitabilit~; 331156 ;, 56-58, See also Sun

INDEX LOCORULM

Editions are not identified for major authors; cross-references to editions are to those cited in Part I of the bibliography. CAG = Comme7zti~i-in in AI-istotelencGmcu; Suppl. An = S~~pplenre?~tz~m A~%totrlicz~?~z.

re/iquiae ed. F. .\hass (1898), 27-75 39.16-20: 3911; 48.16-18: 39117

De anima ed. I. Bruns, S/ippl..-h: 2 . 1 (Berlin, 188;) 41.17-19: 1621126 71.1;-18: 1ojn26 DP R I ~ /ibl-i R v~a~~fi~~il ed. I. Bruns, S~ippl..ln 2.1 (Berlin, 188;) 139.14-1;: 261126 139.17-19: 1.1-1""

Quarstionc~ ed. I. Bruns, Suppl. A4,12.2 (Berlin, 1892) 3.12 105.27-3 j: 29Il4-j IOj.30-3 j: 2 jn21 106.3'-107.4: 2 jnzr A L E X A X D E R O F .APHRODISIAS

ap. Simplicium Iiz Ai-irtotelis de me10 z8j.26-2;: 2yn4j 28j.3'-286.2 (SIT z.j3 j): 28n39 286.6-10: 261131 286.10-23: 271134 286.23-27: 29114j ap. Simplicium h1 Pb~,sica 671.4-13 (SI'Fz.jj2): 26n31 671.8-13 (SW 2.jjz): 271134

APULEIUS

De deo Socmtis ed. C . Aloreschini (Stuttgart and Leipzig, I yy I ) 117-19: 136111

ARRIAN.

See Philoponus In n2etro?alogii.~r

.\RCHI\IFDES

Upt'l77 0771711/1 I1 ed. .I. L.Heiberg, rev. E. S. Stanlatis (Ixipzig, 1972) Fr. I;: 162112j

REROSSCS

Fr.1 8 : 162111~5 (ALCIDILS

C'ornme17ti~rir~s iii Timneurw ed. l.H . 'lljszink, t'I[rtnLnti17rr.r4 (London and Leiden, 1962) 111.8-17: 901117

D E X I E T R I U S L.4CON

ed. C. Romeo (1y;y) col. zo: rojnzh

Set' 'picurus ed. 11. llarcovich (Stuttgart, 109y) 7.45 (ST7: 2.3 5): 101133 ; . j r ( S i ' F z . 6 ~ )yn28 : ; . j t ( S l F r . 6 j 1 ) : 1jn48 ;.132-33 (Posid. Fz j 4 Th.):61119 ro.z;-z8: rzIngj

D I ~ G E S E S L.ILRTICS.

D I O G E U t 5 O t OF.NO \ N D 4

d . \I.

I? Smith (1993)

Fr. 13 (cols. 1.13-11.10): 1061128 Fr. 13 (col. 11.1-10): lo;nj2 Fr. 1 3 (col. 11.5-8): 1181181

Ciltuptrw~ etl. J . I,. IIeiherg (Ixipzig, 189r;) 286.1;-19: 162112j E/ewezt[i ed. J. L. kleiberg, re\. E. S. Stamati\, i vols. (Leipzip, 1969-7;) T Not. comm. j (I: 5.1 1-11): ;p; I prop. 29: 8011~. 81111j 3 df'. 11: 8znr6 4 prop. 15 prism.: I 17n;; j df5. ~ & z 8;nt : 5 df5. 3&4: 8 7 4 7 dfs. 3 , j: 87114 13 prop" 13-18: ;3niy Opticir etl. 1.1..Heibrrg (Leipzig. 189j) prop. j (8.6-7): r ~ z n j o 1431132 . prop. 2; (44.14-1 j): IojnI;, 147118 prop. j+ (112.rj-16): I I ~ I I ; S ,

P~%,N~IIOINPIIN etl. 11. AIenge (Leipzip, 1916) prop. I (10.11-12): 74111 4.26-6.14: 65118

HBLINL'S

De nst?~unomriz ed. -1. Le Reouffle (Paris, 1983) 4.6: jyn;

(S~O~CIIS) .-llleprine (Quaestio17esHornericizr) ed. F. Buffi6re (Paris, 1962) 46: 129119

HERACLITUS

HERODOTUS

3.19: 120n8; 4.42: 1zon8y 4,198: 1201189 8.98: 108n38 HIPPARCHUS

117 A4~wtret E~~ilvriphire~io~~reni~ ed. C . hlanitius (Leipzip. 1894) 1.2.18-20 (20.21-22.9): 891116 1.3.; (26.16-23): j I n j 1.9.12 (94.16-1;): 11;n;; z.1.20-22 (rjz.10-13+2): 8gn16 HIPPOLYTCS

Refimtlo ortrnic~mhirew.iunr ed. .\I. Alarcovich (Berlin and S e v h r k , 1986) 4.8.6 (101.31): 116n6g

\1.4RTIINUS

C \PELL.A

d. J . TT7illis(Leipzig, 1983) 6.595: 123n102 8.848-49: j3n12 8.8;;: 12311102 8 . 8 ~ 852118 :

PAPYRI

T7i?ziti(1 'nstroi~omietl 'npi-i.s E~iosc. ed. !I. Letronne 2nd L1.T: Bmnet de Presle (Pat-ic, 186j) P. IPar.r,col. 19.16-17: 1431129 ed. A. Jones ( ~ y c ~ g ) P. Cl\?. 413th ii.121: 1521132 PI-IILODE\lLTS

DC~.ig/iis ell. P. iind E. de Lacy (I y78) col. 9 (sct. 14):99112 cols. 10-1 1 (sct. 1j): 107113j , 128116

POSIDOSICS

ed. Edelstein and IGdd (E& T 2 2 : j7ll30 T83.2: 64113 T 8 j : 48n17, 66119 '1'91: 1 2 jnrIo '1'9 j: 12 jnr 10 I.'g: y5n39, " p 1 0 Fro: gInz4 F I ~21114 : FIX: 7-8, I-5-17, 5151125. 12611114, 193-204 F18.j-18: 61121 Fr8.20: 66ny F18.22: 48111; Fr8.26: 48111; F18.32-39: 81126 Fr8.39-42: ;nzj F18.46-jo: 61122 Fzza-h: 1zzn9g F42: 1 j q 8 F49.1-145: j6n24 F4y.6-7: 66ny F49.10-36: 5 7 2 9 F49.j1-61: 5 7 2 7 Fqg.131-32: 84112 j F49.134-3.j: i i n z ; Fgo: 61119 F106: I 331118 Frr4: 1021114 F I I ~I:I q n j j F I I ~j8njr :

POSIDOTICS

ed. Edelstein and EjcM ( E K j (coiitir~iieii) Frrg.3-6: izznroo

F1y1.13-~j:Xony Fzoq: ; 6 n z t F ~ I o561124 : F ~ I I561124 : ed. Theilrr Fjh: 6n19,72n31 Fjc: 61119 F2 54: 6n19 Fz84: 581133 Fzgoa: 9 j11j9 F44;: 61119

A41ir/nge.rt6Ty~rtn.~u ~r//~t/~~i//iitii[/) etl. J. L. IIeiherg (Leipzig. \(>l.I [Bks. 1-61 1898, vol. 2 [Bks. ;-1jj 1 ~ 0 3 ) 1.1 (j.19-;.3): 2001118 1.3 (11.14-24): 681116, 6yn21 1.3 (11.24-26): 124111oj 1.3 (11.24-12.18): 12211100 1.3 (13.3-9): I O I I I I I 1.3 (13.11-10): ;jnjr) 1.3 (13.21-14.16): ;3n36 1.4 (15.11-13): 6-1112 1.4 (15.16-1;): ;on24

2.6 (113.6-0): 61114.j 2.6 ~ I I + ~ - M ) 62n46 : 2.6 (114.23):581133 2.6 (115.8-16): 6211th 2.6 (115.8-116.~0):621148 2.6 (116.21-117.9): 62njo 2.7: j-jIII9 3.3: 2021131 3.4 (233.21-24): j3nII 3.4 (23;.20-238.4): 531111 3.9: j41116 4.1 (266.1-4): 92112; 5..3 (364.9-10): 78113 6.;: I ~ I I ~ ; ;.F: 80n15 8.1: Xy11rj 1 2 . 1 : 2021131 Geogi.irp/~iir rtl. C . F. 1.yol)l,e (Txipzig, 1843. 1845: repr. Ilildesheim, 1966) 1.4: 67n12 I~ypriri~na pliriirt~z~w~n d.B. (hlditcin (196;)

5.5: 1621125 162nzt .7.23-26: . Trtnil~~blox ed. F E. Rohhins (Ca~i~lxidpr, JIac\.. and London. 1930) r.rg.+T-42: 421122 SCHO1,IA I T . i R . i T C \ i

YETER.4

ed. J . Jlartin (Stutt~art.ry;q)

98.7-8: 46n9 304.3-j: j r n j 30j.9-306. j: j I n j 320.13-15: 1 1711;; 321.4-6: 1171177 410.8-13: 10jnz4 411.6-10: 1ojn24 411.8: Ioinz4 419.6-4ro.z: roInII SENECA

Epistulile v/o~.~li~.r 88.2 j-28: 61119 88.26: 1ojnz6 88.28: 6nzr Aiztlila1e.s quurstiones 1.2.3: 1o;njI 1.6.j: Iornrr, 162n2j 4B.11.3: 84n:j SESTLTSEMPIRICUS

,4n'i'e?~u.s ?~~itthel.ltittiro.s j.3 j: 4x122 5.75: IIOIl43 7.188: 162n26 7.438: 1621126 Pyi-,-hovpni/>1/poti~p6sris 1.119: 13jn2 7 r.181: 1y;ny 2.90:

39118

2.97: 39118 2.1jX: 661110 SIMPLICICS

111"fU.Ytotc/i~ lie ~ i l t / O ed. J . L.Iieiherg, C4G 7 (Berlin, 1804) 32.29-32: 1g8nro 284.21-24: zjn21, 261129 285.26-2;: 291145 28j.j~-286.2:28njy 286.6-10: 261131 286.10-23: 271134 286.23-2;: z yn+j 488.3-2 j: 203n3; In ,-l~~i.rtoteli.s phy.siixi ed. H . Diels. C4G c)-~~(Kerlin, 1882,189j) 2gr.r1-292.21 (= Posid. Fr8EK): 193-204

STOICORUSI VETERULI F R A G \ I E h T A

(SVT)

2

3 8 / Index Loromm

E.~pos~tio wi-anr mirthen1ntica7~zm ed. E. Hiller (Leipzig, 1878) j-16: 122ny9 3 pp. 198-200: 12611113 2.111

THE\IiTTIUS

117 Aiictotelis plqsiciz ed. H . Schenkl, U G j.2 (Berlin, 1900) 130.13-17 (SbF 2.jj3): 27n34 THEODOSIUS De linbitntio~ziPz~.s ed. R. Fecht (Gottingen, 192;) prop. 2 (16.8-33): +p

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Integrated Coinposition S>-steins

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