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Greek Science of the Hellenistic Era Page i GREEK SCIENCE OF THE HELLENISTIC ERA We all want to understand the world around us, and the ancient Greeks were the first to try to do so in a way we can properly call scientific. Their thought and writings laid the essential foundations for the revivals of science in medieval Baghdad and renaissance Europe. Now their work is accessible to all, with this invaluable introduction to almost a hundred scientific authors active from 320 BCE to 230 CE. The book begins with an outline of a new socio­political model for the development and decline of Greek science. Eleven chapters of fully translated source material follow, with the disciplines covered ranging from the science which the Greeks saw as fundamental—mathematics—through astronomy, astrology and geography, mechanics, optics and pneumatics, and then on to the non­mathematical sciences of alchemy, biology, medicine, and “psychology.” Each chapter contains an accessible introduction on the origins and development of the topic in question, and all the authors are set in context with brief biographies. No other one­volume survey is as up to date, has such broad yet detailed coverage, or offers as many primary sources—several of which are not available elsewhere. With clear, accurate translations, and numerous illustrations, this is an essential resource for students of the history of science in general, and ancient science in particular. Georgia L.Irby­Massie studied mathematics and classics at the University of Georgia, and took her PhD in classics at the University of Colorado. Her publications include works on ancient religion, Roman epigraphy, and ancient science. She currently teaches classics at Louisiana State University. Paul T.Keyser studied physics and classics at St. Andrew’s School, Duke, and Boulder. He did further study at the Center for Hellenic Studies, and has also taught classics. His publications include work on gravitational physics, and on ancient science. He is currently crafting Java for IBM’s Watson Research Center. Page ii This page intentionally left blank. Page iii GREEK SCIENCE OF THE HELLENISTIC ERA A Sourcebook Georgia L.Irby­Massie and Paul T.Keyser London and New York Page iv First published 2002 by Routledge 11 New Fetter Lane, London EC4P 4EE Simultaneously published in the USA and Canada by Routledge 29 West 35th Street, New York, NY 10001 Routledge is an imprint of the Taylor & Francis Group This edition published in the Taylor & Francis e­Library, 2003. Selection and editorial matter © 2002 Georgia L.Irby­Massie and Paul T. Keyser. Individual contributions © 2002 the original copyright holders. All rights reserved. No part of this book may be reprinted or reproduced or utilised in any form or by any electronic, mechanical, or other means, now known or hereafter invented, including photocopying and recording, or in any information storage or retrieval system, without permission in writing from the publishers. British Library Cataloguing in Publication Data A catalogue record for this book is available from the British Library Library of Congress Cataloging­in­Publication Data Irby­Massie, Georgia L. (Georgia Lynette), 1965– Greek Science of the Hellenistic Era: a sourcebook/Georgia L.Irby­Massie and Paul T.Keyser. p. cm. Includes bibliographical references and index. 1. Science—Greece—History—To 1500. 2. Science, Ancient. I. Keyser, Paul T. (Paul Turquand), 1957– II. Title. Q127.G7 172 2002 509.38–dc21 2001041999 ISBN 0­203­46986­0 Master e­book ISBN ISBN 0­203­24385­4 (OEB Format) ISBN 0­415­23847­1 (hbk) ISBN 0­415­23848­X (pbk) Page v BRIEF CONTENTS Detailed contents vii Preface xxi Acknowledgments xxiv Figure and maps credits xxix Timeline of authors excerpted xxxi Map 1 Greece and the Aegean region xxxvi Map 2 The Mediterranean region xxxvii 1 Introduction 1 2 Mathematics 18 3 Astronomy 47 4 Astrology 82 5 Geography 113 6 Mechanics 150 7 Optics 180 8 Hydrostatics and Pneumatics 204 9 Alchemy 226 10 Biology: Botany and Zoology 255 11 Medicine 290 12 “Psychology” 331 Page vi Bibliography 360 Sources of translations quoted 360 Texts newly translated 362 Works cited 364 Select further reading 368 Indexes 371 Index of term 371 Index of all metals, plants, stones, animals 375 Index of people (not including extracted authors) 378 Index of places 382 Concordance of passages cited (not excerpted) 385 Page vii CONTENTS Preface xxi Acknowledgments xxiv Figure and maps credits xxix Timeline of authors excerpted xxxi Map 1 Greece and the Aegean region xxxvi Map 2 The Mediterranean region xxxvii 1 Introduction 1 2 Mathematics 18 2.1 Eukleidês 20 Elements 1. Definitions: in plane geometry; Postulates; Common notions; 1.47: “Pythagoras’ Theorem”; 2.11: constructing the proportion used in the Parthenon; 3.16: the infinitesimal “horn­angle” between a circle and a tangent line; 7. Definitions: in number theory; 9.20: prime numbers; 9.35: sum of geometric series; 10. Definitions: commensurable and incommensurable numbers; 10.1: Eudoxos’ approach to the limit bypassing infinitesimals (‘‘exhaustion”); 10.3: greatest common divisor; 12.2: “exhaustion” used to determine circular area; 12.10: Demokritos’ theorem 2.2 Archimedes of Syracuse 27 Area of the Circle Spirals Definitions 1 Sand­Reckoner 3.1–4: expressing large numbers in base­one­hundred­million Method Praeface: quadrature of the parabola 2.3 Eratosthenes of Kurênê 31 Duplication of the Cube: using a mechanical calculator similar to a slide­rule Epigram: on the same subject Page viii 2.4 Apollonios of Pergê 32 Conics 1. Preface; Proposition 8: our “parabola” 2.5 Combinatorics 35 (in Plutarch, Dinner­table Talk 8.9) 2.6 Heron of Alexandria 35 Mensurations 1.8: area of triangle 2.7 Menelaus of Alexandria 36 Spherics 1. Definitions 2.8 Nikomachos of Gerasa 36 Introduction to Arithmetic 1.13: sieve of Eratosthenes; 2.8–10: polygonal numbers 2.9 Ptolemy of Alexandria 39 Syntaxis 1.10.1–10: Trigonometry 2.10 Diophantos of Alexandria 42 Arithmetika 1. Praeface: “Algebra”; 1.28: quadratic equations; 2.8: 2.11 Anatolios of Alexandria 43 On the Decade About the monad; About the heptad; About the decade 3 Astronomy 47 3.1 Autolukos of Pitanê 50 Moving Sphere 6 Risings and Settings 2.2–4 3.2 Klearchos of Cyprian Soloi 53 (title unknown): “Man in the moon” 3.3 Aristarchos of Samos 53 Sizes and Distances Hypotheses: sun and moon; 2 3.4 Chrusippos of Soloi 55 Providence Book 1: the kosmos periodically is consumed by flame and in a way reborn 3.5 Apollonios of Pergê 56 (title unknown): eccentric circular geocentric orbits are equivalent to epicyclic geocentric orbits 3.6 Hegesianax of Alexandria 57 Phainomena: the face in the moon 3.7 Hupsikles of Alexandria 57 Anaphorikos 4.1–4: rising times of zodiac signs 3.8 Hipparchos of Nikaia 59 (various works): length of the year Displacement of the Solsticial and Equinoctial Points: star alignments; precession 3.9 Theodosios of Bithunia 62 Spherics 1. Definitions; 1.11; 1.17; 1.20; 2.1–2; 2.6–7 Page ix 3.10 Poseidonios of Apamea 64 (title unknown) fr. 131b E­K: origin of comets 3.11 Alexander of Ephesos 65 (title unknown): harmony of the spheres 3.12 Anonymous (traditionally ascribed to Aristotle) 67 Kosmos 2 (392a6–31): aither, star material 3.13 Xenarchos of Kilikian Seleukeia 67 Against the Fifth Element 1–8 3.14 Geminus of Rhodes 69 Phainomena 1.13–17: solstices and equinoxes; 5.54–61, 68–69: horizon 3.15 Aristokles of Messênê 71 Philosophy, the Stoic doctrine of universal conflagration 3.16 Apollinarius (of Aizanoi?) 71 (title unknown): length of month 3.17 Plutarch of Chaironeia 72 The Face in the Moon 8 (924d–f): the moon could be “lunar” material in its proper place; 25 (940a–e): life on the moon? 3.18 Theon of Smurna 73 Mathematics 3.33: a quasi­heliocentric theory 3.19 Ptolemy of Alexandria 74 Syntaxis 7.4 On the method used to record the positions of the fixed stars; 7.5; 9.2: planetary theory is much more difficult Planetary Hypotheses 1.1.8: model of the sun; 1.2.2: arrangement of heavenly bodies; 2.3: the stars are divine and self­willed bodies 3.20 Sosigenes the Peripatetic 80 On the Counteracting Spheres: varying distances from us of the planets 4 Astrology 82 4.1 Berôsos of Babylon 84 Babyloniaka Book 1 (fr. 4): the moon 4.2 Aratos of Soloi 85 Phainomena 19–44: stars and constellations: the Bears; 63–70: constellation of Herakles; 254–267: constellation of the Pleiades 4.3 Eratosthenes of Kurênê 87 Constellations 12: Leo; 43–44: Planets, and the ‘‘Milk” 4.4 Petosiris 88 fr. 7: signs from eclipses fr. 10: signs from comets 4.5 Hipparchos of Nikaia 90 Commentary on Aratos’ “Phainomena” 3.5.1–6: rising times of the fixed stars 4.6 Imbrasios of Ephesos 92 Predictions about the Sick 2: lunar effects on illness; 13: moon in Water­Pourer Page x 4.7 Dorotheos of Sidon 93 Judgments from the Stars about Nativities 1.1; 1.1.9–1.2.2: “upliftings” or “exaltations” and “abasements’’ or “humiliations”; 1.6 The power of the seven planets; 1.24: fortune and property, horoscopes 2, 3, and 4 4.8 Geminus of Rhodes 97 Phainomena 17.1–25: arguments against astrology: weather signs 4.9 Balbillos 98 Astrologoumena: concerning the length of life from starter and destroyer 4.10 Thessalos of Tralles 100 Remedies Praeface 27–28; Book 1, chapter: Twins: holy vervain; Book 2, chapter: Kronos: house­leek 4.11 Pitenius 101 [Hermon’s horoscope]: 31 March 81 4.12 Manethon 103 Apotelesmatika 1(2).399–445: sun and moon signs; 2(3).399–428: length of life; 3(6).1–34: children; 3(6).738–750: Manethon’s nativity 4.13 Ptolemy of Alexandria 106 Tetrabiblos 1.1–2: how astrology works; 2.2: “national” characteristics; 3.1: conception and birth as proper moments for a horoscope 4.14 Antigonos of Nikaia 109 [Hadrian’s horoscope: 24 January 76] 4.15 Vettius Valens of Antioch 111 Anthologies 7.6 127–160: common fate of six men in a boat; 7.4 11–15: infant death 5 Geography 113 5.1 Hanno of Carthage 116 Periplous: voyage down the west coast of Africa 5.2 Putheas of Massalia 118 On the Ocean (in Strabo 2.4.1): the island of Thoulê; (in Geminus 6.9): “the sun’s bedroom” 5.3 Straton of Lampsakos 118 On Heaven (fr.
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