Aristarchus of Samos: The Ancient Copernicus

COPERNICUS

ARISTARCHUS

OF SAMOS

THE ANCIENT COPERNICUS

Sir Thomas Heath

DOVER PUBLICATIONS, INC.

Mineola, New York

Bibliographical Note

This Dover edition, first published in 1981 and republished in 2004, is an unabridged republication of the work originally published in 1913 by the Clarendon Press, Oxford, under the title Aristarchus of Samos, the Ancient Copernicus; a History of Greek Astronomy to Aristarchus, Together with Aristarchus’s Treatise on the Sizes and Distances of the Sun and Moon, a Greek Text with Translation and Notes by Sir Thomas Heath. The Dover edition is published by special arrangement with Oxford University Press.

Library of Congress Cataloging-in-Publication Data

Heath, Thomas Little, Sir, 1861–1940.

Aristarchus of Samos, the ancient Copernicus / Sir Thomas Heath.

p. cm.

Originally published: Oxford : Clarendon Press, 1913.

eISBN-13: 978-0-486-15081-9

1. Astronomy, Greek. 2. Astronomers—Greece—Biography. 3. Aristarchus, of Samos. 4. Aristarchus, of Samos. On the sizes and distances of the sun and moon. I. Aristarchus, of Samos. On the sizes and distances of the sun and moon. English & Greek. II. Title.

QB21.H38 2004

520’.92—dc22

2004058241

Manufactured in the United States of America

Dover Publications, Inc., 31 East 2nd Street, Mineola, N.Y. 11501

PREFACE

THIS work owes its inception to a desire expressed to me by my old schoolfellow Professor H. H. Turner for a translation of Aristarchus’s extant work On the sizes and distances of the Sun and Moon. Incidentally Professor Turner asked whether any light could be thrown on the grossly excessive estimate of 2° for the angular diameter of the sun and moon which is one of the fundamental assumptions at the beginning of the book. I remembered that Archimedes distinctly says in his Psammites or Sand-reckoner , which is very near the truth. The difference suggested that the treatise of Aristarchus which we possess was an early work; but it was still necessary to search the history of Greek astronomy for any estimates by older astronomers that might be on record, with a view to tracing, if possible, the origin of the figure of 2°.

Again, our treatise does not contain any suggestion of any but the geocentric view of the universe, whereas Archimedes tells us that Aristarchus wrote a book of hypotheses, one of which was that the sun and the fixed stars remain unmoved and that the earth revolves round the sun in the circumference of a circle. Now Archimedes was a younger contemporary of Aristarchus; he must have seen the book of hypotheses in question, and we could have no better evidence for attributing to Aristarchus the first enunciation of the Copernican hypothesis. The matter might have rested there but for the fact that in recent years (1898) Schiaparelli, an authority always to be mentioned with profound respect, has maintained that it was not after all Aristarchus, but Heraclides of Pontus, who first put forward the heliocentric hypothesis. Schiaparelli, whose two papers Le sfere omocentriche di Eudosso, di Callippo e di Aristotele and I precursori di Copernico nell’ antichità are classics, showed in the latter paper that Heraclides discovered that the planets Venus and Mercury revolve round the sun, like satellites, as well as that the earth rotates about its own axis in about twenty-four hours. In his later paper of 1898 (Origine del sistema planetario eliocentrico presso i Greci) Schiaparelli went further and suggested that Heraclides must have arrived at the same conclusion about the superior planets as about Venus and Mercury, and would therefore hold that all alike revolved round the sun, while the sun with the planets moving in their orbits about it revolved bodily round the earth as centre in a year; in other words, according to Schiaparelli, Heraclides was probably the inventor of the system known as that of Tycho Brahe, or was acquainted with it and adopted it if it was invented by some contemporary and not by himself. So far it may be admitted that Schiaparelli has made out a plausible case; but when, in the same paper, he goes further and credits Heraclides with having originated the Copernican hypothesis also, he takes up much more doubtful ground. At the same time it was clear that his arguments were entitled to the most careful consideration, and this again necessitated research in the earlier history of Greek astronomy with the view of tracing every step in the progress towards the true Copernican theory. The first to substitute another centre for the earth in the celestial system were the Pythagoreans, who made the earth, like the sun, moon, and planets, revolve round the central fire; and, when once my study of the subject had been carried back so far, it seemed to me that the most fitting introduction to Aristarchus would be a sketch of the whole history of Greek astronomy up to his time. As regards the newest claim made by Schiaparelli on behalf of Heraclides of Pontus, I hope I have shown that the case is not made out, and that there is still no reason to doubt the unanimous testimony of antiquity that Aristarchus was the real originator of the Copernican hypothesis.

In the century following Copernicus no doubt was felt as to identifying Aristarchus with the latter hypothesis. Libert Fromond, Professor of Theology at the University of Louvain, who tried to refute it, called his work Anti-Aristarchus (Antwerp, 1631). In 1644 Roberval took up the cudgels for Copernicus in a book the full title of which is Aristarchi Samii de mundi systemate partibus et motibus eiusdem libellus. Adiectae sunt Æ. P. de Roberval, Mathem. Scient, in Collegio Regio Franciae Professoris, notae in eundem libellum. It does not appear that experts were ever deceived by this title, although Baillet (Jugemens des Savans) complained of such disguises and would have had Roberval call his work Aristarchus Gallus, ‘the French Aristarchus,’ after the manner of Vieta’s Apollonius Gallus and Snellius’s Eratosthenes Batavus. But there was every excuse for Roberval. The times were dangerous. Only eleven years before seven Cardinals had forced Galilei to abjure his ‘errors and heresies’; what wonder then that Roberval should take the precaution of publishing his views under another name?

Voltaire, as is well known, went sadly wrong over Aristarchus (Dictionnaire Philosophique, s.v. ‘Système’). He said that Aristarchus ‘is so obscure that Wallis was obliged to annotate him from one end to the other, in the effort to make him intelligible’, and further that it was very doubtful whether the book attributed to Aristarchus was really by him. Voltaire (misled, it is true, by a wrong reading in a passage of Plutarch, De facie in orbe lunae, c. 6) goes on to question whether Aristarchus had ever propounded the heliocentric hypothesis; and it is clear that the treatise which he regarded as suspect was Roberval’s book, and that he confused this with the genuine work edited by Wallis. Nor could he have looked at the latter treatise in any but a very superficial way, or he would have seen that it is not in the least obscure, and that the commentary of Wallis is no more elaborate than would ordinarily be expected of an editor bringing out for the first time, with the aid of MSS. not of the best, a Greek text and translation of a mathematical treatise in which a number of geometrical propositions are assumed without proof and therefore require some elucidation.

There is no doubt whatever of the genuineness of the work. Pappus makes substantial extracts from the beginning of it and quotes the main results. Apart from its astronomical content, it is of the greatest interest for its geometry. Thoroughly classical in form and language, as befits the period between Euclid and Archimedes, it is the first extant specimen of pure geometry used with a trigonometrical object, and in this respect is a sort of forerunner of Archimedes’ Measurement of a Circle. I need therefore make no apology for offering to the public a new Greek text with translation and the necessary notes.

In conclusion I desire to express my best acknowledgements to the authorities of the Vatican Library for their kindness in allowing me to have a photograph of the best MS. of Aristarchus which forms part of the magnificent Codex Vaticanus Graecus 204 of the tenth century, and to Father Hagen of the Vatican Observatory for his assistance in the matter.

T. L. H.

CONTENTS

PART I

GREEK ASTRONOMY TO ARISTARCHUS OF SAMOS

      I.     SOURCES OF THE HISTORY

     II.     HOMER AND HESIOD

    III.     THALES

    IV.     ANAXIMANDER

     V.     ANAXIMENES

    VI.    PYTHAGORAS

   VII.    XENOPHANES

  VIII.    HERACLITUS

    IX.     PARMENIDES

     X.     ANAXAGORAS

    XI.     EMPEDOCLES

   XII.     THE PYTHAGOREANS

  XIII.     THE ATOMISTS, LEUCIPPUS AND DEMOCRITUS

  XIV.    OENOPIDES

   XV.    PLATO

  XVI.    THE THEORY OF CONCENTRIC SPHERES—EUDOXUS, CALLIPPUS, AND ARISTOTLE

 XVII.   ARISTOTLE

XVIII.   HERACLIDES OF PONTUS

  XIX.   GREEK MONTHS, YEARS, AND CYCLES

PART II

ARISTARCHUS ON THE SIZES AND DISTANCES OF THE SUN AND MOON

      I.     ARISTARCHUS OF SAMOS

     II.    THE TREATISE ON SIZES AND DISTANCES—HISTORY OF THE TEXT AND EDITIONS

    III.    CONTENT OF THE TREATISE

    IV.     LATER IMPROVEMENTS ON ARISTARCHUS’S CALCULATIONS

GREEK TEXT, TRANSLATION, AND NOTES

INDEX

CORRIGENDUM

, is the correct reading in Timaeus in the sense of retrogradations; on the contrary, a ‘forward movement’ and a ‘returning of the circle upon itself’ are quite natural expressions for the different stages of one simple circular motion. Cf. also Republic is used of the ‘counter-revolution’ of the planet Mars; what is meant is a simple circular revolution in a sense contrary to that of the fixed stars, and there is no suggestion of retrogradations.

ARISTARCHUS

OF SAMOS

THE ANCIENT COPERNICUS

PART I

GREEK ASTRONOMY TO ARISTARCHUS OF SAMOS

I

SOURCES OF THE HISTORY

THE history of Greek astronomy in its beginnings is part of the history of Greek philosophy, for it was the first philosophers, Ionian, Eleatic, Pythagorean, who were the first astronomers. Now only very few of the works of the great original thinkers of Greece have survived. We possess the whole of Plato and, say, half of Aristotle, namely, those of his writings which were intended for the use of his school, but not those which, mainly composed in the form of dialogues, were in a more popular style. But the whole of the pre-Socratic philosophy is one single expanse of ruins;¹ so is the Socratic philosophy itself, except for what we can learn of it from Plato and Xenophon.

But accounts of the life and doctrine of philosophers begin to appear quite early in ancient Greek literature (cf. Xenophon, who was born between 430 and 425 B.C.); and very valuable are the allusions in Plato and Aristotle to the doctrines of earlier philosophers; those in Plato are not very numerous, but he had the power of entering into the thoughts of other men and, in stating the views of early philosophers, he does not, as a rule, read into their words meanings which they do not convey. Aristotle, on the other hand, while making historical surveys of the doctrines of his predecessors a regular preliminary to the statement of his own, discusses them too much from the point of view of his own system; often even misrepresenting them for the purpose of making a controversial point or finding support for some particular thesis.

From Aristotle’s time a whole literature on the subject of the older philosophy sprang up, partly critical, partly historical. This again has perished except for a large number of fragments. Most important for our purpose are the notices in the Doxographi Graeci, collected and edited by Diels.² The main source from which these retailers of the opinions of philosophers drew, directly or indirectly, was the great work of Theophrastus, the successor of Aristotle, entitled Physical Opinions of the philosophers was Sotion (towards the end of the third century B.C.); others who wrote ‘successions’ were a certain Antisthenes (probably Antisthenes of Rhodes, second century B.C.), Sosicrates, and Alexander Polyhistor. These works gave little in the way ol doxography, but were made readable by the incorporation of anecdotes and apophthegms, mostly unauthentic. The work of Sotion and the ‘Lives of Famous Men’ by Satyrus (about 160 B.C.) were epitomized by Heraclides Lembus. Another writer of biographies was the Peripatetic Hermippus of Smyrna, known as the Callimachean, who wrote about Pythagoras in at least two Books, and is quoted by Josephus as a careful student of all history.³ Our chief storehouse of biographical details derived from these and all other available sources is the great compilation which goes by the name of Diogenes Laertius (more properly Laertius Diogenes). It is a compilation made in the most haphazard way, without the exercise of any historical sense or critical faculty. But its value for us is enormous because the compiler had access to the whole collection of biographies which accumulated from Sotion’s time to the first third of the third century A. D. (when Diogenes wrote), and consequently we have in him the whole residuum of this literature which reached such dimensions in the period.

In order to show at a glance the conclusions of Diels as to the relation of the various representatives of the doxographic and biographic traditions to one another and to the original sources I append a genealogical table⁴:

Fig. 1

Only a few remarks need be added, ‘Vetusta Placita’ is the name given by Diels to a collection which has disappeared, but may be inferred to have existed. It adhered very closely to Theophrastus, though it was not quite free from admixture of other elements. It was probably divided into the following main sections: I. De principiis; IL De mundo; III. De sublimibus; IV. De terrestribus; V. De anima; VI. De corpore. The date is inferred from the facts that the latest philosophers mentioned in it were Posidonius and Asclepiades, and that Varro used it. The existence of the collection of Aëtius (De placitis) is attested by Theodoretus (Bishop of Cyrus), who mentions it as accessible, and who certainly used it, since his extracts are more complete and trustworthy than those of the Placita Philosophorum and Stobaeus. The compiler of the Placita was not Plutarch, but an insignificant writer of about the middle of the second century A.D., who palmed them off as Plutarch. Diels prints the Placita in parallel columns with the corresponding parts of the Eclogae, under the title of Aëtii Placita; quotations from the other writers who give extracts are added in notes at the foot of the page. So far as Cicero deals with the earliest Greek philosophy, he must be classed with the doxographers; both he and Philodemus (De pietate, fragments of which were discovered on a roll at Herculaneum) seem alike to have used a common source which went back to a Stoic epitome of Theophrastus, now lost.

given by Eusebius in Book I. 8 of the Praeparatio Evangelica comes from an epitome of Theophrastus, arranged according to philosophers. The author of the Stromateis, who probably belonged to the same period as the author of the Placita, that is, about the middle of the second century A.D., confined himself mostly to the sections de principio, de mundo, de astris; hence some things are here better preserved than elsewhere; cf. especially the notice about Anaximander.

The most important of the biographical doxographies is that of Hippolytus in Book I of the Refutation of all Heresies type, shorter and even more untrustworthy than Diogenes Laertius, but containing excerpts from Aristoxenus, Sotion, Heraclides Lembus, and Apollodorus. The other was an epitome of Theophrastus. Hippolytus’s plan was to take the philosophers in order and then to pick out from the successive sections of the epitome of Theophrastus the views of each philosopher on each topic, and insert them in their order under the particular philosopher. So carefully was this done that the divisions of the work of Theophrastus can practically be restored.⁵ Hippolytus began with the idea of dealing with the chief philosophers only, as Thales, Pythagoras, Empedocles, Heraclitus. For these he had available only the inferior (biographical) source. The second source, the epitome of Theophrastus, then came into his hands, and, beginning with Anaximander, he proceeded to make a most precious collection of opinions.

Another of our authorities is Achilles (not Tatius), who wrote an Introduction to the Phaenomena of Aratus.⁶ Achilles’ date is uncertain, but he probably lived not earlier than the end of the second century A.D., and not much later. The foundation of Achilles’ commentary was a Stoic compendium of astronomy, probably by Eudorus, which in its turn was extracted from a work by Diodorus of Alexandria, a pupil of Posidonius. But Achilles drew from other sources as well, including the Pseudo-Plutarchian Placita; he did not hesitate to alter his extracts from the latter, and to mix alien matter with them.

The opinions noted by the Doxographi are largely incorporated in Diels’ later work Die Fragmente der Vorsokratiker.⁷

For the earlier period from Thales to Empedocles, Tannery gives a translation of the doxographic data and the fragments in his work Pour l’histoire de la science hellène, de Thalès à Empédocle, Paris, 1887; taking account as it does of all the material, this work is the best and most suggestive of the modern studies of the astronomy of the period. Equally based on the Doxographi, Max Sartorius’s dissertation Die Entwicklung der Astronomie bei den Griechen bis Anaxagoras und Empedokles (Halle, 1883) is a very concise and useful account. Naturally all or nearly all the material is also to be found in the monumental work of Zeller and in Professor Burnet’s Early Greek Philosophy (second edition, 1908); and picturesque, if sometimes too highly coloured, references to the astronomy of the ancient philosophers are a feature of vol. i of Gomperz’s Griechische Denker (third edition, 1911).

Eudemus of Rhodes (about 330 B.C.), a pupil of Aristotle, wrote a History of Astronomy (as he did a History of Geometry), which, is lost, but was the source of a number of notices in other writers. In particular, the very valuable account of Eudoxus’s and Callippus’s systems of concentric spheres which Simplicius gives in his Commentary on Aristotle’s De caelo is taken from Eudemus through Sosigenes as intermediary. A few notices from Eudemus’s work are also found in the astronomical portion of Theon of Smyrna’s Expositio rerum mathematicarum ad legendum Platonem utilium,⁸ which also draws on two other sources, Dercyllides and Adrastus. The former was a Platonist with Pythagorean leanings, who wrote a book on Plato’s philosophy. His date was earlier than the time of Tiberius, perhaps earlier than Varro’s. Adrastus, a Peripatetic of about the middle of the second century A.D., wrote historical and lexicographical essays on Aristotle; he also wrote a commentary on the Timaeus of Plato, which is quoted by Proclus as well as by Theon of Smyrna.

¹ Gomperz, Griechische Denker, i³, p. 419.

² Doxographi Graeci, ed. Diels, Berlin, G. Reimer, 1879.

³ Doxographi Graeci (henceforth generally quoted as D. G.), p. 151.

⁴ Cf. Günther in Windelband, Gesch. der alten Philosophie (Iwan von Müller’s Handbuch der klassischen Altertumswissenschaft, Band v. 1), 1894, p. 275.

⁵ Diels, Doxographi Graeci, p. 153.

⁶ Excerpts from this are preserved in Cod. Laurentian. xxviii. 44, and are included in the Uranologium of Petavius, 1630, pp. 121–64, &c.

⁷ Second edition in two vols, (the second in two parts), Berlin, 1906–10.

⁸ Edited by E. Hiller (Teubner, 1878).

II

HOMER AND HESIOD

; from this all other waters take their rise, that is, the waters of Oceanus pass through subterranean channels and appear as the springs and sources of other rivers. Over the flat earth is the vault of heaven, like a sort of hemispherical dome exactly covering it; hence it is that the Aethiopians dwelling in the extreme east and west are burnt black by the sun. Below the earth is Tartarus, covered by the earth and forming a sort of vault symmetrical with the heaven; Hades is supposed to be beneath the surface of the earth, as far from the height of the heaven above as from the depth of Tartarus below, i.e. presumably in the hollow of the earth’s disc. The dimensions of the heaven and earth are only indirectly indicated; Hephaestus cast down from Olympus falls for a whole day till sundown; on the other hand, according to Hesiod, an iron anvil would take nine days to pass from the heaven to the earth, and again nine days from the earth to Tartarus. The vault of heaven remains for ever in one position, unmoved; the sun, moon, and stars move round under it, rising from Oceanus in the east and plunging into it again in the west. We are not told what happens to the heavenly bodies between their setting and rising; they cannot pass round under the earth because Tartarus is never lit up by the sun; possibly they are supposed to float round Oceanus, past the north, to the points where they next rise in the east, but it is only later writers who represent Helios as sleeping and being carried round on the water on a golden bed or in a golden bowl.¹

Coming now to the indications of actual knowledge of astronomical facts to be found in the poems, we observe in Hesiod a considerable advance as compared with Homer. Homer mentions, in addition to the sun and moon, the Morning Star, the Evening Star, the Pleiades, the Hyades, Orion, the Great Bear (’ which is also called by the name of the Wain, and which turns round on the same spot and watches Orion; it alone is without lot in Oceanus’s bath ‘²), Sirius (’the star which rises in late summer . . . which is called among men Orion’s dog; bright it shines forth, yet is a baleful sign, for it brings to suffering mortals much fiery heat’), the ‘late-setting Bootes’ (the ‘ploughman’ driving the Wain, i.e. Arcturus, as Hesiod was the first to call it). Since the Great Bear is said to be the only of the sun’, is supposed by some to refer to the solstices, but there is no confirmation of this by any other passage, and it seems safer to take ‘turning’ to mean the turn which the sun takes at setting, when of course he begins his return journey (travelling round Oceanus or otherwise) to the place of his rising, in which case the island would simply be situated on the western horizon where the sun sets.⁴

Hesiod mentions practically the same stars as Homer, the Pleiades, the Hyades, Orion, Sirius, and Arcturus. But, as might be expected, he makes much more use than Homer does of celestial phenomena for the purpose of determining times and seasons in the year. Thus, e. g., he marked the time for sowing at the beginning of winter by the setting of the Pleiades in the early twilight, or again by the early setting of the Hyades or Orion, which means the 3rd, 7th, or 15th November in the Julian calendar according to the particular stars taken;, he makes, in like manner, end 50 days after the summer solstice. Thus he was acquainted with the solstices, but he says nothing about the equinoxes, and only remarks in one place that in late summer the days become shorter and the nights longer. From the last part of the Works and Days we see that Hesiod had an approximate notion of the moon’s period; he puts it at 30 days, and divides the month into three periods of ten days each.⁸

Hesiod was also credited with having written a poem under the title of ‘Astronomy’. A few fragments of such a poem are preserved;⁹ Athenaeus, however, doubted whether it was Hesiod’s work, for he quotes ‘the author of the poem Astronomy which is attributed to Hesiod’ as always speaking of Peleiades. Pliny observes that ‘Hesiod (for an Astrology is also handed down under his name) stated that the matutinal setting of the Vergiliae [Pleiades] took place at the autumnal equinox, whereas Thales made the time 25 days from the equinox’.¹⁰ The poem was thought to be Alexandrine, but has recently been shown to be old; perhaps, if we may judge by the passage of Pliny, it may be anterior to Thales.

¹ Athenaeus, Deipnosoph. xi. 38–9.

² It seems that some of the seven principal stars of the Great Bear do now set in the Mediterranean, e.g., in places further south in latitude than Rhodes (lat. 36°), γ, the hind foot, as well as η, the tip of the tail, and at Alexandria all the seven stars except α, the head. But this was not so in Homer’s time. In proof of this, Sir George Greenhill (in a lecture delivered in 1910 to the Hellenic Travellers’ Club) refers to calculations made by Dr. J. B. Pearson of the effect of Precession in the interval since 750 B.C., a date taken ‘without prejudice’ (Proceedings of the Cambridge Philosophical Society, 1877 and 1881), and to the results obtained in a paper by J. Gallenmüller, Der Fixsternhimmel jetzt und in Homers Zeiten mit zwei Sternkarten (Regensburg, 1884/85). Gallenmüller’s charts are for the years 900 B.C. and A.D. 1855 respectively, and the chart for 900 B.C. shows that the N. P. D. of both β, the fore-foot, and η, the tip of the tail, was then about 25°. But we also find convincing evidence in the original writings of the Greek astronomers. Hipparchus (In Arati et Eudoxi phaenomena commentariorum libri 1res, ed. Manitius, 1894, p. 114. 9–10) observes that Eudoxus [say, in 380 B.C., or 520 years later than the date to which Gallen müller’s chart refers] made the fore-foot (β) about 24°, and the hind-foot (β) about 25°, distant from the north pole. This was perhaps not very accurate; for Hipparchus says (ibid., p. 30.2–8), ‘As regards the north pole, Eudoxus is in error in stating that there is a certain star which always remains in the same spot, and this star is the pole of the universe; for in reality there is no star at all at the pole, but there is an empty space there, with, however, three stars near to it [probably α and κ of Draco and β of the Little Bear], and the point at the pole makes with these three stars a figure which is very nearly square, as Pytheas of Massalia stated.’ (Pytheas, the great explorer of the northern seas, was a contemporary of Aristotle, and perhaps some forty years later than Eudoxus.) But, as Hipparchus himself (writing in this case not later than 134 B.C.) makes the angular radius of the ‘always-visible circle’ 37° at Athens and 36° at Rhodes (ibid., pp. 112. 16 and 114. 24–6), it is evident that in Eudoxus’s time the whole of the Great Bear remained well above the horizon. A passage of Proclus (Hypotyposisthe horizon but should partly set’ ! This passage, written (say) 840 years after Eudoxus’s location of β and γ of the Great Bear, shows that the Great Bear was then much nearer to setting than it was in Eudoxus’s time, and the fact should have made Proclus speak with greater caution. [The star which Eudoxus took as marking the north pole has commonly been supposed to be β of the Little Bear; but Manitius (Hipparchi in Arati et Eicdoxi phaen, comment., 1894, p. 306), as the result of studying a ‘Precession-globe’ designed by Prof. Haas of Vienna, considers that it was certainly a different star, namely, ‘Draconis 16,’ which occupies a position determined as the intersection of (1) a perpendicular from our Polar Star to the straight line joining κ and λ of Draco and (2) the line joining γ and β of the Little Bear and produced beyond β.]

³ Odyssey xv. 403–4.

⁴ Martin has discussed the question at considerable length (’ Comment Homère s’orientait’ in Mémoires de l’Académie des Inscriptions et Belles-Lettrescan only mean the solstice, that by this we must also understand the summer has never, ‘This is where the settings commence’, which Martin interprets as meaning ‘where the sun sets at the commencement of the Greek year’, which was about the time of the summer solstice; but this is a great deal to get out of ‘commencement of setting’.

⁵ Ideler, Handbuch der mathematischen und technischen Chroniologie, 1825, i, pp. 242, 246.

⁶ Ibid. p. 242.

⁷ Ibid. pp. 246, 247.

⁸ Sartorius, op. cit., p. 16; Ideler, i, p. 257.

⁹ Diels, Vorsokratiker, ii². 1, 1907, pp. 499, 500.

¹⁰ Pliny, N. H. xviii, c. 25, § 213; Diels, loc. cit.

III

THALES

SUCH astronomy as we find in Homer and Hesiod was of the merely practical kind, which uses the celestial recurrences for the regulation of daily life; but, as the author of the Epinomis says, ‘the true astronomer will not be the man who cultivates astronomy in the manner of Hesiod and any other writers of that type, concerning himself only with such things as settings and risings, but the man who will investigate the seven revolutions included in the eight revolutions and each describing the same circular orbit [i. e. the separate motions of the sun, moon, and the five planets combined with the eighth motion, that of the sphere of the fixed stars, or the daily rotation], which speculations can never be easily mastered by the ordinary person but demand extraordinary powers’. The history of Greek astronomy in the sense of astronomy proper, the astronomy which seeks to explain the heavenly phenomena and their causes, begins with Thales.

Thales of Miletus lived probably from about 624 to 547 B.C. (though according to Apollodorus he was born in 640/39). According to Herodotus, his ancestry was Phoenician; his mother was Greek, to judge by her name Cleobuline, while his father’s name, Examyes, is Carian, so that he was of mixed descent. In 582/1 B.C. he was declared one of the Seven Wise Men, and indeed his versatility was extraordinary; statesman, engineer, mathematician and astronomer, he was an acute business man in addition, if we may believe the story that, wishing to show that it was easy to get rich, he took the opportunity of a year in which he foresaw that there would be a great crop of olives to get control of all the oil-presses in Miletus and Chios in advance, paying a low rental when there was no one to bid against him, and then, when the accommodation was urgently wanted, charging as much as he liked for it, with the result that he made a large profit.¹ For his many-sided culture he was indebted in great measure to what he learnt on long journeys which he took, to Egypt in particular; it was in Egypt that he saw in operation the elementary methods of solving problems in practical geometry which inspired him with the idea of making geometry a deductive science depending on general propositions; and he doubtless assimilated much of the astronomical knowledge which had been accumulated there as the result of observations recorded through long centuries.

Thales’ claim to a place in the history of scientific astronomy depends almost entirely on one achievement attributed to him, that of predicting an eclipse of the sun. There is no trustworthy evidence of any other discoveries, or even of any observations, made by him, although one would like to believe the story, quoted by Plato,² that, when he was star-gazing and fell into a well in consequence, he was rallied ‘by a clever and pretty maid-servant from Thrace’³ for being so ‘eager to know what goes on in the heavens when he could not see what was in front of him, nay, at his very feet’.

But did Thales predict a solar eclipse? The story is entirely rejected by Martin.⁴ He points out that, while the references to the prediction do not exactly agree, it is in fact necessary, if the occurrence of a solar eclipse at any specified place on the earth’s surface is to be predicted with any prospect of success, to know more of the elements of astronomy than Thales could have known, and in particular to allow for parallax, which was not done until much later, and then only approximately, by Hipparchus. Further, if the prophecy had rested on any scientific basis, it is incredible that the basis should not have been known and been used by later Ionian philosophers for making other similar predictions, whereas we hear of none such in Greece for two hundred years. Indeed, only one other supposed prediction of the same kind is referred to. Plutarch⁵ relates that, when Plato was on a visit to Sicily and staying with Dionysius, Helicon of Cyzicus, a friend of Plato’s, foretold a solar eclipse (apparently that which took place on 12th May, 361 B.C.),⁶ and, when this took place as predicted, the tyrant was filled with admiration and made Helicon a present of a talent of silver. This story is, however, not confirmed by any other evidence, and the necessary calculations would have been scarcely less impossible for Helicon than for Thaïes. Martin’s view is that both Thales and Helicon merely explained the cause of solar eclipses and asserted the necessity of their recurrence within certain limits of time, and that these explanations were turned by tradition into predictions. In regard to Thaïes, Martin relies largely on the wording of a passage in Theon of Smyrna, where he purports to quote Eudemus; ‘Eudemus’, he says, ‘relates in his Astronomies that . . . Thaies was the first to discover understood) the eclipse of the sun referring to predictions; indeed the word ‘predict’ does not go well with ‘solstices’, and is suspect for this reason. Nor does any one credit Thales with having predicted more than one eclipse. No doubt the original passage spoke of ‘eclipses’ and ‘solstices’ in the plural and used some word like ‘discover’ (Theon’s word), not the word ‘predict’. And I think Martin may reasonably argue from the passage of Diogenes that the words ‘according to some’ are Eudemus’s words, not his own, and therefore may be held to show that the truth of the tradition was not beyond doubt.⁹

Nevertheless, as Tannery observes,¹⁰ Martin’s argument can hardly satisfy us so far as it relates to Thales. The evidence that Thales actually predicted a solar eclipse is as conclusive as we could expect for an event belonging to such remote times, for Diogenes Laertius quotes Xenophanes as well as Herodotus as having admired Thales’ achievement, and Xenophanes was almost contemporary with Thales. We must therefore accept the fact as historic, and it remains to inquire in what sense or form, and on what ground, he made his prediction. The accounts of it vary. Herodotus says¹¹ that the Lydians and the Medes continued their war, and ‘when, in the sixth year, they encountered one another, it fell out that, after they had joined battle, the day suddenly turned into night. Now that this transformation of day (into night) would occur was foretold to the Ionians by Thales of Miletus, who fixed as the limit of time this very year in which the change actually took place’.¹² The prediction was therefore at best a rough one, since it only specified that the eclipse would occur within a certain year; and the true explanation seems to be that it was a prediction of the same kind as had long been in vogue with the Chaldaeans. That they had a system enabling them to foretell pretty accurately the eclipses of the moon is clear from the fact that some of the eclipses said by Ptolemy¹³ to have been observed in Babylon were so partial that they could hardly have been noticed if the observers had not been to some extent prepared for them. Three of the eclipses mentioned took place during eighteen months in the years 721 and 720. It is probable that the Chaldaeans arrived at this method of approximately predicting the times at which lunar eclipses would occur by means of the period of 223 lunations, which was doubtless discovered as the result of long-continued observations. This period is mentioned by Ptolemy¹⁴ as having been discovered by astronomers ‘still more ancient’ than those whom he calls ‘the ancients’.¹⁵ Now, while this method would serve well enough for lunar eclipses, it would very often fail for solar eclipses, because no account was taken of parallax. An excellent illustration of the way in which the system worked is on record; it is taken from a translation of an Assyrian cuneiform inscription, the relevant words being the following :

1.   To the king my lord, thy servant Abil-istar.

2.   May there be peace to the king my lord. May Nebo and Merodach

3.   to the king my lord be favourable. Length of days,

4.   health of body and joy of heart may the great gods

5.   to the king my lord grant. Concerning the eclipse of the moon

6.   of which the king my lord sent to me; in the cities of Akkad,

7.   Borsippa, and Nipur, observations

8.   they made and then in the city of Akkad

9.   we saw part. . . .

10.   The observation was made and the eclipse took place.

.   .   .   

17.   And when for the eclipse of the sun we made

18.   an observation, the observation was made and it did not take place.

19.   That which I saw with my eyes to the king my lord

20.   I send. This eclipse of the moon

21.   which did happen concerns the countries

22.   with their god all. Over Syria

23.   it closes, the country of Phoenicia,

24.   of the Hittites, of the people of Chaldaea,

25.   but to the king my lord it sends peace, and according to

26.   the observation, not the extending

27.   of misfortune to the king my lord

28.   may there be.

It would seem, as Tannery says,¹⁷ that these clever people knew how to turn their ignorance to account as well as their knowledge. For them it was apparently of less consequence that their predictions should come true than that they should not let an eclipse take place without their having predicted it.¹⁸

As it is with Egypt that legend associates Thales, it is natural to ask whether the Egyptians too were acquainted with the period of 223 lunations. We have no direct proof; but Diodorus Siculus says that the priests of Thebes predicted eclipses quite as well as the Chaldeans,¹⁹ and it is quite possible that the former had learnt from the latter the period and the notions on which the successful prediction of eclipses depended. It is not, however, essential to suppose that Thales got the information from the Egyptians; he may have obtained it more directly. Lydia was an outpost of Assyrio-Babylonian culture; this is established by (among other things) the fact of the Assyrian protectorate over the kings Gyges and Ardys (attested by cuneiform inscriptions); and ‘no doubt the inquisitive Ionians who visited the gorgeous capital Sardes, situated in their immediate neighbourhood, there first became acquainted with the elements of Babylonian science’.²⁰

If there happened to be a number of possible solar eclipses in the year which (according to Herodotus) Thales fixed, he was not taking an undue risk; but it was great luck that it should have been total.²¹

Perhaps I have delayed too long over the story of the eclipse; but it furnishes a convenient starting-point for a consideration of the claim of Thales to be credited with the multitude of other discoveries in astronomy attributed to him by the Doxographi and others. First, did he know the cause of eclipses? Aëtius says that he thought the sun was made of an earthy substance,²² like the moon, and was the first to declare that the sun is eclipsed when the moon comes in a direct line below it, the image of the moon then appealing on the sun’s disc as on a mirror;²³ and again he says that Thales, as well as Anaxagoras, Plato, Aristotle, and the Stoics, in accord with the mathematicians, held that the moon is eclipsed by reason of its falling into the shadow made by the earth when the earth is between the two heavenly bodies.²⁴ But, as regards the eclipse of the moon, Thales could not have given this explanation, because he held that theearth floated on the water;²⁵ from which it may also be inferred that he, like his successors down to Anaxagoras inclusive, thought the earth to be a disc or a short cylinder. And if he had given the true explanation of the solar eclipse, it is impossible that all the succeeding Ionian philosophers should have exhausted their imaginations in other fanciful explanations such as we find recorded.²⁶

We may assume that Thales would regard the sun and the moon as discs like the earth, or perhaps as hollow bowls which could turn so as to show a dark side.²⁷ We must reject the statements of Aëtius that he was the first to hold that the moon is lit up by the sun, and that it seems to suffer its obscurations each month when it approaches the sun, because the sun illuminates it from one side only.²⁸ For it was Anaxagoras who first gave the true scientific doctrine that the moon is itself opaque but is lit up by the sun, and that this is the explanation no less of the moon’s phases than of eclipses of the sun and moon; when we read in Theon of Smyrna that, according to Eudernus’s History of Astronomy, these discoveries were due to Anaximenes,²⁹ this would seem to be an error, because the Doxographi say nothing of any explanations of eclipses by Anaximenes,³⁰ while on the other hand Aëtius does attribute to him the view that the moon was made of fire,³¹ just as the sun and stars are made of fire.³²

We must reject, so far as Thales is concerned, the traditions that ‘Thales, the Stoics, and their schools, made the earth spherical’,³³ and that ‘the school of Thales put the earth in the centre’.³⁴ For (1) we have seen that Thales made the earth a circular or cylindrical disc floating on the water like a log³⁵ or a cork; and (2), so far as we can judge of his conception of the universe, he would appear to have regarded it as a mass of water (that on which the earth floats) with the heavens superposed in the form of a hemisphere and also bounded by the primeval water. It follows from this conception that for Thales the sun, moon, and stars did not, between their setting and rising again, continue their circular path below the earth, but (as with Anaximenes later) laterally round the earth.

Tannery³⁶ compares Thales’ view of the world with that found in the ancient Egyptian papyri. In the beginning existed the Nū, a primordial liquid mass in the limitless depths of which floated the germs of things. When the