Greek Science After Aristotle

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Greek Science After Aristotle

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ANCIENT CULTURE AND SOCIETY General Editor M. I. FINLEY Professor of Ancimt History in the University of Cambridge

A. W. H. ADKINS Moral Values and Political Behaviour in Ancient Greece H. C. BALDRY The Greek Tragic Theatre P. A. BRUNT Social Conflicts in the Roman Republic M. I. FINLEY Early Greece: the Bronze and Archaic Ages Y. CARLAN War in the Ancient World: A Social History A.H. M.JONES Augustus G. E. R. LLOYD Early Greek Science: Thales to Aristotle G. E. R. LLOYD Greek Science After Aristotle C. MOSS£ The Ancient World at Work R. M. OGILVIE The Romans and Their Gods F. H . SANDBACH The Comic Theatre of Greece and Rome F. H. SANDBACH The Stoics B. H. WARMINGTON Nero: Reality a nd Legend

GREEK SCIENCE AFTER ARISTOTLE G.E.R.LLOYD Senior T utor of King's College, Cambridge


Copyright © 1973 by G. E. R. Lloyd. Printed in the United States of America. Library_of Congress Cataloging in Publication Data Lloyd, Geoffrey Ernest Richard. Greek science after Aristotle. ( Ancient culture and society) Bibliography: p. 1. Science- History-Greece. 2. TechnologyHistory-Greece. I. Title. Ql27.G7L58 509'.38 72- 11959 ISBN ISBN

O 393 O 393

04371 00780


4 5 6 7 8 90

CONTENTS Figures Note on Pronunciation and Acknowledgements Chronological Table Preface Map Chapter

Vl Vlll

lX Xlll


Hellenistic Science: the Social Background Chapter 2 The Lyceum after Aristotle Chapter 3 Epicureans and Stoics Chapter 4 Hellenistic Mathematics Chapter 5 Hellenistic Astronomy Chapter 6 Hellenistic Biology and Medicine Chapter 7 Applied Mechanics and Technology Chapter 8 Ptolemy Chapter 9 Galen Chapter 10 The Decline of Ancient Science Select Bibliography






8 21

33 53 75 91 113

136 1 54


FIGURES An application of the method of exhaustion

40 43

of the earth Conic sections Epicyclic motion Eccentric motion T he equivalence of eccentric and epicyclic motion The inequalities of the seasons explained by the eccentric hypothesis The retrogradation of the planets explained by the epicyclic hypothesis Simple dioptra H ero's dioptra T he precession of the equinoxes An ellipse as a special case of epicyclic motion Ballista Archimedean screw T win screw press Ctesibius' fire engine Constant-head water-clock Libations at an altar Temple doors opened automatically Hero's ball rotated by steam Water-mill Pompeian mill Treadmill to work a crane Chords in a circle Armillary astrolabe Ptolemy's model to explain the moon 's second anomaly The doctrine of 'direction'

50 51 62 62 64

2 Archimedes, On the Sphere and Cylinder I 42-43 3 Eratosthenes' determination of the circumference 4 5 6 7 8 9 IO

II 12

13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 Vl

64 66 68 68 70 74 98 100 IOI

102 102 103 104 105 107 mg I IO


120 12 I 122

FIGURES Ptolemy's model for the planets other than Mercury 30 Ptolemy's model for Mercury 3 1 The relationship between the planets and the sun in Ptolemy 32 Ptolemy's elementary principles of reflection 33 Ptolemy's investigation of refraction 34 Blood flow in the heart according to Galen 29

123 124 126 132 134 148


Note on Pronunciation In Greek the letter e is always a sign of a new syllable, unlike the e in bone. It is either short, as in met, or long, in which case it is pro-

nounced as the ein the French tete. In the Greek words mentioned in this book the vowel is short unless otherwise marked.

ACKNOWLEDGEMENTS THE author and publishers are grateful to the Clarendon Press, Oxford for permission to reproduce five illustrations from A History of Technology volumes 2 and 3 (Figs. 15, 18, 20, 24 and 26); two illustrations from Grain-Mills and Flour in Classical Antiquity by L. A. Moritz (Figs. 22 and 23); one illustration from Greek and Roman Artillery, Historical Development by E.W. Marsden (Fig. 14). Also to Harvard University Press for permission to reproduce one illustration from A Source Book in Greek Science by M . R. Cohen and I. E. Drabkin (Fig. 17) and Munksgaard for one illustration from The Mechanical Technology of Greek and Roman Antiquity by A. G. Drachmann (Fig. 16). Figs. 11, 19 and 21 are reproduced from Heronis Alexandrini, Opera I and III edited by W. Schmidt and H. Schone, (Leipzig 1899, 1903). The remaining diagrams and the map have been drawn by F. Rodney Fraser.


CHRONOLOGICAL· TABLE Only the most important scientists down to Galen are listed (the dates of later scientists are noted when their work is discussed in Chapter IO). The precise dates of birth and death of ancient scientists are not often known: where they are, they are given in brackets. Otherwise the date opposite a scientist's name is intended merely as a rough guide to the period when he may be presumed to have done his chief work.


Contemporary events B.C.

Aristotle of Stagira (384-322) Theophrastus of Eresus (371- 286) Praxagoras of Cos Euclid Epicurus of Athens (341-270) Zeno of Citium (335263) Strato of Lampsacus

3 23

Death of Alexander


Ptolemy I Soter king of Egypt


Ptolemy II Philadelphus joint ruler


Hiero II king of Syracuse


Ptolemy III Euergetes succeeds

300 300


Cleanthes of Assus (331-232) Aristarchus of Samos Ctesibius of Alexandria Herophilus of Chalcedon

2 75 270

Erasistratus of Ceos







Archimedes of Syracuse

Contemporary events


Chrysippus of Soli (280-207) Eratosthenes of Cyrene 225

Apollonius of Perga Philo of Byzantium

210 200

Seleucus of Seleucia


221 216 212

168 Battle of Pydna 146 Rome destroys 145

Hipparchus of Nicaea


Ptolemy IV Philopator succeeds Battle of Cannae Romans take Syracuse

Carthage, and Corinth Ptolemy VIII Euergetes II Physcon

133 Kingdom of Pergamum bequeathed to Rome

Posidonius of Apamea Lucretius

80 60



Strabo of Amasia


Celsus Hero of Alexandria

40 60

Menelaus of Alexandria


Rufus of Ephesus

86 Sulla sacks Athens

48 Bellum Alexandrinum 31 Battle of Actium A.O.

14-37 Tiberius emperor 69-79 Vespasian emperor 98-117 Trajan emperor

100 I


I7-138 Hadrian emperor

CHRONOLOGICAL TABLE Scientists Soranus of Ephesus

Contemporary events A.O.


Ptolemy of Alexandria


Galen of Pergamum



Antoninus Pius emperor


Marcus Aurelius emperor


PREFACE THIS book is a continuation of my Early Greek Science: Thales to Aristotle. Several of the preliminary points that I emphasized in that study must be repeated at the outset. First, science is a modern category, not an ancient one. There is no one term, in Greek or Latin, that is exactly equivalent to our 'science'. The terms in which the ancients themselves describe what we should call their scientific work include, for example, peri physeos historiii (inquiry concerning nature), philosophiii (love of wisdom, philosophy), theoriii (speculation) and epistlme (knowledge), and different ancient authors have quite different conceptions of the nature, aims and methods of the inquiry they were undertaking. Thus a good deal of what we know as early Greek science is embedded in philosophy, and this remains' true, though to a lesser degree, of the period after Aristotle. 'Physics' is treated as one of the three branches of philosophy by the Hellenisticl philosophers, the other two being 'logic' and 'ethics', and the commonest justification offered for the inquiry concerning nature is a philosophical one, that it contributes to wisdom. On the other hand some other writers, including mathematicians and doctors especially, either ignore philosophy or explicitly dissociate themselves from the philosophers. As in my earlier study, we shall be concerned both with the theories, problems and methods of the particular branches of science that engaged the attention of the ancient authors, and with their ideas on the nature of the scientific inquiry itself. The source material available to us, both literary and-in the case of applied science and technology-archaeological, is much richer than for the period down to Aristotle. There are, to be sure, large gaps in our evidence, especially concerning some of the Hellenistic biologists and astronomers. Nevertheless we have a considerable body of texts on which to base our 1 The term Hellenistic is used conventionally to refer to the period that runs roughly from the death of Alexander the Great (323 B.c.) to the end of the Ptolemaic dynasty and the Roman annexation of Egypt (30 B.c.).


PREFACE study, including a substantial proportion of the work of such men as Euclid, Archimedes, Ptolemy and Galen, as well as many lesser figures. Our treatment of this material must necessarily be highly selective in a work of this scope. Only a minute proportion of the specific problems and theories of the ancient writers can be mentioned. We shall devote more attention, proportionately, to the evidence that bears on their views on the nature of the inquiries on which they were engaged. The differing and competing views of the scientific investigation itself, and the interrelations of science and philosophy, science and religion, and science and technology, provide the central themes of our discussion and it is with these general and fundamental topics chiefly in mind that I have selected the material we shall consider. In the first six chapters we shall be concentrating on the H ellenistic period, more specifically on the work done in the 200 years following the death of Aristotle (322 B.c.). The discussion of the relations between science and technology will, however, involve considering later evidence as well. Two scientists of the second century A.D., Ptolemy and Galen, are important enough to merit attention in separate chapters. A final chapter is devoted to a brief consideration of some later writers and to discussing some of the difficulties r aised by the question of the decline of ancient science.




My thanks are due to friends and colleagues from various disciplines who h ave been most generous with their help and advice. Dr J. G. La ndels, Dr V . A. Nutton, Dr R. Sibson a nd Mr K . D . White have read a nd commented on particular chapters. I have learnt much on medical matters from my father, Dr W. E. Lloyd. Both Professor M . I. Finley and M r A. C. Reynell have read the whole book in draft and b een responsible for many improvements in style -and in content. To Professor Finley, who has once again advised me at each stage in the writing of the book, I owe a special d ebt of gratitude. It is a pleasure to express my deep appreciation for their help . G.E.R.L. XlV






I.Srene BC (summer) > DA (winter) > CD (autumn). Given estimates of the length of the seasons obtained by observation, the position of the earth (E) can be calculated. Hipparchus' figures have been recorded by Ptolemy (Almagest III ch 4). Taking slightly different estimates of the lengths of the seasons from those of Callippus (spring 94½ days, summer 92½) he calculated EO, the distance of the earth from the centre of the circle round which the sun moves, as 'very nearly 2\ of the radius of the circle', and he estimated the arc XB at about 24° 30'. A simple eccentric system provided a neat account of the inequality of the seasons and at the same time explained minor variations in the apparent distance of the sun. But the movements of the moon and the planets are much more complex. The main problem, so far as thtS R,@U!;tWU:~£9.DGe.rn