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PURCHASED FOR THE UNIVERSITY OF TORONTO LIBRARY
FROM THE
CANADA COUNCIL SPECIAL GRANT
FOR HIST 501] 168
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 NEW GREEK TEXT WITH TRANSLATION AND NOTES
BY
SIR THOMAS HEATH
K.C.B., Sc.D., F.R.S. SOMETIME FELLOW OF TRINITY COLLEGE, CAMBRIDGE
OXFORD AT THE CLARENDON PRESS
1913
HENRY FROWDE, M.A. PUBLISHER TO THE UNIVERSITY OF OXFORD LONDON, EDINBURGH, NEW YORK, TORONT9 MELBOURNE AND BOMBAY
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« NOV 27 1968 My, 9 <Asiry oF TOROS
᾿ " 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 Ox 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 funda- mental assumptions at the beginning of the book. I remembered _ that Archimedes distinctly says in his Psammites or Sand-reckoner that Aristarchus was the first to discover that the apparent diameter of the sun is about 1/720th part of the complete circle described _ by it im the daily rotation, or, in other words, that the angular _ diameter is about 4°, 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 & be on record, with a view to tracing, if possible, the origin “Or aie figure of 2°. Again, our treatise does not contain amy suggestion of any but
the geoeeritric 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 eatth 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) Schiapareili, 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
ΩΝ PREFACE
hypothesis. Schiaparelli, whose two papers Le sfere omocentriche di Eudosso, di Callippo e di Aristotele and I precursori di Copernico nell’ antichita 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 ἡ Grect) 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 argu- ments were entitled to the most careful consideration, and this again necessitated research in the earlier history of Greek astrorémy” 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
PREFACE } a
_ identifying Aristarchus with the latter hypothesis. Libert Fro- mond, Professor of Theology at the University of Louvain, who _ tried to refute it, called his work Avti-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 A. 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 (Fugemens 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 Ajfollonius 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. ‘Systéme’). He said that Ari- _Starchus ‘is so obscure that Wallis was obliged to annotate him _ from one end to the other, in the effort to make him intelligible’, and furer that it was very doubtful whether the book attributed +o'-\ristarchus was really by him. Voltaire (misled, it is true, by a wrong reading in a passage of Plutarch, De facie in orbe lunae, _ ς, 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.
vi PREFACE
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 ¢rigonometrical object, and in this respect is a sort of fore- runner 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. . 1:32, “ἢ;
CONTENTS
PART I
GREEK ASTRONOMY TO ARISTARCHUS OF SAMOS CHAPTER PAGES . I. Sources OF THE History . ὃ : : : 1-6 II. Homer anpD HEsiop _.. 3 ; : ἢ Ξ ἡπιτ SSS et ee τς .χ.22 IV. ANAXIMANDER. ; : ‘ : f ‘ ; 24-39 V. ANAXIMENES . : 4 : : ᾿ Α ‘ 40-45 VI. PyTHAGoRAs . Ξ : ? Ξ - ‘ ; 46-51 _ VII. XENOPHANES . Ξ : - ᾿ - 52-58 _ VIII. Heractitus . : : : ; . : : 59-61 IX. PARMENIDES . . . s ᾿ Ε ; ; 62-77 X. ANAXAGORAS . > : Ξ : : ᾧ . 78-85 ΧΙ. Empepocies . ὃ 5 ‘ ; : ᾿ : 86-93 _ ΧΗ. THe Pyruacoreans : A 2 ς Σ . 964-120 _ XIII. Tue ΑΤΟΜΙΞΊ5, Leucippus ΑΝῸ DEMocrITUS . 121-129 _ XIV. OEnopipes. τὰ i : : ; τὴν + “330-133 XV. Puato . 2 ἥ ν : ἃ : : . 134-189
XVI. THe THErory or ConceNnTRIC SPHERES—EUDOXUS, | CALLIPPUS, AND ARISTOTLE. ‘ P ? . 190-224 8 XVII. ARISTOTLE (continued) . : y : ‘ . 225-248 XVIII. HeEraciipes or Pontus. . . Ξ ξ . 249-283 XIX. Greek Montus, Years, AND CYCLES . ς . 284-297 PART II
ARISTARCHUS ON THE SIZES AND DISTANCES OF THE SUN AND MOON
I, ARISTARCHUS OF SaMos. ᾿ : ς ᾿ . 299-316 II. Tue TREATISE ΟΝ SIzEs AND DisTaNceS—HIsTORY OF THE TEXT AND EDITIONS. : ; . 317-327 III. ConTENT oF THE TREATISE . ‘ . : . 328-336 IV. Later ImprovEMENTs ΟΝ ARISTARCHUS’s CALCULA- TIONS . ὃ : ἢ : = ; . 337-350 GREEK TEXT, TRANSLATION, AND NoTES . Η . 251-414
. INDEX . : : Ξ d : % ς - : . 415-425
CORRIGENDUM
P. 179, lines 26 and 31. It appears that προχωρήσεις, not προσχωρήσεις, is the correct reading in 7imaeus 40 C. The meaning of προχωρήσεις is of course ‘forward movements’, but the change to this reading does not make it any the more necessary to take ἐπανακυκλήσεις 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 617 B, where ἐπανακυκλούμενον 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.
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, Tonian, 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 ;' 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 philo- sophers; those in Plato are not very numerous, but he had the _ power of entering into the thoughts of other men and, in stating Ὁ _ 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 contro- _ versial 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
1 Gomperz, Griechische Denker, i*, Ὁ. 419.
1410 B
2 SOURCES OF THE HISTORY PARTI
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.1_ 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 (Φυσικῶν δοξῶν Tm). It would appear that it was Theophrastus’s plan to trace the progress of physics from Thales to Plato in separate chapters dealing severally with the leading topics, First the leading views were set forth on broad lines, in groups, according to the affinity of the doctrine, after which the differences between individual philosophers within the same group were carefully noted. In the First Book, however, dealing with the Principles, Theophrastus adopted the order of the various schools, Ionians, Eleatics, Atomists, &c., down to Plato, although he did not hesitate to connect Diogenes of Apollonia and Archelaus with the earlier physicists, out of their chronological order; chronological order was indeed, throughout, less regarded than the connexion and due arrangement of subjects. This work of Theophrastus was naturally the chief hunting-ground for those who collected the ‘ opinions’ of philosophers. There was, however, another main stream of tradition besides the doxographic; this was in the different form of biographies of the philosophers. The first to write a book of ‘successions’ (διαδοχαΐ) 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 ot 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.2_ Our chief storehouse of biographical details derived from these and all other available sources is the great compilation which goes by the
1 Doxographi Graeci, ed. Diels, Berlin, G. Reimer, 1879. * Doxographi Graeci (henceforth generally quoted as D.G.), p. 151.
CE.I SOURCES OF THE HISTORY 3
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.
' ἴῃ 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 table’:
: Eusebrus Gi Cent AND ua pra TACLO Bks XIV) ο
Fig. I
__-? Cf. Giinther in Windelband, Gesch, der alten Philosophie (Iwan yon Miiller’s Handbuch der klassischen Altertumswissenschaft, Band v. 1), 1894, p. 275.
B2
4 SOURCES OF THE HISTORY PARTI
- 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; II. 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 Aétius (De placitis, περὶ ἀρεσκόντων) 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 Aclogae, under the title of Aétz 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 jietate, περὶ εὐσεβείας, 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.
The greater part of the fragment of the Pseudo-Plutarchian στρωματεῖς 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 (the sub- title of the particular Book is φιλοσοφούμενα), probably written between 223 and 235 A.D. It is derived from two sources. The
᾿
ΟῚ SOURCES OF THE HISTORY 5 _ one was a biographical compendium of the διαδοχή type, shorter
and even more untrustworthy than Diogenes Laertius, but con-
taining 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 Theo-
phrastus 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.1_ 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.* 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®
For the earlier period from Thales to Empedocles, Tannery gives a translation of the doxographic data and the fragments in his work Pour Vhistoive de la science helléne, de Thales ἃ 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 Dorographi, Max Sartorius’s
dissertation Die Entwicklung der Astronomie bei den Griechen bis
* Diels, Doxographi Graeci, p. 153.
* Excerpts from this are preserved in Cod. Laurentian. xxviii. 44, and are included in the Uranologium of Petavius, 1630, pp. 121-64, &c.
* Second edition in two vols. (the second in two parts), Berlin, 1906-10.
ό SOURCES OF THE HISTORY
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 Callip- pus’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,: 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 Zzmaeus of Plato, which is quoted by Proclus as well as by Theon of Smyrna.
1 Edited by E. Hiller (Teubner, 1878).
II
HOMER AND HESIOD
WE take as our starting-point the conceptions of the structure of the world which are to be found in the earliest literary monuments of Greece, that is to say, the Homeric poems and the works of Hesiod. In their fundamental conceptions Homer and Hesiod _ agree. The earth is a flat circular disc; this is not stated in so many words, but only on this assumption could Poseidon from _ the mountains of Solym in Pisidia see Odysseus at Scheria on the further side of Greece, or Helios at his rising and setting descry his cattle on the island of Thrinakia. Round this flat disc, on the horizon, runs the river Oceanus, encircling the earth and flowing back into itself (ἀψόρροος) ; 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 hemi- spherical 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. pre- sumably 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
8 HOMER AND HESIOD PARTI
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.?
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’ *),
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°), y, the hind foot, as well as n, the tip of the tail, and at Alexandria all the seven stars except a, 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 Ὃν pra ; (Proceedings of the Cambridge Philosophical Soctety, 1877 and 1881), and to the results obtained in a paper by J. Gallenmiiller, Der Fixsternhimmel jetzt und in Homers Zeiten mit zwei Sternkarten (Regensburg, 1884/85). Gallenmiiller’s charts are for the years 900 B.C. and A.D. 1855 respectively, and the chart for goo B.C. shows that the N.P. Ὁ. of both 8, 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 (J Avrati et Eudoxi phaeno- mena commentariorum libri tres, 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- miiller’s chart refers] made the fore-foot (8) about 24°, and the hind-foot (y) 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 a 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 (Hyfotyposis, c. 7, δὲ 45-8, p. 234, ed. Manitius) is not without interest in this connexion. He is trying to controvert the theory of astronomers that the fixed stars themselves have a movement about the pole of the ecliptic (as distinct from the pole of the universe) of about 1° in 100 years
CH. II HOMER AND HESIOD 9
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 Bodtes’ (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 constellation which never sets, we may perhaps assume that the stars and constellations above named are all that _ were definitely recognized at the time, or at least that the Bear was the only constellation recognized in the northern sky. There is little more that can be called astronomy in Homer. There are vague uses of astronomical phenomena for the purpose of fixing localities or marking times of day or night; as regards the day, the morning twilight, the rising and setting of the sun, midday, and the onset of night are distinguished ; the night is divided into three thirds. Aristotle was inclined to explain Helios’s seven herds of cattle and sheep respectively containing 50 head in each herd {i.€. 350 in all of each sort) as a rough representation of the number of days in a year. Calypso directed Odysseus to sail in such a way as to keep the Great Bear always on his left. One passage,! relating to the island called Syrie, ‘which is above Ortygia where are the turnings (τροπαΐ) 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
(this is Ptolemy’s estimate). ‘ How is it’, says Proclus, ‘that the Bears, which have always been visible above the horizon through countless ages, still remain so, if they move by one degree in 100 years about the pole of the zodiac, which is different from the world-pole ; for, if they had moved so many degrees as this would imply, they should now no longer graze (παραξέειν) the horizon but should partly set’! This passage, written (say) 840 years after Eudoxus’s location of 8 and y 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 Eudoxi 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 of Draco and (2) the line joining y and β of the Little Bear and produced beyond β.] 1 Odyssey xv. 403-4.
10 HOMER AND HESIOD PARTI
rising, in which case the island would simply be situated on the western horizon where the sun se¢s.1
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 ;* the time for harvest he fixed by the early rising of the Pleiades, which means the Julian 19th of May ;* threshing-time he marked by the early rising of Orion (Julian gth of July), vintage-time by the early rising of Arcturus (Julian 18th of September), and so on. With Hesiod, Spring begins with the late rising of Arcturus; this would in his time and climate be the 24th February of the Julian calendar, or 57 days after the winter solstice, which in his time would be the 29th December. He him-- self makes Spring begin 60 days after the winter solstice ; he may be intentionally stating a round figure, but, if he made an error of
1 Martin has discussed the question at considerable length (‘Comment Homére s’orientait’ in Mémoires de ? Académie des Inscriptions et Belles- Lettres, xxix, Pt. 2, 1879, pp. 1-28). He strongly holds that τροπαὶ ἠελίοιο can only mean the solstice, that by this we must also understand the summer solstice, and that the expression ὅθι τροπαὶ ἠελίοιο must therefore be in the direction of the place on the horizon where the sun sets at the summer solstice, i.e. west-north-west. Martin’s ground is his firm conviction that τροπαὶ nediovo has mever, in any Greek poet or prose writer, any other than the technical meaning of ‘ solstice’. This is, however, an assumption not susceptible of proof; and Martin is not very successful in his search for confirmation of his view. Identifying Ortygia with Delos, and Syrie with Syra or Syros, he admits that the southern part of Syra is due west of the southern part of Delos ; only the northern portion of Syra stretches further north than the northern portion of Delos; therefore, geographically, either west or west-north-west would describe the direction of Syra relatively to Ortygia well enough. Of the Greek com- mentators, Aristarchus of Samothrace and Herodian of Alexandria take rpomai to mean ‘ setting’ simply; Martin is driven therefore to make the most he can of Hesychius who (s.v. ’Oprvyin) gives as an explanation τοῦτο δέ ἐστιν ὅπου ai δύσεις ἄρχονται, ‘This is where the settings commence’, which Martin interprets as meaning ‘ where the sun sets a¢ 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’.
2 Ideler, Handbuch der mathematischen und technischen Chronologie, 1825, i, ΡΡ. 242, 246.
Ibid, p. 242. * Ibid. pp. 246, 247. ©
»
—_ ἈΨΎΥΥ oan ae 7 ΕΝ »
CH. II HOMER AND HESIOD II
three days, it would not be surprising, seeing that in his time there were no available means for accurately observing the times of the solstices. His early summer (θέρος), as distinct from late summer (ὀπώρα), he makes, in like manner, end 50 days after the sum- mer 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.!
Hesiod was also credited with having written a poem under the title of ‘Astronomy’. A few fragments of such a poem are pre- served ;* 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’. 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 Sartorius, op. cit., p. 16; Ideler, i, p. 257.
3 Diels, Vorsokratiker, ii*. 1, 1907, pp. 499, 500. 5. Pliny, WV. H. xviii, c. 25, ὃ 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 Epznomis says, ‘the true astronomer will not be the man who cultivates astronomy in the manner of Hesiod and any other writers of that type, concern- ing 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 ἡ 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). Accord- ing 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 ver- satility 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 For his many-sided culture he
1 Aristotle, Politics i. 11. 9, 1259 a 6-17.
“τ <= ea
eae ae ae ee σον
THALES ; 13
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 prac- tical 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,! that, when he was star-gazing and fell into a well in con- sequence, he was rallied ‘by a clever and pretty maid-servant from Thrace’? 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.* He points out that, while the references to the prediction do not exactly agree, it is in fact necessary, if the oceurrence 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. Plutarch* relates that, when Plato was on a visit to Sicily and stay- ing with Dionysius, Helicon of Cyzicus, a friend of Plato’s, foretold a solar eclipse (apparently that which took place on 12th May,
1 Theaetetus 174 A;.cf. Hippolytus, Refuz. i. 1. 4 (D. G. p. 555. 9-12).
? There is another version not so attractive, according to which [Diog. Laert. i. 34], being taken out of the house by an old woman to look at the stars, he fell into a hole and was reproached by her in similarterms. This version might
suggest that it was the old woman who was the astronomer rather than Thales. Revue Archéologique, ix, 1864, pp. 181 sq. “ Life of Dion, c. 19, p. 966A.
14 THALES PART I
361 B.C.),1 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 im- possible for Helicon than for Thales. 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 Thales, Martin relies largely on the word- ing of a passage in Theon of Smyrna, where he purports to quote Eudemus; ‘ Eudemus’, he says, ‘ relates in his Astronomies that... Thales was the first to discover (εὗρε πρῶτος understood) the eclipse of the sun and the fact that the sun’s period with respect to the solstices is not always the same’,? and the natural mean- ing of the first part of the sentence is that Thales discovered the explanation and the cause of a solar eclipse. It is true that Diogenes Laertius says that ‘ Thales appears, according to some, to have been the first to study astronomy and to predict both solar eclipses and solstices, as Eudemus says in his History of Astronomy ’,® and Diogenes must be quoting from the same passage as Theon ; but it is pretty clear, as Martin says, that he copied it inaccurately and himself inserted the word (προειπεῖν) 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.
1 Boll, art. ‘Finsternisse’ in Pauly-Wissowa’s eal-Encyclopidie der classischen Altertumswissenschaft, vi. 2, 1909, pp. 2356-7; Ginzel, Handbuch der mathematischen und technischen Chronologie, vol. ii, 1911, p. 527.
3 Theon of Smyrna, ed. Hiller, p. 198. 14-18.
® Diog. L. 1.23 (Vorsokratiker, 15, p. 3. 19-21).
* There is, however, yet another account purporting to be based on Eudemus, Clement of Alexandria (S¢vomat. i. 65) says : ‘Eudemus observes in his History of Astronomy that Thales predicted the eclipse of the sun which took place at the time when the Medes and the Lydians engaged in battle, the king of the
Sa Se
CH, ΠῚ THALES ᾿ 15
Nevertheless, as Tannery observes, 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 ave 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 says? 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.’* The prediction was therefore at best a rough one, Medes being Cyaxares, the father of Astyages, and Alyattes, the son of Croesus, being the king of the Lydians; and the time was about the 5oth Olympiad [58ο-
577].’ The last sentence was evidently taken from Tatian 41 ; but, if the rest of the passage correctly quotes Eudemus, it would appear that there must have
been two passages in Eudemus dealing with the subject.
1 Tannery, Pour ’histoire de la science helléne, p. 56.
3 Herodotus, i. 74.
3. Other references are as follows: Cicero, De Divinatione i. 49. 112, observes that Thales was said to have been the first to predict an eclipse of the sun, which eclipse took place in the reign of Astyages; Pliny, V.H. ii, c. 12, ὃ 53, ‘Among the Greeks Thales first investigated (the cause of the eclipse) in the fourth year of the 48th Olympiad [585/4 B.c.], having predicted an eclipse of the sun which took place in the reign of Alyattes in the year 170 A.U.C.’; Eusebius, Chron. (Hieron.), under year of Abraham 1433, ‘An eclipse of the sun, the occurrence of which Thales had predicted: a battle between Alyattes and Astyages’. The eclipse so foretold is now most generally taken to be that which took place on- the (Julian) 28th May, 585. A difficulty formerly felt in regard to this date seems now to have been removed. Herodotus (followed ‘by Clement) says that the eclipse took place during a battle between Alyattes and Cyaxares. Now, on the usual assumption, based on Herodotus’s chronological data, that Cyaxares reigned from about 635 to 595, the eclipse of 585 B.c. must have taken place during the reign of his son; and perhaps it was the knowledge of this fact which made Eusebius say that the battle was between Alyattes and Astyages. But it appears that Herodotus’s reckoning was affected by an error on his part in taking the fall of the Median kingdom to be coincident with Cyrus’s accession to the throne of Persia, and that Cyaxares really reigned from 624 to 584, and Astyages from 584 to 550 B.C. (Ed. Meyer in Pauly-Wissowa’s Real-Encyclo- padie, ii, 1896, p. 1865, ὅς.) ; hence the eclipse of 585 B.c. would after all come in Cyaxares’ reign. Oftwo more solar eclipses which took place in the reign of Cyaxares one is ruled out, that of 597 B.C., because it took place at sunrise, which would not agree with Herodotus’s story. The other was on 30th September, 610, and, as regards this, Bailly and Oltmanns showed that it was not total on the
τό THALES PARTI
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 Ptolemy’ 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 doubt- less discovered as the result of long-continued observations. This period is mentioned by Ptolemy* as having been discovered by astronomers ‘still more ancient’ than those whom he calls ‘the ancients’.. 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
presumed field of battle (in Cappadocia), though it would be total in Armenia (Martin, Revue Archéologiqgue, ix, 1864, pp. 183, 190). Tannery, however (Pour Phistotre de la science helléne, p. 38), holds that the latter eclipse was that associated with Thales. The latest authorities (Boll, art. ‘Finsternisse’, in Pauly- Wissowa’s Real-Encyclopidie, vi. 2, 1909, pp.2353-4, and Ginzel, Spesieller Kanon der Sonnen- und Mondjinsternisse and Handbuch der mathematischen und tech- nischen Chronologie, vol. ii, 1911, p. 525) adhere to the date 28th May, 585.
1 Ptolemy, Syntaxis iv, c. 6 sq.
* Ptolemy, Syztaxis iv, c. 2, p. 270, 1 sq., ed. Heiberg.
* Suidas understands the Chaldaean name for this period to have been savos, but this seems to be a mistake. According to Syncellus (Chronographia, p. 17; A-B), Berosus expressed his periods in savs, #ers, and sosses, a sar being 3,600 years, while 2267 meant 600 years, and soss 60 years ; but we learn that the same words were also used to denote the same numbers of days respectively (Syncellus, p. 32 C). Nor were they used of years and days only; in fact sar, 2167, and 5055 were collective numerals simply, like our words ‘gross’, ‘ score’, ἄς. (Cantor, Gesch. d. Mathematik, 15, p. 36).
4 See George Smith, Assyrian Discoveries, p. 409.
‘CH. IM THALES 17
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. ...
το. 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 lace.
19. That which I saw with my eyes to the king my lord
20. Isend. 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,’ 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 predic- tions should come true than that they should not let an eclipse take place without their having predicted it.*
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,* 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
Ea ea ν Ἔ4 -
1. Tannery, op. cit., p. 57. ob τς :
* Delambre (Hist. de /astronomie ancienne, i, p. 351) quotes a story that in China, in 2159 B.C., the astronomers Hi and Ho were put to death, according to law, in consequence of an eclipse of the sun occurring which they had not
3 Cf. Diodorus, i, c. 50; ii, c. 30.
1410 G
18 THALES PARTI _
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’.? .
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.?
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? Aétius says that he thought the sun was made of an earthy substance,® 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 appearing on the sun’s disc as on a mirror ;* 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. But, as regards the eclipse of the moon, Thales could not have given this _ explanation, because he held that theearth floated on the water ; ° 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 capigee’ tions such as we find recorded.”
We may assume that Thales would regard the sun and the moon as discs like the earth, or perhaps as hollow bowls which could
1 Gomperz, Griechische Denker, 15, p. 421. ἃ Torey. op. cit., p. 60. ® Aét. li. 20. 9 (D. G. p. 349). * Aét. ii. 24.1 (20. Ὁ. pp. 353, 354). 5 Aét. ii. 29. 6 (D. G. p. 360). ὁ. Theophrastus.apud Simpl. zz Phys. p. 23. 24 (D.G. p. 475; Vors. i’, p. 9. 22); cf. Aristotle, Metaph. A. 3, 983b 21; De caedo ii. 13, hg 28. 1 Tannery, op. cit., p. 56.
a - rs
pe ye
CH.III | | THALES 19
turn so as to show a dark side.1 We must reject the statements of Aétius 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.2_ 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 Eudemus’s History of Astronomy, these discoveries were due to Anaximenes,* this would seem to be an error, because the Doxographi say nothing of any explanations of eclipses by Anaximenes,* while on the other hand Aétius does attribute to him the view that the moon was made of fire, just as the sun and stars are made of fire.®
We must reject, so far as Thales is concerned, the traditions that *Thales, the Stoics, and their schools, made the earth spherical’,’ and that ‘the school of Thales put the earth in the centre’.® For (1) we have seen that Thales made the earth a circular or cylindrical disc floating on the water like a log® 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 de/ow the earth, but (as with Anaximenes later) laterally round the earth. Tannery *° compares Thales’ view of the world with that found © in the ancient Egyptian papyri. In the beginning existed the Vz, a primordial liquid mass in the limitless depths of which floated the germs of things. When the sun began to shine, the earth was flattened out and the waters separated into two masses. The one gave rise to the rivers and the ocean ; the other, suspended above,
_ formed: the vault of heaven, the waters above, on which the stars
1 Tannery, op. cit., p. 70. * Aét.ii.28.5; 29.6(D. G. p. 358. 19; p. 360. 16). 5 Theon of Smyrna, p. 198. Aes 2
* Tannery, op. cit., pp. 56, I 5 Aét. ii. 25. 2 (D. G. p. 356. 1). ® Aéte ii. 20. 2 (D. G. p. 348. Ὁ; Hippol. Refut. i. 7. 4 (D. G.-p. ey: 3). 7 Aét. iii. το. τ (D. G. p. 376. 22). Aét. iti. 11. 1 (D.G. p. 377. 7). * Aristotle, De cae/o ii. 13, 294 a 30. 10 Tannery, op. cit., p. 71.
C2
20 THALES . PARTI
and the gods, borne by an eternal current, began to float. The sun, standing upright in his sacred barque which had endured millions of years, glides slowly, conducted by an army of secondary gods, the planets and the fixed stars. The assumption of an upper and lower ocean is also old-Babylonian (cf. the division in Gen. i. 7 of the waters which were under the firmament from the waters which were above the firmament).
In a passage quoted by Theon of Smyrna, Eudemus attributed to Thales the discovery of ‘the fact that the period of the sun with respect to the solstices is not always the same’! The expres- sion is ambiguous, but it must apparently mean the inequality of the length of the four astronomical seasons, that is, the four parts of the tropical year? as divided by the solstices and the equinoxes. Eudemus referred presumably to the two written works by Thales On the Solstice and On the Equinox,’ which again would seem to be referred to in a later passage of Diogenes Laertius: ‘Lobon of Argos says that his written works extend to 200 verses’. Now Hesiod, in the Works and Days, advises the commencement of certain operations, such as sowing, reaping, and threshing, when particular constellations rise or set in the morning, and he uses the solstices as fixed periods, but does not mention the equinoxes. Tannery ἢ thinks, therefore, that Thales’ work supplemented Hesiod’s by the addition of other data and, in particular, fixed the equinoxes in the same way as Hesiod had fixed the solstices. The inequality of the intervals between the equinoxes and the solstices in one year would thus be apparent. This explanation agrees with the remark of Pliny that Thales fixed the matutinal setting of the Pleiades on the 25th day from the autumnal equinox. All this knowledge Thales probably derived from the Egyptians or the Babylonians. The Babylonians, and doubtless the Egyptians also,
1 Theon of Smyrna, p. 198. 17 (Θαλῆς εὗρε πρῶτος) . . . τὴν κατὰ Tas τροπὰς αὐτοῦ περίοδον, ὡς οὐκ ἴση ἀεὶ συμβαίνει.
3 The ‘tropical year’ is the time required by the sun to return to the same position with reference to the equinoctial points, while the ‘sidereal year’ is the time taken to return to the same position with reference to the fixed stars.
8 Diog. L. i. 23 (Vors. i*, p. 3. 18).
4 Tannery, op. cit., p. 66.
5 Pliny, ΔΝ. H. xviii, c. 25, ὃ 213 (Vors.i?, p.9. 44). This datum points to Egypt as the source of Thales’ information, for the fact only holds good for Egypt and not for Greece (Zeller, 15, p. 184; cf. Tannery, op. cit., p. 67).
μ᾿ Ἢ ’
CH. III THALES 21
were certainly capable of determining more or less roughly the solstices and the equinoxes; and they would doubtless do this by means of the gzomon, the use of which, with that of the folos, the Greeks are said to have learnt from the Babylonians.'
Thales equally learnt from the Egyptians his division of the year into 365 days;* it is possible also that he followed their arrangement of months of 30 days each, instead of the practice
_ already in his time adopted in Greece of reckoning by lunar months.
The Doxographi associate Thales with Pythagoras and his school as having divided the whole sphere of the heaven by five circles, the arctic which is always visible, the summer-tropical, the equatorial, the winter-tropical, and the antarctic which is always invisible ; it is added that the so-called zodiac circle passes obliquely to the three middle circles, touching all three, while the meridian
Ἷ circle, which goes from north to south, is at right angles to all the
five circles.* But, if Thales had any notion of these circles, it must have been of the vaguest; the antarctic circle in particular
_ presupposes the spherical form for the earth, which was not the
form which Thales gave it. Moreover, the division into zones is elsewhere specifically attributed to Parmenides and Pythagoras; and, indeed, Parmenides and Pythagoras were the first to be in a position to take this step,* as they were the first to hold that the earth is spherical in shape. Again, Eudemus is quoted® as distinctly attributing the discovery of the ‘cincture of the zodiac (circle)’ to Oenopides, who was at least a century later than Thales.
Diogenes Laertius says that, according to some authorities, Thales was the first to declare the apparent size of the sun (and the moon) to be 1/720th part of the circle described by it.6 The version of this story given by Apuleius is worth quoting for a human touch which it contains:
? Herodotus, ii. 109. - ® Herodotus (ii. 4) says that the Egyptians were the first of men to discover the year, and that they divided it into twelve parts, ‘therein adopting a wiser system (as it seems to me) than the Greeks, who have to put in an intercalary
month every third year, in order to keep the seasons right, whereas the Egyptians give their twelve months thirty days each and add five every year outside the
4 number (of twelve times 30)’. As regards Thales, cf. Diog. L. i. 27 and 24
(Vors. 15, pp. 3. 27; 4. 9). 5. Aét. ii. 12. 1 (D. G. p. 340. 11 sq.). * As to Parmenides cf. Aét. iii. 11. 4 (2. G. p. 377. 18-20). Rig τὰ ® Theon of Smyrna, p. 198. 14. -* Diog. L. i. 24 ( Vorsokratiker, i*, p. 3. 25).
22 THALES “PARTI
‘The same Thales in his declining years devised a marvellous calculation about the sun, which I have not only learnt but verified by experiment, showing how often the sun measures by its own size the circle which it describes. Thales is said to have communi- cated this discovery soon after it was made to Mandrolytus of Priene, who was greatly delighted with this new and unexpected information and asked Thales to say how much by way of fee he required to be paid to him for so important a piece of knowledge. “T shall be sufficiently paid”, replied the sage, “1, when you set to work to tell people what you have learnt from me, you will not take credit for it yourself but will name me, rather than another, as the discoverer.” }
Seeing that in Thales’ system the sun and moon did not pass under the earth and describe a complete circle, he could hardly have stated the result in the precise form in which Diogenes gives it. If, however, he stated its equivalent in some other way, it is again pretty certain that he learnt it from the Egyptians or Babylonians, Cleomedes,? indeed, says that, by means of a water- clock, we can compare the water which flows out during the time that it takes the sun when rising to-get just clear of the horizon with the amount which flows out in the whole day and night; in this way we get a ratio of 1 to 750; and he adds that this method is said to have been first devised by the Egyptians. Again, it has been suggested® that the Babylonians had already, some sixteen centuries before Christ, observed that the sun takes 1/30th of an hour to rise. This would, on the assumption of 24 hours for a whole day and night, give for the sun’s apparent diameter 1/720th of its circle, the same excellent approximation as that attributed to Thales. But there is the difficulty that, when the Babylonians spoke of 1/goth of an hour in an equinoctial day as being the ‘measure’ (ὅρος) of the sun’s course, they presumably meant 1/30th of their doudble-hour, of which there are 12 in a day and night, so that, even if we assume that the measurement of the sun’s apparent diameter was what they meant by ὅρος, the equivalent
? Apuleius, F/or. 18 (Vors. i*, p. 10. 3-11).
* Cleomedes, De motu circulari corporum caelestium ii. 1, pp. 136. 25-138. 6, ed. Ziegler.
* Hultsch, Poseidonios iiber die Grisse und Entfernung der Sonne, 1897, pp- 41, 42. Hultsch quotes Achilles, /sagoge in Arati phaen.18(Uranolog. Petavii, Paris, 1630, p. 137); Brandis, M/iinz-, Mass- und Gewichtswesen in Vorderasien, p. 17 sq.3 Bilfinger, Die babylonische Doppelstunde, Stuttgart, 1888, p. 21 sq. The passage of Achilles is quoted 7” extenso by Bilfinger, p. 21.
= Soe ὑμὴν ᾿
—
CH. THALES 23
would be 1°, not 3° as Hultsch supposes.1 However, it is difficult to believe that Thales could have made the estimate of 1/720th of the sun’s circle known to the Greeks; if he had, it would be very strange that it should have been mentioned by no one earlier than Archimedes, and that Aristarchus should in the first instance have used the grossly excessive value of 2° which he gives as the angular diameter of the sun and moon in his treatise On the sizes and
distances of the sun and moon, and should have been left to dis-
cover the value of 4° for himself as Archimedes says he did.?
A few more details of Thales’ astronomy are handed down. He said of the Hyades that there are two, one north and the other south. According to Callimachus,* he observed the Little Bear ;
_. ‘he was said to have used as a standard [i.e. for finding the pole]
the small stars of the Wain, that being the method by which Phoenician navigators steer their course. According to Aratus® the Greeks sailed by the Great Bear, the Phoenicians by the Little Bear. Consequently it would seem that Thales advised the Greeks to follow the Phoenician plan in preference to their own. This use of the Little Bear was probably noted in the handbook under the title of Nautical Astronomy attributed by some to Thales, and by others to Phocus of Samos,*® which was no doubt intended to improve upon the Astronomy in poetical form attributed to Hesiod, as in its turn it was followed by the Astrology of Cleostratus.?
1 An estimate amounting to 1° is actually on record in Cleomedes (De motu circulari, ii. 3, p. 172. 25, Ziegler), who says that ‘ the size of the sun and moon
ike appears to our perception as 12 dactyli’._ Though this way of describing the angle follows the Babylonian method of expressing angular distances | between stars in terms of the e// (πῆχυς) consisting of 24 dactyli and equivalent to 2°, it does not follow that the estimate itself is Babylonian. For the same system of expressing angles may have been used by Pytheas and was certainly
used by Hipparchus (cf. Strabo, ii. 1. 18, p. 75 Cas., Hipparchiin Arati et Eudoxi phaenomena
comment. ii. 5. 1, Ὁ. 186. 11, Manit., and Ptolemy, Syzfazis vii. 1, vol. ii, pp. 4-8, Heib.). 2 Archimedes, ed. Heiberg, vol. ii, p. 248.19; The Works 07 Archimedes, ed. Heath, p. 223. 3 Schol. Arat. 172, p. 369. 24 (Vors. ii. 1*, p. 652). * In Diog. L. i. 23 (Vors. i?, p. 3. 14; cf. ii. 2, p. v). 5 Aratus, lines 27, 37-39; cf. Ovid, 77tstia iv. 3. 1-2: ‘ Magna minorque ferae, quarum regis altera Graias, ; Altera Sidonias, utraque sicca, rates’ ; Theo in Arati phaen. 27. 39: Scholiast on Plat. Rep. 600 A. δ Diog. L. i, p. 23; Simpl. # Phys.p. 23. 29; Plutarch, Pyth. or. 18, 402 F(Vors. i?, pp. 3. 125 11. 7, 13). 7 Diels, Vors. ii. 1°, p. 6525 cf. pp. 499, 502.
IV ANAXIMANDER
ANAXIMANDER of Miletus (born probably in 611/10, died soon after 547/6 B.C.), son of Praxiades, was a fellow citizen of Thales, with whom he was doubtless associated as a friend if not as a pupil. A remarkably original thinker, Anaximander may be regarded as the father or founder of Greek, and therefore of western, philosophy. He was the first Greek philosopher, so far as is known, who ventured to put forward his views in a formal written treatise. This was a work Adout Nature? though possibly that title was given to it, not by Anaximander himself, but only by later writers.* The amount of thought which went to its composition and the maturity of the views stated in it are indicated by the fact that it was not till the age of 64 that he gave it. to the world. The work itself is lost, except for a few lines amounting in no case to a complete sentence.
Anaximander boldly maintained that the earth is in the centre of the universe, suspended freely and without support,° whereas Thales regarded it as resting on the water, and Anaximenes as supported by the air. It remains in its position, says Anaximander, because it is at an equal distance from all the rest (of the heavenly bodies). Aristotle expands the explanation thus:’ ‘for that which is located in the centre and is similarly situated with reference to the extremities can no more suitably move up than
1 Themistius, Orationes, 36, p. 317 C (Vors. i*; p. 12. 43).
? Ibid. ; Suidas, 5. Ὁ.
® Zeller, Philosophie der Griechen, ἴδ, p. 197.
* Diog. L. ii. 2 (Vors. i?, p. 12. 7-10).
° Hippol. Refuz. i. 6. 3 (D.G. p. 559. 22; Vors. i*, p. 14. 5).
® Ibid.; cf. Plato’s similar view in Phaedo 108 E-109 A.
7 De caelo ii. 13, 295 Ὁ 10-16. It is true that Eudemus (in Theon of Smyrna, p- 198. 18) is quoted as saying that Anaximander held that ‘the earth is suspended freely and moves (κινεῖται) about the centre of the universe’; but there must clearly be some mistake here ; perhaps κινεῖται should be κεῖται (‘ lies’).
;
, β
5
3 : ᾿ ἶ ᾿
as
ANAXIMANDER 25
down or laterally, and it is impossible that it should move in opposite directions (at the same time), so that it must necessarily remain at rest.’ Aristotle admits that the hypothesis is daring and brilliant, but argues that it is not true: one of his grounds is amusing, namely, that on this showing a hungry and thirsty man with food and wine disposed at equal distances all round him would have to starve because there would be no reason for him to stretch his hand in one direction rather than another! (presumably the first occurrence of the well-known dilemma familiar to the schoolmen as the ‘ Ass of Buridan’).
According to Anaximander, the earth has the shape of a cylinder, round, ‘like a stone pillar’;* one of its two plane faces is that on which we stand, the other is opposite ;* its depth, moreover, is one- third of its breadth.*
Still more original is Anaximander’s conception of the origin and substance of the sun, moon, and stars, and of their motion. As there is considerable difference of opinion upon the details of the
_ system, it will be well, first of all, to quote the original authorities,
beginning with the accounts of the cosmogony.
‘ Anaximander of Miletus, son of Praxiades, who was the successor and pupil of Thales, said that the first principle (i.e. material cause) and element of existing things is the Infinite, and he was the first to introduce this name for the first principle. He maintains that it is neither water nor any other of the so-called elements, but another sort of substance, which is infinite, and from which all the heavens and the worlds in them are produced ; and into that from which existent things arise they pass away once more, — “as is ordained ; for they must pay the penalty and make reparation to one another for the injustice they have committed, according to the Sequence of time”, as he says in these somewhat poetical terms.’
1 Aristotle, De cae/o ii. 13, 295 Ὁ 32.
3 Hippol. Refus. i. 6. 3 (D.G. p. 559. 24; Vors. i?, p. 14.6); Aét. iii. το. 2 (D. G. p. 376; Vors. i*, p. 16. 34).
3 Hippol., loc. cit.
* Ps. Plut. Stromat. 2 (D.G. p. 579. 12; Vors. i?, p. 13. 34).
® Simplicius, ix Phys. p. 24. 13 (Vors. 15, p.13.2-9). The passage is from Theophrastus’s Phys. Ofin., and the words in inverted commas at all events are
_ Anaximander’s own. I follow Burnet (Zarly Greek Philosophy, p. 54) in making
the quotation begin at ‘as is ordained’; Diels includes in it the words just preceding ‘and into that from which...’
a6 ANAXIMANDER PARTI
‘ Anaximander said that the Infinite contains the whole cause of the generation and destruction of the All; it is from the Infinite that the heavens are separated off, and generally all the worlds, which are infinite in number. He declared that destruction and, long before that, generation came about for all the worlds, which arise in endless cycles from infinitely distant ages.’ ὦ
‘He says that this substance [the Infinite] is eternal and ageless, and embraces all the worlds. And in speaking of time he has in mind the separate (periods covered by the) three states of coming into being, existence, and passing away. ἢ
‘Besides this (Infinite) he says there is an eternal motion, in the course of which the heavens are found to come into being.’ ὃ
‘Anaximander says eternal motion is a principle older than the moist, and it is by this eternal motion that some things are generated and others destroyed.’
‘ He says that (the first principle or material cause) is boundless, in order that the process of coming into being which is set up may not suffer any check.’ ὅ
‘Anaximander was the first to assume the Infinite as first principle in order that he may have it available for his new births without stint.’ ®
‘ Anaximander ... said that the world is perishable.’ ἴ
‘Those who assumed that the worlds are infinite in number, as did Anaximander, Leucippus, Democritus, and, in later days, Epicurus, assumed that they also came into being and passed away, ad infinitum, there being always some worlds coming into being and others passing away; and they maintained that motion is eternal; for without motion there is no coming into being or passing away. ὃ
‘ Anaximander says that that which is capable of begetting the hot and the cold out of the eternal was separated off during the coming into being of our world, and from the flame thus produced a sort of sphere was made which grew round the air about the earth as the bark round the tree; then this sphere was torn off and
1 Ps. Plut. Stromat.2 (D.G. p. 579; Vors.i*®, p. 13. 29 sq.). This passage again is from Theophrastus.
2 Hippol. Refut. i. 6.1 (D. G. p. 559; Vors. i*, pp. 13. 44-14. 2).
Z ee 1) 6; ᾿: ive
ermias, /rris. 10 (D. G. p. 653; Vors. i*, p. 14. 21).
5 Aét. i. 3. 3 (D. G. Ὁ. 277 ΑΝ ἐδ; 14. An
δ Simplicius on De caelo, p. 615. 13 (Vors. 13, p. 15. 24). In this passage Simplicius calls Anaximander a ‘fellow citizen and friend’ of Thales (Θαλοῦ πολίτης καὶ ἑταῖρος) ; these appear to be the terms used by Theophrastus, to judge by Cicero’s equivalent ‘ popularis et sodalis’ (Acad. gr. ii. 37. 118).
7 Aét. ii. 4. 6 (D.G. p. 3315 Vors. 13, p. 15. 33).
8 Simplicius, 7 Phys. p, 1121. αὶ (Vors. i*, p. 15. 34-8).
.
CH. IV ANAXIMANDER 27
became enclosed in certain circles or rings, and thus were formed _ the sun, the moon, and the stars.’! _ *The stars are produced as a circle of fire, separated off from the _ fire in the universe and enclosed by air. They have as vents certain _ pipe-shaped passages at which the stars are seen; it follows that it is when the vents are stopped up that eclipses take place.’ *
‘ The stars are compressed portions of air, in the shape of wheels,
- filled with fire, and they emit flames at some point from small _ openings.’ 8 ΠΟ *The moon sometimes appears as waxing, sometimes as waning, to an extent corresponding to the closing or opening of the
passages.’ * _ Further particulars are given of the circles of the sun and moon, including the first speculation about their sizes:
‘The sun is a circle 28 times the size of the earth; it is like a wheel of a chariot the rim of which is hollow and full of fire, and lets the fire shine out at a certain point in it through an _ opening like the tube of a blow-pipe ; such is the sun.’® _ ‘The stars are borne by the circles and the spheres on which each (of them) stands.’ ὃ
1 Ps. Plut. Stromat. loc. cit. " Hippol. ἜΡΟΝ bs 4 (D.G. pp. 559 560; ai i*, p. 14. 8). Aét. ii. 13. 7 (D.G. p. 342; Vors. i*, Ὁ. 15. 39). ἢ * Hippol., loc. ἐς : . ᾿ς §& Aé€t. ii. 20. 1 (D. G. p. 348; Vors. i*, p. 16. 8). ἢ ® Aét. ii. 16. 5 (D.G. p. 345; Vors.i*, p. 15. 43. This sentence presents diffi- _ culties. It occurs in a collection of passages headed ‘ Concerning the motion of stars’, and reads thus: ᾿Αναξίμανδρος ὑπὸ τῶν κύκλων καὶ τῶν σφαιρῶν, ἐφ᾽ ὧν ἕκαστος βέβηκε, φέρεσθαι. If ἕκαστος Means ἕκαστος τῶν ἀστέρων, each of the _ stars, the expression ἐφ᾽ ὧν ἕκαστος βέβηκε, ‘on which each of them stands’ or ‘is fixed’, is certainly altogether inappropriate to Anaximander’s system; it ~ suggests Anaximenes’ system of stars ‘fixed like nails on a crystal sphere’; I am therefore somewhat inclined to suspect, with Neuhauser (Anaximander Milesius, Ρ. 362 note), that the words ἐφ᾽ ὧν ἕκαστος βέβηκε (if not καὶ τῶν σφαιρῶν also) are wrongly transferred from later theories to that of Anaximander. It occurred to me whether ἕκαστος could be ἕκαστος τῶν κύκλων, ‘each of the circles’ ; for it would be possible, I think, to regard the circles as ‘standing’ or ‘ being fixed’ on (imaginary) spheres in order to enable them to revolve about the axis of such spheres, it being difficult to suppose a wheel to revolve about its centre when it has no spokes to connect the centre with the circumference. Diels (‘Ueber Anaximanders Kosmos’ in Archiv fiir Gesch. d. Philosophie, x, 1897, p. 229) suggests that we may infer from the word ‘spheres’ here used that the _ tings are not separate for each star, but that the fixed stars shine through vents _ On one ring (which is therefore a sphere); the planets with their different motions _ would naturally be separate from this. I doubt, however, whether this is _ correct, since @// the rings are supposed to be like wheels; they are certainly not spheres. But no doubt the Milky Way may be one ring from which
28 ANAXIMANDER PART I
‘The circle of the sun is 27 times as large (as the earth and that) of the moon (is 19 times as large as the earth).’ }
‘ The sun is equal to the earth, and the circle from which the sun gets its vent and by which it is borne round is 27 times the size of the earth.’ ?
‘The eclipses of the sun occur through the opening by which the fire finds vent being shut up.’ 8
‘The moon is a circle 19 times as large as the earth; it is similar to a chariot-wheel the rim of which is hollow and full of fire, like the circle of the sun, and it is placed obliquely like the other ; it has one vent like the tube of a blowpipe; the eclipses of the moon depend on the turnings of the wheel.’ 5
‘The moon is eclipsed when the opening in the rim of the wheel is stopped up.’®
‘The sun is placed highest of all, after it the moon, and under them the fixed stars and the planets.’ ®
We are now in a position to make some comments. First, what is the nature of the eternal motion which is an older principle than water and by which some things are generated and others destroyed ? Teichmiiller held it to be circular revolution of the Infinite, which he supposed to be a sphere, about its axis ;’ Tannery adopted the same view.® Zeller® rejects this for several reasons. There is no evidence that Anaximander conceived the spherical envelope of fire to be separated off by revolution of the Infinite and spread out over the surface of its mass; the spherical envelope lay, not round the Infinite, but round the atmosphere of the earth, and it was only the world, when separated off, which revolved ; it is the world too, not the Infinite, which stretches at equal distances, and therefore in the shape of a sphere, round the earth as centre. Lastly, a spherical Infinite is in itself a gross and glaring contra- diction, which we could not attribute to Anaximander without a multitude of stars flame forth at different vents: this may indeed be the idea from which the whole theory started (Tannery, op. cit., Ρ. 91; Burnet, Zarly Greek Philosophy, p. 69).
1 Hippol., Refut. i. 6. 5 (D. G. p. 560; Vors. i*, p. 14. 12, and ii. 1°, p. 653).
? Aét. ii. 21.1 (D.G. p. 351; Vors. i®, pe 16. 11).
8 Aét. ii, 24. 2 (D.G. p. 354; Vors. 13, p. 16. 13).
* Aét. ii. 25. 1 (22. α. p. 355; Vors. i*, p. 16. 15).
5 Aét. ii. 29. 1 (D. G. p. 359; Vors. i*, p. 16. 19).
6 Aét. ii. 15.6 (D.G. p. 345; Vors. i*, p. 15. 41).
, Ὁ Teichmiiller, Studien zur Gesch. der Begriffe, Berlin, 1874, pp. 25 564.
® Tannery, op. cit., pp. 88 sqq. 9. Zeller, i°, p. 221.
~~
a le
Se a eee eT eS ae ee ΣΤῊ
CH. IV ANAXIMANDER 29
direct evidence. Tannery! gets over the latter difficulty by the assumption that the Infinite was not something infinitely extended in space but qualitatively indeterminate only, and in fact finite in
extension. This is rather an unnatural interpretation, especially
in view of what we are told of the ‘infinite worlds’ which arise
_ from the Infinite substance. The idea here seems to be that the
Infinite is a boundless stock from which the waste of existence is
continually made good? With regard to the ‘infinite worlds’ _ Zeller* held that they were an infinity of successive worlds, not an unlimited number of worlds existing, or which may exist, at _ the same time, though of course all are perishable; but in order
to sustain this view Zeller was obliged to reject a good deal of the
evidence. Burnet* has examined the evidence afresh, and adopts the other view. In particular, he observes that it would be very unnatural to understand the statement that the Boundless ἶ ‘encompasses the worlds’ of worlds succeeding one another in time; for on this view there is at a given time only one world
to ‘encompass’. Again, when Cicero says Anaximander’s opinion
‘was that there were gods who came into being, rising and setting _ at long intervals; and that these were the ‘innumerable worlds’ ® (cf. _ Aétius’s statement that,according to Anaximander, the ‘innumerable _ heavens’ were gods‘), it is more natural to take the long intervals _ as intervals of space than as intervals of time ;7 and, whether this is so or not, we are distinctly told in a passage of Stobaeus that ‘of those who declared the worlds to be infinite in number,
Anaximander said that they were at equal distances from one another’, a passage which certainly comes from Aétius.2 Neu- ~ hauser,? too, maintains that Anaximander asserted the infinity of worlds in two senses, holding both that there are innumerable worlds co-existing at one time and separated by equal distances, and that these worlds are for ever, at certain (long) intervals of
1 Tannery, op. cit., pp. 146, 147.
? Burnet, Zarly Greek Philosophy, p. 55.
5 Zeller, i5, pp. 229-36.
* Burnet, Zarly Greek Philosophy, pp. 62-6.
5 Cicero, De nat. deor. i. το. 25 (Vors. i*, p. 15. 27).
5 Aét. i. 7. 12 (D. G. p. 302; Vors. i*, p. 15. 26).
7 Probably, as Burnet says, Cicero found διαστήμασιν in his Epicurean source. 8. Aét. ii. 1. 8 (D. G. p. 329; Vors. i?, p. 15. 32).
* Neubauser, Anaximander Milesius, pp. 327-35.
30 ANAXIMANDER PART I
time,! passing away into the primordial Infinite, and others con- tinually succeeding to their places.”
The eternal motion of the Infinite would appear to have been the ‘separating-out of opposites’,? but in what way this operated is not clear. The term suggests some process of shaking and sifting as in a sieve.‘ Neuhduser® holds that it is not spatial motion at all, but motion in another of the four Aristotelian senses, namely generation, which takes the form of the ‘separating-out of opposites’, condensation and rarefaction incidentally playing a part in the process.
As regards the motion by which the actual condition of the world was brought about (the earth in the centre in the form of a flat cylinder, the sun, moon, and stars at different distances from the earth, and the heavenly bodies revolving about the axis of the universe), Neuhauser ὃ maintains that it was the motion of a vortex such as was assumed by Anaxagoras, the earth being formed in the centre by virtue of the tendency of the heaviest of the things whirled round in a vortex to collect in the centre. But there is no evidence of the assumption of a vortex by Anaximander; Neuhiuser relies on a single passage of Aristotle, which however — does not justify the inference drawn from it."
1 κατὰ τὴν τοῦ χρόνου τάξιν, Simpl. 7” Phys. p. 24. 20 (Vors. i*, p. 13. 9).
2 Cf. Simpl. 72 Phys. p. 1121. 5 (Vors. i*, p. 15. 34-8, quoted above, p. 26).
® of δὲ ἐκ τοῦ ἑνὸς ἐνούσας τὰς ἐναντιότητας ἐκκρίνεσθαι, ὥσπερ ᾿Αναξίμανδρός φησι, Aristotle, Phys. i. 4, 187 ἃ 20.
* Burnet, Zarly Greek Philosophy, p. 61.
δ᾽ Neuhauser, Anaximander Milesius, pp. 305-15.
ὁ Neuhduser, Anaximander Milesius, pp. 409-21.
7 The passage is Aristotle, De cae/o ii. 13, 295 ἃ 9sqq. It is there stated that ‘if the earth, as things are, is kept dy force where it is, it must also have come together (by force) through being carried towards the centre by reason of the whirling motion; for this is the cause assumed by everybody on the ground of what happens in fluids and with reference to the air, where the bigger and the heavier things are always carried towards the middle of the vortex. Hence it is that all who describe the coming into being of the heaven say that the earth came together at the centre; but the cause of its remaining fixed is still the subject of speculation. Some hold...’ Now Neuhauser paraphrases the passage thus: ‘All philosophers who hold that the world was generated or brought into being maintain that the earth is not only kept 4y force in the middle of the world, but was, at the beginning, also brought together by force. For all assign as the efficient cause of the concentration of the earth in the middle of the world a vortex (δίνη), arguing from what happens in vortices in water or air.” It is clear that Aristotle says no such thing. He says that the philosophers referred to assert that the earth comes together at the centre, but not that they hold that it is kept there 4y force ; indeed he expressly says later (295 b 10-16) that Anaxi-
a ΨΥ
ΨΥ Ἂς
CH.IV ANAXIMANDER 31
We come now to Anaximander’s theory of the sun, moon, and stars. The idea of the formation of tubes of compressed air within which the fire of each star is shut up except for the one opening is not unlike Laplace’s hypothesis with reference to the origin of Saturn’s rings.’ A question arises as to how, if rings constituting the stars are nearer than the circles of the sun and moon, they fail to obstruct the light of the latter. Tannery? suggests that, while of course the envelopes of air need not be opaque, the rarefied
fluid within the hoops, although called by the name of fire, may
also be transparent, and not be seen as flame except on emerging at the opening. The idea that the stars are like gas-jets, as it were, burning at holes in transparent tubes made of compressed air is a sufficiently original conception.
_ But the question next arises, in what position do the circles, wheels, or hoops carrying the sun, moon, and stars respectively revolve about the earth? Zeller and Tannery speak of them as ‘concentric’, their centres being presumably the same as the centre of the earth ; and there is nothing in the texts to suggest any other supposition. The hoops carrying the sun and moon ‘lie obliquely’, this being no doubt an attempt to explain, in addition to the daily rotation, the annual movement of the sun and the monthly move- ment of the moon. Tannery raises the question of the heights (‘hauteurs’) of these particular hoops, by which he seems to mean their dreadihs as they would be seen (if visible) from the centre. Thus, if the bore of the sun’s tube were not circular but flattened (like a hoop), in the surface which it presents towards the earth, to several times the breadth of the sun’s disc, it might be possible . to explain the annual motion of the sun by supposing the opening through which the sun is seen to change its position continually on the surface of the hoop. But there is nothing in the texts to support this. Zeller* feels difficulty in accepting the sizes of the hoops as given, on the supposition that the earth is the centre.
mander regarded the earth as remaining at the centre without any force to keep it there. Again ‘everybody’ is not ‘all philosophers’, but ‘ people in general’. Lastly, the tendency of the heavier things in a vortex to collect at the centre might easily suggest that the earth had come together in the centre because it was heavy, without its being supposed that a vortex was the only thing that could Cause it to come together.
* Tannery, op. cit., p. 88. 3. Ibid. p. 92.
* Zeller, i°, pp. 224, 225.
32 ANAXIMANDER PART I
For we are told that the sun’s circle or wheel is 27 or 28 times the size of the earth, while the sun itself is the same size as the earth; this would mean that the apparent diameter of the sun’s disc would be a fraction of the whole circumference of the ring represented by 1/287, that is, the angular diameter would be about 360°/88, or a little over 4°, which is eight times too large, and would be too great an exaggeration to pass muster even in those times. Zeller therefore wonders whether perhaps the sun’s circle should be 27 times the moon’s circle, which would make it 513 times the size of the earth. But the texts, when combined, are against this, and further it would make the apparent diameter of the sun much too small. According to Anaximander, the sun itself is of the same size as the earth; therefore, assuming d to be the diameter of the sun’s disc and also the diameter of the earth, the circumference of the sun’s hoop would be 5137rd, so that the apparent diameter of the sun would be about 1/1600th part of its circle, or less than half what it really is. Teichmiiller? and Neuhduser® try to increase the size of the sun’s hoop 3-1416 times, apparently by taking the diameter of the hoop to be 28 times the circumference of the earth, ‘because the measurement clearly depended on an unrolling’; but this is hardly admissible; the texts must clearly be comparing like with like. Sartorius* feels the same difficulty, and has a very interesting hypothesis designed to include provision for the sun’s motion in the ecliptic as well as the diurnal rotation. He bases himself on a passage of Aristotle which, according to a statement of Alexander Aphrodisiensis made on the authority of Theophrastus, refers to Anaximander’s system. Aristotle speaks of those who explain the sea by saying that
‘at first all the space about the earth was moist, and then, as it was dried up by the sun, one portion evaporated and set up winds and the turnings (τροπαί) of the sun and moon, while the remainder formed the sea’ ; 5
1 Teichmiiller, Studien zur Geschichte der Begriff, 1874, pp. 16, 17.
? Neuhauser, Anaximander Milesius, p. 371.
5. Sartorius, Die Entwicklung der Astronomte bei den Griechen bis Anaxagoras und Empedokles, pp. 29, 30.
* Aristotle, Metcorologica ii. 1, 353b 6-9. A note of Alexander (in Meteor. Ῥ.- 67.3; see D.G. p. 494; Vors. i’, p. 16. 45) explains the passage thus: ‘For, the space round the earth being moist, part of the moisture is then evaporated by the sun, and from this arise winds and the turnings of the sun and moon, the
Ε΄
CH. IV ANAXIMANDER 33
and again he says in another place :
‘The same absurdity also confronts those who say that the earth,
_ too, was originally moist, and that, when the portion of the world
_ immediately surrounding the earth was warmed by the sun, air was
produced and the whole heaven was thus increased, and that this is
_ how winds were caused and the turnings of the heaven brought _ about.’?
It is on these passages that Zeller® grounds his view that the _ heavens are moved by these winds (πνεύματα) and not by the eternal rotational movement of the Infinite about its axis assumed by Teichmiiller and Tannery; accordingly, Zeller cannot admit that the word τροπαΐ in these passages is used in its technical sense of ‘solstices’.* Sartorius, however, clearly takes the τροπαί to refer _ specially to the solstices (so does Neuhauser*), and he shows how the motions of the sun could be represented by two different but simultaneous revolutions of the sun’s wheel or hoop. Suppose the _wheel to move bodily in such a way that (1) its centre describes
a circle in the plane of the equator, the centre of which is the centre of the earth, while (2) the plane of the wheel is always at right angles to the plane of the aforesaid circle, and always _ touches its circumference; lastly, suppose the wheel to turn about
_ meaning being that it is by reason of these vapours and exhalations that the sun and moon execute their turnings, since they turn in the regions where they receive abundant supplies of this moisture ; but the part of the moisture which is left in the hollow places (of the earth) is the sea.’
1 Aristotle, Meteorologica ii. 2, 355 a 21. 3 Zeller, 15, p. 223.
3 Zeller (15, pp. 223, 224) has a note on the meanings of the word τροπή. Even in Aristotle it does not mean ‘solstice’ exclusively, because he speaks of ‘ rporai _of the stars’ (De caelo ii. 14, 296 Ὁ 4), “ τροπαί of the sun and moon’ (Meteor. ii. I, 353 b 8), and ‘rpomai of the heaven’ (according to the natural meaning of ras τροπὰς αὐτοῦ, 3558 25). It is true that τροπαΐ could be used of the moon in a sense sufficiently parallel to its use for the solstices, for, as Dreyer says (Planetary Systems, p. 17, note 1), the inclination of the lunar orbit to that of the sun is so small (se) that the phenomena of ‘turning-back’ of sun and moon are very similar. But the use of the word by Aristotle with reference to the stars and the Aeaven shows that it need not mean anything more than the ‘turnings’ or revolutions of the different heavenly bodies. Zeller’s view is, I think, strongly supported by a passage in which Anaximenes is made to speak of Stars ‘executing their turnings’ (τροπὰς ποιεῖσθαι Aét. ii. 23. 1, D. G. p. 352) and the passage in which Anaximander himself is made to say that the eclipses of tl “agg rot on ‘the turnings (τροπάς) of its wheel’ (Aét. ii, 25.1, D. G.
355 D 22).
* Neuhdauser, op. cit., p. 403.
1410 D
34 ANAXIMANDER PARTI
its own centre at such speed that the opening representing the sun completes one revolution about the centre of the wheel in a year, and suppose the centre of the wheel to describe the circle in the plane of the equator at uniform speed in one day. In the figure appended, Z represents the earth, the C’s are posi- tions of the centre of the sun’s hoop or wheel ; S, represents the sun’s position at the vernal equinox ;
Se ᾿ “ τῆ οἱ summer solstice ; Ss δ: Ἄ τ δ autumnal equinox ; S, " i ;: winter solstice.
Fig. 2.
At the winter solstice the sun is south of the equator, at the summer solstice north of it, and the diameter of the wheel corresponds to an angle at E& which is double of the obliquity of the ecliptic, say 47°. . Now, as the diameter of the sun’s wheel is 28 times the diameter of the earth, i.e. of the sun itself (which is the same size as the earth), the angular diameter of the sun at & will be about 47°/28 or 1°41’. This is still far enough from the real approximate value 3°, but it is much nearer than the 4° obtained from the hypothesis of a hoop with its centre at the centre of the earth.
CH. IV ANAXIMANDER 35
Let us consider what would be the distance of the sun from the earth on the assumption that the sun’s diameter (supposed to be equal to that of the earth) subtends at Z an angle of 13°. If d be the diameter of the earth, and D the distance of the sun from the earth, we shall have approximately 360 d/12 = 27D,
or D = 34-4 times the diameter of the earth.
But Sartorius’s hypothesis is nothing more than an ingenious guess, as the texts give no colour to the idea that Anaximander
Fig. 3.
intended to assign a double motion to the sun, nor is there anything to suggest that the hoops of the sun and moon moved in any different way from those of the stars, except that they were both ‘placed obliquely’. The hypothesis of concentric rings with centres at the centre of the earth seems therefore to be the simplest. Neuhiuser,} in his attempted explanation of Anaximander’s theory _ of the sun’s motion, contrives to give to τροπαὶ ἡλίου the technical _ meaning of solstices, while keeping the ring concentric with the earth. The flat cylinder (centre O) is the earth, V.P. and S.P. are the north and south poles, the equator is the circle about 4A’ as
? Neuhdauser, pp. 405-8 and Fig. 2 at end. D2
46 ANAXIMANDER PARTI
diameter and perpendicular to the plane of the paper. Neuhduser then supposes the plane of the sun’s circle or hoop to be differently inclined to the circle of the equator at different times of the year, making with it at the summer solstice and at the winter solstice angles equal to the obliquity of the ecliptic in the manner shown in the figure, where the circle on 4A’ as diameter in the plane of the paper is the meridian circle and SS’ is the diameter of the sun’s ring at the summer solstice, BB’ the diameter of the sun’s ring at the winter solstice. Between the extreme positions at the solstices the plane of the sun’s hoop changes its inclination slightly day by day, its section with the meridian plane moving gradually during one half of the year from the position S.S’ to the position B&B’, and during the other half of the year from BB’ back to SS” As it approaches the summer-solstitial position, it is prevented from swinging further by the winds, which are caused by exhalations, and which by their pressure on the sun’s ring force it to swing back again. The exhalations and winds only arise in the regions where there is abundant water. Neuhduser supposes that Anaximander had the
Mediterranean and the Black Sea in mind, and that their positions —
sufficiently ‘ correspond’ (?) to the summer-solstitial position SS’ to enable the winds to act as described. There is no sea in such a position as would enable winds arising from it to repel the sun’s ring in the reverse direction from BB’ to SS’; consequently Neuhdauser has to suppose that the ring has an automatic tendency to swing towards the position SS’ and that it begins to go back from BB’, of itself, as soon as the force of the wind which repelled it from SS’ ceases to operate. There is, however, no evidence in the texts to confirm in its details this explanation of the working of Anaximander’s system ; on the contrary, there seems to be positive evidence against it in the phrase ‘ /yizg obliquely ’, used of the hoops of the sun and moon, which suggests that the hoops remain at fixed inclinations to the plane of the equator instead of oscillating, as Neuhiuser’s theory requires, between two extreme positions rela- tively to the equator.
In any case Anaximander’s system represented an enormous advance in comparison with those of the other Ionian philosophers in that it made the sun, moon, and stars describe circles, passing right under the earth (which was freely suspended in the middle),
δον ὦ ἃ
ek ίλρων. ςς ο..
—
cH.IV ANAXIMANDER . 37
instead of moving laterally round from the place of setting to the place of rising again.
We are told by Simplicius that
‘ Anaximander was the first to broach the subject of sizes and
distances ; this we learn from Eudemus, who however refers to the reans the first statement of the order (of the planets) in 71
space. This brings us back to the question of the sizes of the hoops of
_ the sun and moon as given by Anaximander. We observe that in
one passage the sun’s circle is said to be 28 times as large as the earth, while in another the circle ‘from which it gets its vent’ is 27 times as large as the earth. Now, on the hypothesis of concentric rings, we, being in the centre, of course see the inner circumference at the place where the sun shines through, the
_ sun’s light falling, like a spoke of the wheel, towards the centre.
The words, then, used in the second passage, referring to the circle
Srom which the sun gets tts vent, suggest that the ‘27 times’ refers _ to the inner circumference of the wheel, while the ‘28 times’ refers _ to the outer ;? the breadth therefore of the sun’s wheel measured _ in the direction from centre to circumference is equal to once the
diameter of the earth. A like consideration suggests that it is the outer circumference of the moon’s hoop which is 19 times the size of the earth, and that the zaner circumference is 18 times the size of the earth ; nothing is said in our texts about the size of the moon itself. Nor are we told the size of the hoops from which the stars shine, but, as they are in Anaximander’s view nearer to the earth
1 Simplicius on De caelo, p. 471. 4,ed. Heib. (Vors. i*, p. 15.47). Simplicius adds: ‘ Now the sizes and distances of the sun and moon as determined up to now were ascertained (by calculations) starting from (observations of) eclipses, and the discovery of these things might reasonably be supposed to go back as far as Anaximander.’ If by ‘these things’ Simplicius means the use of the phenomena of eclipses for the purpose of calculating the sizes and distances of the sun and moon, his suggestion is clearly inadmissible. On Anaximander’s theory eclipses of the sun and moon were caused by the stopping-up of the vents in their respective wheels through which the fire shone out ; moreover, the moon was itself bright and was not an opaque body receiving its light from the sun, notwithstanding the statement of Diogenes Laertius (ii. 1; Vors. i*, pp. 11. 40- 12. 1) to the contrary; it is clear, therefore, that Anaximander’s estimates of sizes and distances rested on no such basis as the observation of eclipses afforded to later astronomers.
® Diels, ‘ Uber Anaximanders Kosmos’ in Archiv fiir Gesch. d. Philosophie, x, 1897, p. 231; cf. Tannery, p. 91.
48 ANAXIMANDER PART I
than the sun and moon are, it is perhaps a fair inference that he would assume for a third hoop or ring containing stars an inner circumference representing 9 times the diameter of the earth ; the three rings would then have inner circumferences of 9, 18, 27, being multiples of 9 in arithmetical progression, while 9 is the square of 3; this is appropriate also to the proportion of 1:3 between the depth of the disc representing the earth and the diameter of one of its faces. These figures suggest that they were not arrived at by any calculation based on geometrical construc- tions, but that we have merely an illustration of the ancient cult of the sacred numbers 3 and ο. 3 is the sacred number in Homer, g in Theognis, 9 being the second power of 3. The cult of 3 and its multiples 9 and 27 is found among the Aryans, then among the Finns and Tartars,and next among the Etruscans (the Semites connected similar ideas with 6 and 7). Therefore Anaximander’s figures really say little more than what the Indians tell us, namely that three Vishnu-steps reach from earth to heaven.
The story that Anaximander was the first to discover the gnomon*® (or sun-dial with a vertical needle) is incorrect, for Herodotos says that the Greeks learnt the use of the guomon and the golos from the Babylonians.* Anaximander may, however, have been the first to ‘introduce’ * or make known the gnomon in Greece, and to show on it ‘ the solstices, the times, the seasons, and the equinox’. He is said to have set it up in Sparta.® He is also credited with constructing a sphere to represent the heavens,’ as was Thales before him.®
But Anaximander has yet another claim to undying fame. He was the first who ventured to draw a map of the inhabited earth. The Egyptians had drawn maps before, but only of particular dis- tricts ;1° Anaximander boldly planned out the whole world with ‘the circumference of the earth and of the sea’.14 Hecataeus, a much-travelled man, is said to have corrected Anaximander’s map,
1 Diels, loc. cit., p. 233. 2 Diog. L. ii. 1 (Vors. i*, p. 12. 3). 8. Herodotus, ii. 109. 4 εἰσήγαγε, Suidas (Vors. 15, p. 12. 18). δ Euseb. Praep. Evang. x. 14. 11 (Vors. i*, p. 12. 24).
δ Diog. L. ii. 1. 7 Ibid. ii. 2. 8. Cic. De rep. i. 14. 22.
* Agathemerus (from Eratosthenes), i. 1 (Vors. i?, p. 12. 36). 19 Gomperz, Griechische Denker, 18, pp. 41, 422. 1 Diog. L. ii. 2 (Vors. 15, Ὁ. 12. 5).
ANAXIMANDER 39
‘so that it became the object of general admiration. According to another account, Hecataeus left a written description of the world based on the map. In the preparation of the map Anaximander _ would of course take account of all the information which reached his Ionian home as the result of the many journeys by land and sea undertaken from that starting-point, journeys which extended to the limits of the then-known world ; the work involved of course an attempt to estimate the dimensions of the earth. We have, however, no information as to his results.*
Anaximander’s remarkable theory of evolution does not concern us here.?
-_10On Anaximander’s map see Berger, Geschichte der wissenschaftlichen _Erdkunde der Griechen, 2 ed., 1903, pp. 35 544. __ 53 See Plut. Symp. viii. 8. 4 ( Vors.i*, p. 17.24) ; Aét. v. 19.4 (D. G. p. 430; Vors. 2 B17 18); Ps. Plut. Stromat. 2 (D. G. p. $79) ; Hippol. Refut. i. 6. 6 (D. G. ; 560). According to Anaximander, animals first arose from slime evaporated the sun; ote τῷ first lived in the sea and had prickly coverings; men at first resembled fishes.
ν ANAXIMENES
For Anaximenes of Miletus (whose date Diels fixes at 585/4- 528/4 B.C.) the earth is still flat, like a table,’ but, instead of resting on nothing, as with Anaximander, it is supported by air, riding upon it, as it were. Aristotle explains this assumption thus :*
‘Anaximenes, Anaxagoras, and Democritus say that its flatness is what makes it remain at rest; for it does not cut the air below it but acts like a lid to it, and this appears to be characteristic of those bodies which possess breadth. Such bodies are, as we know, not easily displaced by winds, because of the resistance they offer. The philosophers in question assert that the earth resists the air below it, in the same way, by its breadth, and that the air, on the other hand, not having sufficient space to move from its position, remains in one mass with that which is below it, just as the water does in water-clocks.’
The sun, moon, and stars are evolved originally from earth; for it is from earth that moisture arises ; then, when this is rarefied, fire is produced, and the stars are composed of fire which has risen aloft. The sun, moon, and stars are all made of fire, and they ride on the air because of their breadth. The sun is flat like a leaf ;® it derives its very adequate heat from its rapid motion.’ The stars, on the other hand, fail to warm because of their distance.®
The stars are fastened on a crystal sphere, like nails or studs.°
1 Aét. iii. 10. 3 (D.G. p. 377; Vors. 13, p. 20. 26). ® Ps. Plut. Stromat. 3 (1). Ο. p. 580; Vors. i’, p. 18.27); Hippol. Refut. i. 7. 4 (ῦ. G. p. 560; Vors. i*, p. 18. 40); Aét. iii. 15. 8 (D. G. p. 380; Vors. 1, . 20. 34). He De caelo ii. 13, 294 Ὁ 13 (Vors. i*, p. 20. 27). * Ps, Plut. Stromat. 3 (D.G. p. 580; Vors. i*, p. 18.27); Hippol. Refud. i. 7.5 (D.G. p. 561; Vors. i*, p. 18. 42). ν δ Hippol., loc. cit. (Vors. 15, p. 18. 41). 6 Aét. ii, 22. 1 (D. G. p. 352; Vors. 15, p. 20. 5). 7 Ps. Plut. Stromat. 3 (1). G. p. 580; Vors. i*, p, 18. 28). 8. Hippol., loc. cit. ( Vors. i*, p. 19. 1). 9. Aét. 11, 14.3 (D. G. p. 3445 Vors. 13, p. 19. 38).
ANAXIMENES 41
_ The stars do not move or revolve under the earth as some suppose, gut round the earth, just as a cap can be turned round the head. Phe sun i is hidden from sight, not because it is under the earth, but Ee ecause it is covered by the higher parts of the earth and because 5 distance from us is greater.' With this statement may be com- d the remark of Aristotle that
δι τ πον of the ancient meteorologists were persuaded that the sun is ποῖ carried under the earth, but round the earth, and in particular
_our northern portion of it, and that it disappears and produces night ‘because the earth is lofty towards the north.”?
es * 4
‘Th allusion is also to Anaximenes when we are told that some (ie. Anaximenes) make the universe revolve like a millstone (μυλοειδῶς), others (i.e. Anaximander) like a wheel.* _ Now it is difficult to understand how the stars which, being fixed ἢ a crystal sphere, move bodily with it round a diameter of the sphere, and which are seen to describe circles cutting the plane of e horizon at an angle, can do otherwise than describe the portion of their paths between their setting and rising again by passing 4 er the earth; and all sorts of attempts have been made to ‘explain the contradiction. Schaubach pojnted out that the circles ‘described by the stars could not all converge and meet, say, on the ‘horizon to the north; for then they could not be parallel.* Ottingey® supposed that the attachment of the stars to the crystal sphere only held good while they were above the horizon; then, when they reached the horizon, they became detached and passed round in the plane of the horizon till they reached the east again! _ _ Zeller, Martin, and Teichmiiller all have explanations which are More or less violent attempts to make ‘under’ mean pot exactly ‘under’, but something else. Teichmiiller,* to explain the simile of the cap, observes that the ancients wore their caps, not as we wear our hats, but tilted back on the neck. The simile of the cap worn
J Hippol., loc. cit, (Vors. i*, pp. 18. 45-19. 1); cf. Aét. ii, 16. 6 (D.G. p. 346; Vers i’, Ρ. 19. 39)- 3. Aristotle, Meteorologica ii. 1, 354. 28. 5. Aét. ii. 2. 4 (D. G. p. 329 Ὁ, note; Vors. i*, p. 19. 32). 45 Geschichte der griechischen Astronomie bis auf Eratosthenes,
uoted by Sartorius, op. cit; p, 33. uller, Studien sur Geschichte der Begriffe, 1874, p. 100.
42 ANAXIMENES Ρ ΤΙ
in this way would no doubt be appropriate if Anaximenes >ied confined his comparison to some stars only, namely those # ΠῚ north which are always above the horizon and never set; b» th does not make this limitation; and this view of the cap doe® ,.ἢ
correspond very well to the revolution ‘like a millstone’. ea
More important is the distinction between the motion of 2 fixed stars, which are fastened like nails on the spheres “ἢ the motion of the sun and moon. Anaximenes says that ἃ
‘The sun and the moon and the other stars float on the air account of their breadth.’ 1
This is intelligible as regards the sun, because it is like a leaf; b
as regards ‘the other stars’ it seems clear that floating on the aix inconsistent with their being fastened to the heavenly sphere ; it, almost necessary therefore to suppose that ‘the other stars’ q here, not the fixed stars, but the planets, and that this ‘ floating « the air’ is a hypothesis to explain the disagreement between t observed motions of the sun, moon, and planets on the one han and the simple rotation of the stars in circles on the other. We ai told in another place that, while Anaximenes said that the stars ar, fastened like nails on the crystal sphere, ‘some’ say that they arc ‘leaves of fire, like pictures’ ;? it is tempting, therefore, to read} instead of ἔνιοι in the nominative, the accusative ἐνίους (ἀστέρας), when the meaning would be ‘ but that some of the stars are leaves of fire’, &c. The idea that the planets are meant in the above passage is further supported by another statement that
‘The stars execute their turnings (τὰς τροπὰς ποιεῖσθαι) in conse- quence of their being driven out of their course by condensed air which resists their free motion.’ 3:
It seems clear that the ‘turnings’ here referred to are not the
‘solstices’, but simply the turnings of the stars in the sense of their
revolution in their respective orbits, so far as they are not fixed on
the crystal sphere;* that is to say, the statement refers to the planets only.
1 Hippol. Refut. i. 7. 4
3. Aét. ii. 14. 4 (D.G. p.
»G. p.
3 Aét. ii. 23. 1(D. * Zeller, 15, p. 250.
(D. 561; Vors. iP. 18. 41).
344 ors. it, p, 19. 38). seat Vors. i*, p. 20. 5).
Se Ue
cH ANAXIMENES 43
rece’ 7ould seem certain therefore that Anaximenes was the first one. ‘inguish the planets from the fixed stars in respect of their οἵ lar movements, which he accounted for in the same way as _iotions of the sun and moon. This being so, it seems not wo’ sible that the passages about the sun and the stars not Ἐπ 6 under, but laterally round, the earth refer exclusively to ἘΠῚ 4n, moon, and planets;’ the fact of their floating on the air -* t be supposed to be a reason why they should not ever fall ‘5: w the earth, which itself rests on the air, and in this way the ee culty with regard to the motion of the fixed stars would £ ppear.
», snother improvement on the system of Anaximander is the ΠΣ gation of the stars to a more distant region than that in which @ sun moves. Anaximander had made the sun’s wheel the most ~~ 0te, the moon’s next to it, and those of the stars nearer still _ the earth; Anaximenes, however, explains that the stars do not ' e warmth because they are too far off, and with this may be ᾿ς mpared his statement that _ ‘The rotation which is the furthest away from the earth is (that _ ) the heaven,’?
‘which view is attributed to him in common with Parmenides. _ Anaximenes made yet another innovation of some significance. _ He said that
‘ There are also, in the region occupied by the stars, bodies of an earthy nature which are carried round along with them,’ *
and that,
‘While the stars are of a fiery nature, they ‘also include (or _ contain) certain earthy bodies which are carried round along with them but are not visible.’ 5
Zeller® interprets these passages as ascribing an earthy nucleus to the stars; and this is not unnaturally suggested by the second of the two passages. But the first passage suggests another possible
1 This was the suggestion of Heeren (Stobaeus, i, p. 511). ® Aét. ii. 11. 1 (D.G. p. 339; Vors. i*, p. 19. 34).
3 Hippol. Refut. i. 7. 5 (2. σ. p. 561; Vors. i, p. 18. 44). * Aét. ii. 13. 10 (2. G. p. 342; Vors. i*, p. 19. 36).
5 Zeller, i*, pp. 247, 248.
44 ANAXIMENES PAR'I
interpretation ; bodies of an earthy nature iz the region occufed by the stars (ἐν τῷ τόπῳ τῶν ἀστέρων) might be separate frm them and not ‘contained in them’, although carried round wih them. ‘The stars’ in the two passages no doubt include the sm and moon; but the sun is flat like a leaf; why then shotd Anaximenes attach to it an earthy substance as well? The object of the invisible bodies of an earthy nature carried round along with ‘the stars’ is clearly to explain eclipses and the phases of the moon. If, then, Anaximenes supposed that one side in both the sun and the moon was bright and the other dark, his idea would doubtless be that they might sometimes turn their dark side to us in such a way as to hide from us more or less the bright side. (This was the idea of Heraclitus, though with him the heavenly bodies had not a flat surface but were hollowed out like a basin or bowl.) But the phenomena of eclipses are more simply accounted for if we suppose the earthy bodies of Anaximenes to be separate from the sun and moon, and to get in front of them; we need not therefore hesitate to attribute to him this fruitful idea which ultimately led to the true explanation. Anaxagoras said that the moon is eclipsed because the earth is interposed, but, not being able to account for all the phenomena in this way, he conceived that eclipses were also sometimes due to obstruction by bodies ‘below the moon’, which he describes in almost the same words as Anaximenes, namely as ‘certain bodies (in the region) below the stars which are carried round with the sun and moon and are invisible to us’. Clearly therefore Anaxagoras was indebted to Anaximenes for this con- ception ; and again the réle of the counter-earth in the Pythagorean system is much the same as that of the ‘earthy bodies’ now in question.
Tannery ' goes further and maintains that Anaximenes’ hypothesis was bound to lead to the true explanation of eclipses. ‘ For, if any one asked himself why these dark bodies were not seen at all, the question of their being illuminated by the sun would present itself, and it was easy to recognize that, under the most general conditions, the phenomena which such a dark body would necessarily present were really similar to the phases of the moon. From this to the
1 Tannery, Pour l'histoire de la science helldne, pp. 153, 154.
.
. recognition of the fact that the moon itself is opaque there was only one step more. The réle of the moon in regard to the eclipses _ of the sun was easy to deduce, while the question of the lighting _ up of the moon by the sun at night naturally brought into play the _ shadow of the earth and, through that, led to the discovery of the
cause of eclipses of the moon. The hypothesis then of Anaximenes _ has a true scientific character, and constitutes for him a title to fame, the more rare because the conception appears to have been absolutely original, while his other ideas are not in general of the same stamp.’ While the successive steps towards the discovery _ of the truth may no doubt have been taken in the order suggested,
it must, I think, be admitted that, at the point where the question of the illumination of the opaque bodies by the sun would present
: CH. V ANAXIMENES 45
— μους ὧν ΡῈ
itself (‘se posait’), a very active imagination would be required to
suggest the transition to this question ; and, even after the transition _ was made, it would be necessary to assume further that the opaque _ bodies are spherical in form, an assumption nowhere suggested by _ Anaximenes.
Tannery ' adds that the only feature of Anaximenes’ system that was destined to an enduring triumph is the conception of the stars being fixed on a crystal sphere as in a rigid frame. Although attempts were made later to arrive at a more immaterial and less gross conception of the substance rigidly connecting the fixed stars, the character of this connexion was not modified, and the rigidity of the sphere really remained the fundamental postulate of all astronomy up to Copernicus. The exceptions to the general adoption of this view were, curiously enough, the Ionian physicists of the century immediately following Anaximenes.
It would appear that Anaximenes anticipated the Pythagorean notion that the world breathes, for he says:
‘Just as our soul, being air, holds us together, so does breath and air encompass the whole world.’ 3
1 Tannery, op. cit., p. 154. 3 Fragment in Aét. i. 3. 4 (D.G. p. 278; Vors. i*, p. 21. 17).
VI PYTHAGORAS
PYTHAGORAS, undoubtedly one of the greatest names in the history of science, was an Ionian, born at Samos about 572 B.C., the son of Mnesarchus. He spent his early manhood in Samos, removed in about 532 B.C. to Croton, where he founded his school, and died at Metapontium at a great age (75 years according to one authority, 80 or more according to others). His interests were as various as those of Thales, but with the difference that, whereas Thales’ knowledge was mostly of practical application, with Pythagoras the subjects of which he treats become sciences for the first time. Mathematicians know him of course, mostly or exclusively, as the reputed discoverer of the theorem of Euclid I. 47; but, while his share in the discovery of this proposition is much disputed, there is no doubt that he was the first to make theoretical geometry a subject forming part of a liberal education, and to investigate its first principles.1 With him, too, began the Theory of Numbers. A mathematician then of brilliant achieve- ments, he was also the inventor of the science of acoustics, an astronomer of great originality, a theologian and moral reformer, founder of a brotherhood ‘ which admits comparison with the orders of mediaeval chivalry.’ ?
The epoch-making discovery that musical tones depend on numerical proportions, the octave representing the proportion of 2:1, the fifth 3:2, and the fourth 4: 3, may with sufficient certainty be attributed to Pythagoras himself,’ as may the first exposition of the theory of means, and of proportion in general applied to commensurable quantities, i.e. quantities the ratio between which can be expressed as a ratio between whole numbers. The all-
? Proclus, Comm. on Eucl. I, Ὁ. 65. 15-19.
3 Gomperz, Griechische Denker, 15, pp. 80, 81. 8. Burnet, Early Greek Philosophy, p. 118.
PYTHAGORAS 47
pervading character of number being thus shown, what wonder - that the Pythagoreans came to declare that number is the essence of all things? The connexion so discovered between number and music would also lead not unnaturally to the idea of the ‘harmony of the heavenly bodies’.
Pythagoras left no written exposition of his doctrines, nor did _ any of his immediate successors in the school; this statement is _ true even of Hippasus, about whom the different stories arose _ (1) that he was expelled from the school because he published _ doctrines of Pythagoras,! (2) that he was drowned at sea for revealing the construction of the dodecahedron in a sphere and claiming it as his own,? or (as others have it) for making known the discovery of the irrational or incommensurable.* Nor is the absence of any written record of early Pythagorean doctrine to _ be put down to any pledge of secrecy binding the school; there _ does not seem to have been any secrecy observed at all unless perhaps in matters of religion or ritual; the supposed secrecy _ seems to have been invented to explain the absence of any trace _ of documents before Philolaus. The fact appears to be merely that oral communication was the tradition of the school, and the _ closeness of their association enabled it to be followed without _ inconvenience, while of course their doctrine would be mainly too abstruse to be understood by the generality of people outside.
Philolaus was the first Pythagorean to write an exposition of the Pythagorean system. He was a contemporary of Socrates and Democritus, probably older than either, and we know that he lived in Thebes in the last decades of the fifth century.*
It is difficult in these circumstances to disentangle the portions of the Pythagorean philosophy which may safely be attributed to the founder of the school. Aristotle evidently felt this difficulty ; he clearly knew nothing for certain of any ethical or physical doctrines going back to Pythagoras himself; and, when he speaks of the Pythagorean system, he always refers it to ‘ the Pythagoreans’, Ἷ sometimes even to ‘the so-called Pythagoreans’.6 The account | 2 Clem. Stromat. v. 58 (Vors. i®, p. 30.18); Iamblichus, Vit. Pyth. 246, 247 (Vors. i, p. 30. 10, 14).
* Iamblichus, Vit. Pyth. 88 (Vors. 15, p. 30. 2).
* Ibid. 247 (Vors. i*, p. 30. 17). * Zeller, i°, pp. 337, 338. 5 Burnet, Early Greek Philosophy, p. 100.
48 PYTHAGORAS PART:
which he gives of the Pythagorean planetary system correspond: to the system of Philolaus as we know it from the Dorographi.
For Pythagoras’s own system, therefore, that of Philolaus afford: no guide; we have to seek for traces, in the other writers of the end of the sixth and the beginning of the fifth centuries, of opinions borrowed from him or of polemics directed against him. On thess principles we have seen reason to believe that he was the first tc maintain that the earth is spherical and, on the basis of thi: assumption, to distinguish the five zones.
How Pythagoras came to conclude that the earth is spherica in shape is uncertain. There is at all events no evidence that he borrowed the theory from any non-Greek source. On the assump. tion, then, that it was his own discovery, different suggestions ὃ have been put forward as to the considerations by which Pythagoras convinced himself of its truth. One suggestion is that he may have based his opinion upon the correct interpretation of phenomena and above all, on the round shadow cast by the earth in the eclipses of the moon. But it is certain that Anaxagoras was the first te suggest this, the true explanation of eclipses. The second possibility is that Pythagoras may have extended his assumption of a spherical sky to the separate luminaries of heaven; the third is that hi: ground was purely mathematical, or mathematico-aesthetical, and that he attributed spherical shape to the earth for the simple reason that ‘the sphere is the most beautiful of solid figures’ I prefe: the third of these hypotheses, though the second and third have the point of contact that the beauty of the spherical shape may have
1 Tannery, op. cit., p. 203.
* The question is discussed by Berger (Geschichte der wissenschaftlichen Erdkunde der Griechen, pp. 171-7) who is inclined to think that, along with the facts about the planets and their periods discovered, as the result of observations continued through long ages, by the Egyptians and Babylonians, the doctrine οἱ a suspended spherical earth also reached the Greeks from Lydia, Egypt, οἱ Cyprus. Berger admits, however, that Diodorus (ii. 31) denies to the Babylonians any knowledge of the earth’s sphericity. Martin, it is true, in a paper quoted by Berger (p. 177, note), assumed that the Egyptians had grasped the idea οἱ a spherical earth, but, as Gomperz observes (Grtechische Denker, i®, p. 430), this assumption is inconsistent with the Egyptian representation of the earth's shape as explained by one of the highest authorities on the subject, Maspero, in his Hist. ancienne des peuples de l’ Orient classique, Les origines, pp. 16, 17.
8. Gomperz, Griechische Denker, 15, p. 90. :
4 Diog. L. viii. 35 (Vors. 13, p. 280. 1) attributes this statement to the Pythagoreans,
Ι CH. VI PYTHAGORAS 49
4
ὲ dictated its application doth to the universe and to the earth. But, bs whatever may have been the ground, the declaration that the earth ‘ is spherical was a great step towards the true, the Copernican _ view of the universe.!_ It may well be (though we are not told) that Pythagoras, for the same reason, gave the same spherical _ shape to the sun and moon and even to the stars, in which case _ the way lay open for the discovery of the true cause of eclipses and _ of the phases of the moon. _ There is no doubt that Pythagoras’s own system was geocentric. _ The very fact that he is credited with distinguishing the zones is an indication of this; the theory of the zones is incompatible with _ the notion of the earth moving in space as it does about the central _ fire of Philolaus. But we are also directly told that he regarded _ the universe as living, intelligent, spherical, enclosing the earth _ in the middle, the earth, too, being spherical in shape.* Further, _ it seems clear that he held that the universe rotated about an axis _ passing through the centre of the earth. Thus we are told by Aristotle that
‘Some (of the Pythagoreans) say that ¢¢me is the motion of the whole (universe), others that it is the sphere itself’ ; ὃ
and by Aétius that
᾿ς ‘Pythagoras held time to be the sphere of the enveloping eaven).’ +
᾿ς Alemaeon, a doctor of Croton, although expressly distinguished _ from the Pythagoreans by Aristotle,° is said to have been a pupil _ of Pythagoras ;*® even Aristotle says that, in the matter of the
Pythagorean pairs of opposites, Alemaeon, who was a young man *
_ when Pythagoras was old, expressed views similar to those of the _ Pythagoreans, ‘ whether he got them from the Pythagoreans or they | from him’. Hence he was clearly influenced by Pythagorean
i] δ
* Gomperz, Griechische Denker, i*, p. 90.
® Alexander Polyhistor in Diog. L, viii.
5 Aristotle, Phys. iv. 10, 218 a 33.
* Aét. i. 21. 1 (D.G. p. 318; Vors. i*, p. 277. 19).
® Aristotle, Metaph. A. 5, ee 27-31.
5 Diog. L. viii. 83 (Vors. i*, p. 100. 19); Iamblichus, #4. Pyth. 104. 7 Aristotle, Metaph. i. 5, οἶδα 28
1410 Ἑ
5ο PYTHAGORAS PART I
doctrines. Now the doxographers’ account of his astronomy includes one important statement, namely that
‘Alcmaeon and the mathematicians hold that the planets have a motion from west to east, in a direction opposite to that of the fixed stars.’ ἢ
Incidentally, the assumption of the motion of the fixed stars suggests the immobility of the earth. But this passage is also the first we hear of the important distinction between the diurnal revolution of the fixed stars from east to west and the independent movement of the planets zz the opposite direction; the Ionians say nothing of it (though perhaps Anaximenes distinguished the planets as having a different movement from that of the fixed stars); Anaxagoras and Democritus did not admit it; the discovery, therefore, appears to belong to the Pythagorean school and, in view of its character, it is much more likely to have been made by the Master himself than by the physician of Croton. For the rest of Alcmaeon’s astronomy is on a much lower level ; he thought the sun was flat,? and, like Heraclitus, he explained eclipses and the phases of the moon as being due to the turning of the moon’s bowl-shaped envelope.* It is right to add that Burnet® thinks
that the fact of the discovery in question being attributed to ©
Alcmaeon implies that it was zo¢ due to Pythagoras. Presumably this is inferred from the words of Aristotle distinguishing Alemaeon from the Pythagoreans; but either inference is possible, and I prefer Tannery’s. It is difficult to account for Alcmaeon being credited with the discovery if, as Burnet thinks, it was really Plato’s.
But we have also the evidence of -Theon of Smyrna, who states categorically that Pythagoras was the first to notice that the planets move in independent circles :
‘The impression of variation in the movement of the planets is produced by the fact that they appear to us to be carried through the signs of the zodiac in certain circles of their own, being fastened in spheres of their own and moved by their motion, as Pythagoras
1 Aét. ii. 16. 2-3 (D. G. p. 345; Vors. 15, p, 101. 8).
3 Tannery, op. cit., p. 208.
3 Aét. ii. 22. 4 ΤΑ G. p. 352; Vors. i?, p. τοι. 10).
* Aét. ii. 29. 3 (29, G. p. 359; Vors. 15, p. 101. 10-12), 5 Burnet, Zarly Greek Philosophy, p. 123, note.
HI PYTHAGORAS 51
was the first to observe, a certain varied and irregular motion being thus grafted, as a qualification, upon their simply and uniformly ordered motion in one and the same sense’ [i.e. that of the daily _ rotation from east to west].
It appears probable, therefore, that the theory of Pythagoras himself was that the universe, the earth, and the other heavenly bodies are spherical in shape, that the earth is at rest in the centre,
at the sphere of the fixed stars has a daily rotation from east to st about an axis passing through the centre of the earth, and that the planets have an independent movement of their own in a sense opposite to that of the daily rotation, i.e. from west to east.
* Theon of Smyrna, p. 150. 12-18.
VII XENOPHANES
XENOPHANES of Colophon was probably born about 570 an died after 478 B.c. What we know for certain is that he spoke c Pythagoras in the past tense,’ that Heraclitus mentions him alon with Pythagoras,? and that he says of himself that, from the ti when he was 25 years of age, three-score years and seven hai ‘tossed his care-worn soul up and down the land of Hellas.’ He may have left his home at the time when Ionia became a Persia province (545 B.C.) and gone with the Phocaeans to Elea,* found by them in 540/39 B.C., six years after they left Phocaea.6 As he w writing poetry at 92 and is said to have been over 100 when h died,* the above dates are consistent with the statement that he w a contemporary of Hieron, who reigned from 478 to 467 B.C. According to Theophrastus, he had ‘ heard’ Anaximander. ;
Xenophanes was more a poet and satirist than a natural phil sopher, but Heraclitus credited him with wide learning,® and h is said to have opposed certain doctrines of Pythagoras and Thales,! We are told that he wrote epics as well as elegies and iambic attacking Homer and Hesiod. In particular, 2,000 verses on th foundation of Colophon and the settlement at Elea are attribute to him. He is supposed to have written a philosophical poem ; Diels refers about sixteen fragments to such a poem, to which th
1 Fr. 7 (Vors. i?, p. 47. 20-23). 2 Heraclitus, Fr. 40 ( Vors. 13, p. 68. το).
3 Fr. 8 (Vors. i’, p. 48. 3-6).
* Gomperz, Griechische Denker, 15, pp. 127, 436.
5 Herodotus, i. 164-7.
® Censorinus, De die natali c. 15. 3, p. 28. 21, ed. Hultsch.
7 Timaeus in Clem. Stromat. i. 14, p.353 (Vors. 15, p. 35. 2).
8. Diog. L. ix. 21 (Vors. i*, p. 34. 35).
9. Heraclitus, loc. cit.: ‘Wide learning does not teach one to have under- standing ; if it did, it would have taught Hesiod and Pythagoras, and again Xenophanes and Hecataeus.’ |
10 Diog. L. ix. 18 (Vors. 15, p. 34. 12). 1 Ibid. ix. 20 (Vors. i*, p. 34. 26).
.
=. XENOPHANES 53
name On Nature (Περὶ φύσεως) was given; but such titles are of later date than Xenophanes, and Burnet? holds that all the ‘fragments might have come into the poems directed against Homer and Hesiod, the fact that a considerable number of them come from commentaries on Homer being significant in this connexion.
Xenophanes attacked the popular mythology, proving that God ‘must be one, not many (for God is supreme and there can only ‘be one supreme power),? eternal and not born (for it is as impious to say that the gods are born as it would be to say that they die; in either case there would be a time when the gods would not be) ;* he reprobated the scandalous stories about the gods in Homer and Hesiod * and ridiculed the anthropomorphic view which gives the bodies, voices, and dress like ours, observing that the Thracians made them blue-eyed and red-haired, the Aethiopians snub-nosed _and black,® while, if oxen or horses or lions had hands and could ἔχων, they would draw them as oxen, horses, and lions respectively.® God is the One and the All, the universe ;7 God remains unmoved in one and the same place ;* God is eternal, one, alike every way, "finite, spherical and sensitive in all parts,? but does not breathe.?° ‘It is difficult to reconcile the finite and spherical God with _ Xenophanes’ description of the world, which may be summarized as follows.
The world was evolved from a mixture of earth and water," and the earth will gradually be dissolved again by moisture; this he infers from the fact that shells are found far inland and on mountains, and in the quarries of Syracuse there have been found imprints (fossils) of a fish and of seaweed, and so on, these imprints showing that everything was covered in mud long ago,
? Burnet, Early Greek Philosophy, p. 128. * Simpl. iw Phys. p. 22. 31 (Vors. i*, p. 40. 30). ® Aristotle, Rhetoric ii. 23, 1399 Ὁ 6. * Fr. 11 (Vors. i, p. 48. 13). 5 Fr. 14, 16 (Vors. i?, p. 49. 2, 11). ® Fr. 15 (Vors. 1", Ρ 49. 5). _," Aristotle, Metaph. A. 5, οΒ6 Ὁ 21 (Vors. i, p. 40. 15); Simpl., loc. cit. (Vors. ΠΡ. 40. 29); cf. Cicero, De nat, deor.i. ττ. 28 ( Vors. #, p. 41. 44); Acad. pr. ii. 37. 118 (Vors. i*, p. 41. 42). ® Fr. 26 (Vors. i*, p. 50. 22). " Hippol. Refut. i. 14. 2 (D. G. p. 565; Vors. i*, p. 41. 26). 39 Diog. L. ix. 19 (Vors. i*, p. 34. 18). 4 Fr. 29. 33 (Vors.i*, p. 51. 5, 20). ᾿Ξ I read, with Burnet, after Gomperz φυκῶν (seaweed) instead of φωκῶν.
54 XENOPHANES PARTI
arid that the imprints dried on the mud. All men will disappear when the earth is absorbed into the sea and becomes mud, after which the process of coming into being starts again; all the worlds — (alike) suffer this change.! This is, of course, the theory οὗ _Anaximander. ᾿ As regards the earth we are told that »
‘This upper side of the earth is seen, at our feet, to touch the air, © but the lower side reaches to infinity.’ ?
‘This is why some say that the lower portion of the earth is infinite, asserting, as Xenophanes of Colophon does, that its roots extend without limit, in order that they may not have the trouble of investigating the cause (of its being at rest). Hence Empedocles’ rebuke in the words “if the depths of the earth are without limit and the vast aether (above it) is so also, as has been said by the tongues of many and vainly spouted forth from the mouths of men who have seen little of the whole ”.’*
‘Xenophanes said that on its lower side the earth has roots extending without limit.’ *
‘The earth is infinite, and is neither surrounded by air nor by the heaven.’ ὅ
Simplicius ® (on the second of the above passages) observes that, not having seen Xenophanes’ own verses on the subject, he cannot _ say whether Xenophanes meant that the under side of the earth — extends without limit, and that this is the reason why it is at rest, or meant to assert that the space below the earth, and the aether, is infinite, and consequently the earth, though it is in fact being carried downwards without limit, appears to be at rest ; for neither Aristotle nor Empedocles made this clear. Presumably, however, as Simplicius had not seen Xenophanes’ original poem, he had not seen Fr. 28, the first of the above passages; for this passage seems to be decisive ; there is nothing in it to suggest motion downwards, and, if it meant that there was infinite air below the earth as there is above, there would be no contrast between the upper and the under side such as it is the obvious intention of the author to draw.’
1 i ἢ ps . 12 is
: Fes (Vee fie Asha G. p. 566; Vors. i*, p. 41. 33-41).
5 Aristotle, De cae/o ii. 13, 294 ἃ 21-28.
* Aét. iii. 9.45 11. 1,2 (D. G. pp. 376, 377; Vors. i*, p. 43. 33, 35).
5 Hippol. Refut. i. 14. 3 (D. G. p. 565; Vors. i?, p. 41. 29).
® Simplicius on De cae/o, Ρ. 522. 7, ed. Heib. ( Vors. i*, p. 43. 28). 7 As witness the μέν and the δέ and the clear opposition of ‘touching the air’
‘CH.VII XENOPHANES 55
According to Xenophanes the stars, including comets and meteors, are made of clouds set on fire; they are extinguished each day and are kindled at night like coals, and these happenings ' constitute their setting and rising respectively.1 The so-called _Dioscuri are small clouds which emit light in virtue of the motion, _ whatever it is, that they have.? _ Similarly the sun is made of clouds set on fire; clouds formed _ from moist exhalation take fire, and the sun is formed from the resulting fiery particles collected together.* The moon is likewise 80 formed, the cloud being here described as ‘compressed’ (πεπιλημένον),, following an expression of Anaximander’s for _ compressed portions of air; the moon’s light is its own.® | When the sun sets, it is extinguished, and when it next rises, it is a fresh one; it is likewise extinguished when there is an eclipse.®
_ of the fragment and the passage of Aristotle other than the literal interpretation. _ The significant words in the passage of Aristotle are ‘saying that it (the earth) _ is rected ad infinitum (ἐπ᾿ ἄπειρον ἐρριζῶσθαι)᾽. Berger (p.194, note) holds that the ᾿ ession is not used in the literal sense of having roots extending ad infinitum, that ‘ we use the word ἐρριζῶσθαι only as an expression for a supporting force _ hot capable of closer definition’; he can only quote in favour of this certain _ metaphorical uses of ῥίζα ‘ root’ and other words connected with it, ῥιζώματα and _ pases, which of course do not in the least prove that ἐρριζῶσθαι is used in a metaphorical sense in our passage; indeed, if it is used in so vague a sense, it ‘is difficult to see how Xenophanes thereby absolved himself from giving a further explanation of the cause of the earth’s remaining at rest, which, according to Aristotle, was his object. As regards the fragment from Xenophanes’ own poem, Berger says that he prefers to regard it as an attempt to give in few words an idea of the Aorizon which divides earth and heaven into an upper, visible, half, and an invisible lower half. This again leaves no contrast between the upper and lower sides of the earth such as the fragment is obviously intended to draw. On both points Berger’s arguments are of the nature of special pleading, which can hardly carry conviction. * A&t. ii. 13. 14, iii. 2. 11 (D. G. pp- 343, 367 ; Vors. i?, pp. 42. 39, 43. 15).
_. * Aét. ii. 18. 1 (2. G. p. 347; Vors.i®, p. 42. 42). ἥ Coy ii. 20. 3 (D. G. p. 348; Vors. i*, p. 42. 45) ; Hippol. Refut. i. 14. 3 (D.C. ΟΡ. 505). * Aét. ii. 25. 4 (D.G. p. 356; Vors. 13, p. 43. 12). _ + 5 Aét. ii. 28. 1 (2. G. p. 358; Vors. i?, p. 43. 13). ᾿ς * Aét. ii. 24. 4 (2. G. p. 354; Vors. i*, p. 43. 1). The passage, which is under _ the heading ‘ On eclipse of the sun’, implies that it is an eclipse which comes about by way of extinguishment (xara σβέσιν), but the next words to the effect _ that the sun is a new one on rising again suggest that it is ‘setting’ rather ‘than ‘ eclipse’, which should be understood.
56 XENOPHANES PARTI
The phases of the moon are similarly caused by (partial) ex- tinction.?
According to Xenophanes, the sun is useful with reference to the coming into being and the ordering of the earth and of living things in it; the moon is, in this respect, otiose.?
More remarkable are Xenophanes’ theory of a multiplicity of suns and moons, and his view of the nature of the sun’s motion; and here it is necessary to quote the actual words of Aétius :
‘Xenophanes says that there are many suns and moons according to the regions (κλίματα), divisions (ἀποτομαί) and zones of the earth; and at certain times the disc lights upon some division of the earth not inhabited by us and so, as it were, stepping on emptiness, suffers eclipse.
‘The same philosopher maintains that the sun goes forward ad infinitum, and that it only appears to revolve in a circle owing to it distance (away from us).’ ὃ
The idea that the sun, on arriving ‘at an uninhabited part of ’ earth, straightway goes out, as it were, is a curious illustratior the final cause. For the rest, the passage, according to the n _ natural interpretation of it, implies that the sun does not rev about the earth in a circle, but moves in a straight line ad infini- that the earth is flat, and that its surface extends without li On this interpretation we are presumably to suppose that the of any one day passes out of our sight and is seen successive’ regions further and further distant towards the west until it is f extinguished, while in the meantime the new sun of the nex ~ follows the first, at an interval of 24 hours, over our part « earth, and so on, with the result that at any given time the many suns all travelling in the same straight direction ad injfim If this is the correct interpretation of Xenophanes’ theory (and is the way in which it is generally understood), it shows no advan upon, but a distinct falling off from, the systems of Anaximande. and Anaximenes. Berger,’ deeming it incredible that Xenophanes could have put forward views so crude, not to say childish, at a time when the notion of the sphericity of the earth discovered by
1 Aét. ii, 29. 5 G. p. 360; Vors. i*, p. 43.14).
2 Aét, ii. 30. 8 (D. G. p. 362; Vors. i*, p. 43. 9).
> Aét. ii. 24. 9 (D.G. p. 355; Vors. i*, p. 43. 3-8).
* Tannery, op. cit., p. 133. ° Berger, op. cit., pp. 190 sqq.
.
᾿ Ϊ
Se et aA ae τινα
CH. VII XENOPHANES 57
the earliest Pythagoreans and by Parmenides must already have spread far and wide, seeks to place a new interpretation upon the passages in question.
For the Ionians, with their flat earth, there was necessarily one horizon, so that the solar illumination and the length of the day were the same for all parts of the inhabited earth. As soon, how- ever, as the spherical shape of the earth was realized, it would necessarily appear that there were different horizons according to the particular spot occupied by an observer on the earth’s surface. It was then, argues Berger, the different horizons which Xenophanes _ had in view when he spoke of many suns and moons according to _ the different regions or climates, divisions and zones of the earth ; ' he realized the difference in the appearances and the effects of the
_ same phenomena at different places on the earth’s surface, and he Ss “nay have been the first to introduce, in this way, the mode of ' «pression by which we commonly speak of different suns, the a Spical sun, the Indian sun, the midnight sun, and the like. This _ ‘ingenious, but surely not reconcilable with other elementary
- hions stated by Xenophanes, such as that there is a new sun
“ty day. Then again, Berger has to explain the sun’s ‘going- Ward ad infinitum’ as contrasted with circular motion; as, on
"theory, it cannot be motion zz a straight line without limit, he οἴ it to be the motion in a sfiral which the sun actually exhibits
‘4g to the combination of its two motions, that of the daily
_ ‘fon, and its yearly motion in the ecliptic, which causes a slight
τὰ in its latitude day by day. But in the first place this
ὅπ in a spiral is not motion forward ad infinitum, for the spiral Ὁ
‘ns on itself in a year just as a simple circular motion would in
“hours. Indeed, Berger’s interpretation would make Xeno-
‘ines’ system purely Pythagorean, and advanced at that, for
ve do not hear of the spiral till we find it in Plato.1 And, if
‘Heraclitus’s system also represents (as we shall find it does) a set-
j back in astronomical theory, why should not Xenophanes’ ideas ie have been equally retrograde?
There remains the story that Xenophanes told of an eclipse of
Mf the sun which lasted a whole month.2_ Could he have intended, by
1 Plato, Timaeus 39 A. * Aét. il. 24. 4 (D.G. p. 354 ; Vors. i, p. 43. 2-3).
TO eee ee
=
58 XENOPHANES
this statement, to poke fun at Thales?! Berger, full of his theory that Xenophanes’ ideas were based on the sphericity of the earth, thinks that he must have inferred that the length of the day would vary in different latitudes and according to the position of the sun in the ecliptic, and must have seen that, at the winter solstice for example, there would be a point on the earth’s surface at which the longest night would last 24 hours, another point nearer the north pole where there would be a night lasting a month, and so on, and finally that at the north pole itself there would be a night six months long as soon as the sun passes to the south of the equator ; Xenophanes therefore, according to Berger, must simply have been alluding to the existence of a place where a night may last a month. If, as seems certain, Xenophanes’ earth was flat, this explanation too must fall to the ground.
1 Tannery, op. cit., p. 132.
AS ar er eg ee Heal ge, ---,..ὕ»ὕ. Ξ =:
Vill
HERACLITUS
| : | q β ᾿ f
IF the astronomy of Xenophanes represents a decided set-back _ in comparison with the speculations of Anaximander and Anaxi- _menes, this is still more the case with Heraclitus of Ephesus (fil. 504/0, and therefore born about 544/0B.C.); he was indeed no astronomer, and he scarcely needs mention in a history of astronomy except as an illustration of the vicissitudes, the ups and downs, through which a science in its beginnings may have to pass. Hera- clitus’s astronomy, if it can be called such, is of the crudest descrip- tion. He does not recognize daily rotation; he leaves all the ‘apparent motions of the heavenly bodies to be explained by a ' continued interchange of matter between the earth and the heaven." His original element, fire, condenses into water, and water into earth ; this is the downward course. The earth, on the other hand, may partly melt; this produces water, and water again vaporizes into air and fire; this is the upward course. There are two kinds _ of exhalations which arise from the earth and from the sea; the one kind is bright and pure, the other dark; night and day, the months, seasons of the year, the years, the rains and the winds, &c., are
_ exhalations. In the heavens are certain basins or bowls (σκάφαι) _ turned with their concave sides towards us, which collect the bright alations or-vaporizations, producing flames; these are the 2 The sun and the ὭΡΩΝ are bowl-shaped, like the stars, and are ee: lit up.2 The flame of the sun is brightest
τ δὰ
60 HERACLITUS PARTI
consequently they give out less light and warmth. The moon, although nearer the earth, moves in less pure air and is conse- quently dimmer than the sun; the sun itself moves in pure and transparent air and is at a moderate distance from us, so that it warms and illuminates more.’ ‘If there were no sun, it would be night for anything the other stars could do.* Both the sun and the moon are eclipsed when the bowls are turned upwards (i.e. so that the concave side faces upwards and the convex side faces in our direction); the changes in the form of the moon during the months are caused by gradual turning of the bowl.’
According to Heraclitus there is a new sun every day,* by which is apparently meant that, on setting in the west, it is extinguished or spent,’ and then, on the morrow, it is produced afresh in the east by exhalation from the sea.°
The question arises, what happens to the bowl or basin supposed to contain the sun if the sun has to be re-created in this way each morning? Either a fresh envelope must be produced every day for the rising of the sun in the east or, if the envelope is supposed to be the same day after day, it must travel round from the west to the east, presumably in the encircling water, laterally.’ Diogenes Laertius (i.e. in this case Theophrastus) complains that Heraclitus
1 Diog. L., loc. cit.; Aét. ii. 28. 6 (D. G. p. 358; Vors. i’, p. 59. 10).
? Plutarch, De fort. 3, p. 98 c ( Vors. 13, p. 76. 8).
5 Diog. ἴω, loc. cit.; Aét. ii. 24. 3 (D. G. p. 354; Vors. i*, p. 59. 5). T explanation that the hollow side of the basins is turned towards us itself sho how crude were the ideas of Heraclitus. For it is clear that to account for t actual variations which we’see in the shape of the moon, it is the ouf¢er side a hemispherical bowl which should be supposed bright and turned towards when the moon is full.
* Aristotle, Meteor. ii. 2, 355 a 14.
® Plato, Rep. vi. 498 A.
®° Aristotelian Problems, xxiii. 30, 934b 35. It is true that a certain passage of Aristotle may be held to imply that Heraclitus did not maintain that the moon and the stars, as well as the sun, are fed and renewed by exhalations. Aristotle (AZeZeor. ii. 2, 354 Ὁ 33 5644.) is speaking of those who maintain that the sun is fed by moisture. He first argues that, although fire may be said to be nourished by water (the flame arising through continuous alternation between the moist and the dry), this cannot take place with the sun; ‘and if the sun were fed in this same way, then it is clear that not only is the sun new every day, as Heraclitus says, but it is continuously becoming new (every moment) ’ (355 a 11-15). ‘ And,’ he adds (355 a 18-21), ‘it is absurd that these thinkers should only concern themselves with the sun, and neglect the conservation of the other stars, seeing that their number and their size is so-great.’
7 Zeller, 1δ, p. 684.
_ . alia « ee a ae eee 2 a Dn rns 2 AG
CH. VIII HERACLITUS 61
gave no information as to the nature of these cups or basins. The idea, however, of the sun and moon being carried round in these σκάφαι reminds us forcibly of the Egyptian notion of the sun in his barque floating over the waters above, accompanied by a host of secondary gods, the planets and the fixed stars.
Heraclitus held (as Epicurus did long afterwards) that the diameter of the sun is one foot,? and that its actual size is the same as its apparent size.* This in itself shows that Heraclitus was no mathematician; as Aristotle says, ‘it is too childish to suppose that each of the moving heavenly bodies is small in size because it appears so to us observing it from where we stand.’ *
He called the arctic circle by the more poetical name of ‘the Bear’, saying that ‘the Bear represents the limits of morning and evening’. .. whereas of course it is the arctic circle, not the Bear itself, which is the confine of setting and rising® (i.e. the stars _ within the arctic circle never set).
According to Diogenes Laertius, Heraclitus said absolutely nothing about the nature of the earth;® but we may judge that _in his conception of the universe he was closer to Thales than to _ Anaximander; that is, he would regard the universe as a hemi- ' sphere rather than a sphere, and the base of the hemisphere as "a plane containing the surface of the earth surrounded by the
sea; if he recognized a subterranean region, under the name of ᾿ς “ades, he does not seem to have formed any idea with regard to 3 Ἐν beyond what was contained in the current mythology.’ τ δ ~, When he gave 10,800 solar years as the length of a Great Year,* ᾿ ect no astronomical Great Year, but the period of duration ἢ ᾿ς of the world from its birth to its resolution again into fire and
' vice versa. He arrived at it, apparently, by taking a generation of 30 years as τ day and multiplying it by 360 as the number of ἃ yi in a year.”
_ +} See pp. 19, 20 above. 3 Aét. ii. 21. 4 (D. G. p. 351; Vors. 15, p. 62. 7). :. ; Diog. L. ix. 7 (Vors. 15, p. 55. 12). __ * Aristotle, 2Ze¢eor. i. 3, 339 534. 5. Strabo, i: 1. 6, p. 3 (Vors. i*, p. 78. 15). ' * Diog. L. ix. 11 (Vors. ®, p. 55. 46). ; ᾿ς ἢ Tannery, op. cit., p. 169. fe > Aét.’ ii. 32. 3 (D. G. p. 364: Vors. i*, p. 59. 13); Censorinus, De die natalt ᾿ 18. 11 (Vors. i*, p. 59. 16). 5 Tannery, op. cit., p. 168. :
ΙΧ PARMENIDES
WITH regard to the date of Parmenides there is a conflict of authority. On the one hand Plato says that Parmenides and Zeno paid a visit to Athens, Parmenides being then about 65 and Zeno nearly 40 years of age, and that Socrates, who was then very young (σφόδρα νέος), conversed with them on this occasion! Now if we assume that Socrates was about 18 or 20 years of age at this time, the date of the meeting would be about 451 or 449 B.C., and this would give 516 or 514 as the date of Parmenides’ birth. On the other hand, Diogenes Laertius* says (doubtless on the authority of Apollodorus) that Parmenides flourished in Ol. 69 (504/0 B.C.), in which case he myst have been born about 540 B.C. In view of the number of cases in which, for artistic reasons, Plato indulged in anachronisms, it is not unnatural to feel doubt as to whether the meeting of Socrates with Parmenides was a historical fact. Zeller® firmly maintained that it was a poetic fiction on the part of Plato; but Burnet, on grounds which seem to be convincing, accepts it as a fact, exposing at the same time the rough and ready methods on which Apollodorus proceeded in fixing his dates.‘
1 Plato, Parmenides 127 A-C. 2 Diog. ἵν. ix. 23 ( Vors. i*, p, 106. 10)
ἢ Zeller, ἢ, pp. 555, 556. ,
* Burnet, Early Greek Philosophy, pp. 192,193. The story was early qnestic Athenaeus (xi. 15,p.505¥; Vors. 12, p. 106, 47) doubted whether the age of Sc would make it possible for him to have conyersed with Parmenides or at a1 to have held or listened to such a discourse, But Plato refers to the mee two other places (Zheaet. 183 Ἔ, Sophist 217 Ο), and (as Brandis and I also pointed out) we should have to assume a deliberate falsification of { the part of Plato if he had inserted these two allusions solely for the pu inducing people to believe a fiction contained in another dialogue, ¥ too, independent evidence of the visit of Zeno to Athens. Plutarch
4. 3) says that Pericles ‘heard’ Zeno. The date given by Apollodoru oa
other hand, seems to be based solely on that of the foundation of Elea adopts that date as the loruit of Xenophanes, so he makes it the δὲ Parmenides’ birth. In like manner he makes Zeno’s birth contem,
ν
—— Δι με σὠ- νων
4 Γ, §
PARMENIDES 63
Parmenides is said to have been a disciple of Xenophanes;! he was also closely connected with the Pythagorean school, being specially associated with a Pythagorean, Ameinias Diochaites, for whom he conceived such an affection that he erected a ἡρῷον to him after his death;? Proclus quotes Nicomachus as authority for the statement that he actually belonged to the school,* and Strabo has a notice to the same effect.‘ It is not therefore unnatural that Parmenides’ philosophical system had points in common with that of Xenophanes, while his cosmogony was on Pythagorean lines, with of course some differences. Thus his Being corresponds to the One of Xenophanes and, like it, is a well- rounded sphere always at rest; he excluded, however, any idea of its infinite extension; according to Parmenides it is definitely limited, rounded off on all sides, extending equally in all directions
_ from the centre. Parmenides differs from Xenophanes in denying
genesis and destruction altogether; these phenomena, he holds, are only apparent.® Being is identified with Truth; anything else is Not-Being, the subject of opinion. Physics belongs to the latter
_ deceptive domain.”
_ The main difference between the cosmologies of Parmenides and the Pythagoreans appears to be this. It seems almost certain that Pythagoras himself conceived the universe to be a sphere, and attributed to it daily rotation round an axis® (though this was denied by Philolaus afterwards); this involved the assumption
ΟΠ that it is itself finite but that something exists round it; the
Pythagoreans, therefore, were bound to hold that, beyond the
finite rotating sphere, there was limitless void or empty space;
h Parmenides’ floruit, thereby making Zeno forty years younger than Par- ides, whereas Plato makes him about twenty-five years younger. Burnet gE. Meyer (Gesch. des Alterth. iv. § 509, note) in support of his view. _ssistotle, Me/aph.a.5,986b 22 ; Simplicius, Jz Phys. p.22. 27(Vors. i2, p. 107. τ Diog. L. (ix. 21; Vors. 15, p, 105. 26) says that Parmenides ‘heard’ » Ranes but did not follow him. ig. L. ix. 21 ( Vors. 15, p. 105. 29). “slus, Jn Parm., i, ad init. ( Vors. 13, p. τοῦ. 30). bo, vi. I. 1, Ὁ. 252 (Vors. i?, p. 107. 39). otle, Phys. iii. 6, 207 ἃ 16; Fr. 8, line 42 (Vors. i?, p. 121. 3). — De caelo iii. τ, 298 Ὁ 14; Aét. 1. 24.1 (D.G. p. 320; Vors. i2,
= τς 50-53 (Vors. i*, p. 121. 11-13),
gry, ΟΡ. cit., p. 123.
64 PARMENIDES PARTI
this agrees with their notion that the universe breathes, a supposition which Tannery attributes to the Master himself because Xenophanes is said to have denied it.2 Parmenides, on the other hand, denied the existence of the infinite void, and was therefore obliged to make his finite sphere motionless, and to hold that its apparent rotation is only an illusion.’
As in other respects the cosmology of Parmenides follows so closely that of the Pythagoreans, it is not surprising that certain astronomical innovations are alternatively attributed to Parmenides and to Pythagoras. Parmenides is said to have been the first to assert that the earth is spherical in shape and lies in the centre ;* this statement has the great authority of Theophrastus in its favour ; there was, however, an alternative tradition stating that it was Pythagoras who first called the heaven κόσμος, and held the earth to be round (στρογγύλην). As the idea that the earth is spherical was probably suggested by mathematical considerations, Pythagoras is the more likely to have conceived it, though Parmenides may
have been the first to state it publicly (the Pythagorean secrecy, |
such as it was, seems to have applied only to their ritual, not to their mathematics or physics). Parmenides is associated with Democritus as having argued that the earth remains in the centre because, being equidistant from all points (on the sphere of the universe), it is in equilibrium, and there is no more reason why it should tend to move in one direction than in another. Parmenides therefore here practically repeats the similar argument used by Anaximander (see above, p. 24), and we shall find that in other physical portions of his system he follows Anaximander and other Ionians pretty closely.
* Aristotle, Phys. iv. 6, 213 Ὁ 24.
2 Tannery, Op. cit., p. 121. Zeller (i5, p. 525), however, does not believe that the remark μὴ μέντοι ἀναπνεῖν, if Xenophanes really made it, is directed against the Pythagorean view. He points out, too, that the statement in Diog. L. ix. 19 (Vors. i*, p. 34. 18), so far as these words (‘but that it does not breathe’) are concerned, may only represent an inference from the fact that Fr. 24 only mentions seeing, hearing, and thinking. This, however, assumes greater intelli- gence on the part of Diogenes than we are justified in attributing to him.
3. Tannery, op. Cit., p. 125.
* Diog. L. ix. 21 (Vors. 15, p. 105. 32).
5 Diog. L. viii. 48 (Vors. 2, p- 111. 38).
6 Aét. ili. 15. 7 (D. G. p. 380 ; Vors. 15, p. 111. 40); cf. Aristotle, De caelo, i ii. 13, 295 b 10, and the similar views in Plato, Phaedo 108 E-109 A.
.
ΘΗ. ΙΧ PARMENIDES 65
Secondly, Parmenides is said to have been the first to ‘define the habitable regions of the earth under the two tropic zones’ : 1 on the other hand we are told that Pythagoras and his school declared that the sphere of the whole heaven was divided into five circles which they called ‘zones’.* Hultsch® bids us reject the attribution to Pythagoras on the ground that these zones would only be possible on a system in which the axis of the universe about which it revolves passes through the centre of the earth; the zones are therefore incompatible with the Pythagorean system, according to which the earth moves round the central fire. Hultsch admits, however, that this argument does not hold if the hypothesis of the central fire was not thought of by any one before Philolaus; and there is no evidence that it was. As soon as Pythagoras had satisfied himself that the universe and the earth were concentric spheres, the centre of both being the centre of the earth, the definite portion of the heaven marked out by the extreme deviations of the sun in latitude (north and south) might easily present itself to him as a zone on the heavenly sphere. The Arctic Circle, already known in the sense of the circle including within it the stars which never set, would make another division, while a corresponding Antarctic Circle would naturally be postulated by one who had realized the existence of antipodes.* With the intervening two zones, five divisions of the heaven were ready to hand. It would next be seen that straight lines drawn from the centre of the earth to all points on all the dividing circles in the heaven would cut the surface of the earth in points lying on exactly corresponding circles, and the zone-theory would thus be transferred to the earth.2 We are told, however, that Parmenides’ division of the earth into zones was different from the division which would be arrived at in this way, in that he made his torrid zone about
1 Aét. iii. 11. 4 (D. G. p. 377).
2 Aét. ii. 12. 1 (D. G. p. 340).
5 Hultsch, art. ‘Astronomie’ in Pauly-Wissowa’s Real-Encyclopddie der classischen Altertumswissenschaft, ii. 2, 1896, p. 1834.
* Alexander Polyhistor in Diog. L. viii. 1. 26.
5 Aét. iii. 13. 1 (D.G. p. 378), ‘ Pythagoras said that the earth was divided, correspondingly to the sphere of the universe, into five zones, the arctic, antarctic, summer and winter zones, and the equatorial zone; the middle of these defines the middle portion of the earth, and is for this reason called the torrid zone; then comes the habitable zone which is temperate.’
1410 Ε
66 PARMENIDES PARTI
twice as broad as the zone intercepted between the tropic circles, so that it spread over each of those circles into the temperate zones.’ This seems to be the first appearance of zones viewed from the standpoint of physical geography.
Thirdly, Diogenes Laertius says, on the authority of Favorinus, that Parmenides is thought to have been the first to recognize that the Evening and the Morning Stars are one and the same, while others say that it was Pythagoras.2 In this case, although Parmenides may have learnt the fact from the Pythagoreans, it is probable that Pythagoras did not know it as the result of observations of his own, but acquired the information from Egypt or Chaldaea along with other facts about the planets.®
On the purely physical side Parmenides in the main followed one or other of the Ionian philosophers. The earth, he said, was formed from a precipitate of condensed air.4 He agreed with Heraclitus in regarding the stars as ‘compressed’ fire (literally close-pressed packs of fire, πιλήματα πυρός).
Parmenides’ theory of ‘wreaths’ (στεφάναι) seems to be directly -
adapted from Anaximander’s theory of hoops or wheels. Anaxi- mander had distinguished hoops belonging to the sun, the moon, and the stars respectively, which were probably concentric with the earth; the hoops were of different sizes, the sun’s being the largest, the moon’s next, and those of the stars smaller still. These hoops were rings of compressed air filled with fire which burst out in flame at outlets, thereby producing what we see as the sun, moon, and stars. The corresponding views of Parmenides are not easy to understand ; I will therefore begin by attempting a transla- tion of the passage of Aétius in which they are set out.®
‘There are certain wreaths twined round, one above the other [relatively to the earth as common centre]; one sort is made of the rarefied (element), another of the condensed; and between these are others consisting of light and darkness in combination. That
1 Posidonius in Strabo, ii. 2. 2, p. 94.
2 Diog. L. ix. 23 (Vors. i*, p. 106. 11).
8. Tannery, op. cit., p. 229.
4 Λέγει δὲ τὴν γῆν πυκνοῦ καταρρυέντος ἀέρος γεγονέναι, Ps. Plut. Stromat. § (D. G. p. 581.4; Vors. 13, p. 109. 1).
5 Aét. il. 13. 8 (D. G. p. 342; Vors. 13, p. 111. 25). Cf. Anaximander’s πιλήματα ἀέρος. :
® Aét, ii, 7. 1 (2. G. p. 3353 Vors. 15, p. 111. 5-16).
CH. Ix PARMENIDES 67
which encloses them all is solid like a wall, below which is a wreath of fire; that which is in the very middle of all the wreaths is solid, about which (περὶ 6) [under which (ὑφ᾽ 6, Diels)] again is a wreath of fire. And of the mixed wreaths the midmost is to all of them the beginning and cause of motion and becoming,‘ and this he calls the Deity which directs their course and holds sway (κληροῦχον) 5 cooks the keys(xAndodxor, Fiilleborn) |, namely Justice and Necessity. oreover, the air is thrown off the earth in the form of vapour owing to the violent pressure of its condensation ; the sun and the Milky Way are an exspiration 5 of the fire; the moon is a mixture of both elements, air and fire. And, while the encircling aether is uppermost of all, below it is ranged that fiery (thing) which we call heaven, under which again are the regions round the earth.’
But in addition we are told that
‘It is the mixture of the dense and the rarefied which produces the colour of the Milky Way.’*
‘The sun and the moon were separated off from the Milky Way, the sun arising from the more rarefied mixture which is hot, and the moon from the denser which is cold.’®
The fragments of Parmenides do not add much to this. The relevant lines are as follows:
‘The All is full of light and, at the same time, of invisible darkness, which balance each other; for neither of them has any share in the other.’ ®
‘Thou shalt learn the nature of the aether and all the signs in the aether, the scorching function of the pure clear sun, and whence they came; thou shalt hear the wandering function and the nature of the round-eyed moon, and thou shalt learn of the surrounding heaven, whence it arose, and how Necessity, guiding it, compelled - it to hold fast the bounds of the stars.’ 7
“(1 will begin by telling) how the earth, the sun and the moon, the common aether, the milk of the heaven, furthest Olympus, and the hot force of the stars strove to come to birth.’®
1 I follow the reading adopted by Diels in the Vorsokratiker, ἁπάσαις (ἀρχήν) τε καὶ Cairiay) κινήσεως καὶ γενέσεως ὑπάρχειν.
2 Burnet (Zarly Greek Philosophy, p. 219) observes that κλῆρος in the Myth of Er suggests κληροῦχον as the right reading. Fiilleborn suggested κληδοῦχον
_ in view of the use of xAnidas (keys) in Fr. 1. 14.
* The word ἀναπνοή is of course ambiguous ; I follow Diels’ interpretation, * Ausdiinstung’, ‘evaporation’ or ‘exhalation’. Diels (Parmenides Lehrgedicht, 1897, p. 105) compares ἀναπνοὰς ἴσχον in the Timaecus 85 A.
* Aét. iii. 1. 4 (D. G. p. 365).
5 Aét. ii. 20. 8a (D. G. p. 349; Vors. i*, p. 111. 35).
© Fr. 9 (Vors. i?, p. 122. 11-12).
7 Fr. τὸ von i’, pp. 122. 21-123. 2).
® Fr. 11 (Vors. 15, p. 123. 5-7).
F2
68 PARMENIDES PARTI
Of the wreaths he says that
‘The narrower (wreaths) were filled with unmixed’ fire; those next in order to them (were filled) with night, and along with them the share of flame spreads itself. In the middle of these is the Deity which controls all.’ ?
It is not surprising that there have been a number of interpreta- tions of these passages taken in combination. To begin with the outside, there is a doubt as to the relative positions of the ‘ heaven’ and the aether. According to Aétius ‘the encircling aether is uppermost of all, and below it is ranged that fiery thing which we call heaven’, whereas the fragments suggest that the ‘common aether’ is within the ‘encircling heaven’ or ‘furthest Olympus’, which latter clearly seems to be the solid envelope compared to a wall. The fragments presumably better represent Parmenides’ own statement, and possibly Aétius’s version (which seems practi- cally to interchange the ‘ heaven’ and the ‘aether ’) is due to some confusion.
The next question is, what was the shape of the ‘wreaths’ or bands?* Zeller, in view of the spherical form of the envelope, does not see how they can be anything but hollow globes.’ But surely ‘wreaths’ or ‘garlands’, i.e. bands, would not in that case be a proper description. Tannery® takes them to be cylindrical bands fixed one inside the other, comparing with our passage the description in Plato’s Myth of Er,’ where ‘the distaff of Necessity by means of which all the revolutions of the universe are kept up’ distinctly suggests that Plato had Parmenides’ system in mind; Plato there speaks of eight whorls (σφόνδυλοι), one inside the other, ‘like those boxes which fit into one another,’ and of the Zs of
1 Reading dxpyrow, The reading ἀκρίτοιο (literally ‘ confused’ or ‘ undistin- guishable’, that is to say, dz/u¢ed fire) is impossible, because (1) it does not give the required sense, and (2) it offends against prosody, since ¢ in ἄκριτος is short (Diels, Parmenides Lehrgedicht, p. 104).
2 Fr. 12 (Vors. 13, p. 123. 18-20).
® Zeller (i°, p. 573) gives references to the explanations suggested by Brandis, Karsten, and Krische. More recent views (those of Tannery, Diels, Berger, and Otto Gilbert) are referred to in the text above. ©
* στεφάνη is sometimes translated as ‘crown’; but this rendering is open to the objection of suggesting a definite shape. Moreover, it is inapplicable to a series of wreaths or bands entwined the one within the other.
® Zeller, i°, p. 572. δ. Tannery, op. cit., p. 230. 7 Plato, Republic x. 616 D. Υ
.
CH. Ix PARMENIDES 69
the whorls. In the 7imaeus too there are no spheres, but bands or strips crossing one another at an angle. We may perhaps take the bands to be, not cylinders, but zones of a sphere bisected by a great circle parallel to the bounding circles. Burnet? thinks that the solid circle which surrounds all the bands cannot be a sphere either, because in that case ‘like a wall’ would be inappropriate. I do not, however, see any real difficulty in such a use of ‘like a wall’, and certainly Parmenides’ All was spherical.*
We now come to the main question of the nature of the bands, their arrangement relatively to one another, and the meaning to be attached to them severally. What we learn about them from Aétius and the fragments taken together amounts to this. First, the material of which they are composed is of two kinds; one is alternatively described as the ‘rarefied’ (ἀραιόν), light, flame (φλόξ) or fire; the other as the ‘condensed’ (πυκνόν), darkness, or night. The bands are of three kinds, the first composed entirely of the ‘rarefied’ element or fire, the second of the ‘ condensed’ or darkness, and the third of a mixture of the two. Secondly, as regards their arrangement, we are told that there is a solid envelope, a spherical shell, enclosing them all; two bands of unmixed fire are mentioned, of which one is immediately under the envelope, the other is about (reading περί with the MSS.) or wnder (reading ὑπό with Diels) ‘that which is in the very midst of all the bands’ and which is ‘solid’; these two bands are also ‘narrower’ (than something), where ‘ narrower’ means that their radii are smaller, that is to say, their inner surfaces are nearer (than something) to the centre of. the earth, which is the common centre of all the bands. The mixed bands, according to Aétius, are ‘ between’ the bands of fire and the bands of darkness ; the fragment (12) makes them come next to both the ‘narrower’ bands, the bands of fire.
There seems to be general agreement that the ‘mixed’ bands include the sun, the moon, and the planets; it is with regard to the meaning and position of the bands of fire, and to the place occupied by the Deity called by the names of Justice and Necessity, that there has been the greatest difference of opinion. Tannery’s
1 Plato, Zimaeus 36 B. 3 Burnet, Early Greek Philosophy, p. 216. * *It is complete on every side, like the mass of a well-rounded sphere poised from the centre in every direction’ (Fr. 8. 42-4; Vors. i*, p. 121. 3-5).
70 PARMENIDES PARTI
view is that the outermost band of fire under the solid envelope (which envelope may be regarded as one of the bands made of the ‘condensed’ element) is the Milky Way. In that case, however, the fire is not pure; for ‘it is the mixture of the dense and the rarefied which produces the colour of the Milky Way’. Tannery would get over this difficulty by supposing the band to be only fw// of fire, like the hoops of Anaximander, the almost continuous brightness being due to exspiration through the covering. But Aétius says that both the Milky Way and the sun are an exspiration of fire, and the sun is certainly represented by one of the mixed bands, so that the Milky Way should also be one of the mixed bands. The band of fire which (with the reading περί) is about the solid in the very centre of all the bands (i.e. the earth) Tannery takes to be our atmosphere. This seems possible, for Parmenides may have re- garded air it up as being fire. In Diels’ interpretation a similar view seems to be taken of the outermost band of fire which he calls ‘aether-fire’; and the assumption that the aether is fire is perhaps justified by the fact, if true, that Parmenides declared the heaven to be of fire. The intermediate bands consisting of the two elements, light and dark, in combination correspond in Tannery’s view to the orbits of the moon, the sun, and the planets respectively, which (starting from the earth) come in that order; possibly among these mixed bands there may be bands entirely dark as well (cf. Fr. 12).
Diels? takes the bands which consist exclusively of the ‘condensed’ element to be made of earth simply. There are two of these; one is the solid envelope, the solid firmament, ‘Outer Olympus’ ; the other is the crust of the earth. Just beneath the solid envelope comes the outer band of fire, which is the aether-fire. Next within this come the mixed class of bands which are the bands of stars containing both elements, earth and fire, not separate from one another but mixed together. Such dark rings, out of which the fire flashes out here and there, are the Milky Way, the sun, the moon, and the planets. After the mixed bands comes the solid earth-crust, below which again (reading ὑφ᾽ @, which Diels substitutes
1 Aét. ii, 11. 4 (D. G. p . 340; Vors. i*, p. 111. 23). 2 Diels, Vors. ii’, i, p. ‘Gre ; cf. Parmenides οὐ eg εν pp. 104 5644.
CH. Ix PARMENIDES γι
for περὶ 6) comes the inner band of fire, which therefore is inside the earth and forms a sernel of fire.
It will be seen that the idea of Anaximander that stars are dark rings with fire shining out at certain points is supposed, both by Tannery and Diels, to be more or less present in Parmenides’ con- ception, though Tannery only assumes it as applying to the Milky Way, which he wrongly identifies with the outer band of undiluted fire. _ Diels, more correctly, implies that it is the mixed rings made up of light and darkness in combination which exhibit the pheno- menon of ‘fire shining out here and there’, these mixed rings including the Milky Way as well as the sun, moon, and planets. It is possible that Aétius’s ‘mixed rings’ may be no more than his interpretation of the line in Fr. 12 which says that after the ‘narrower’ bands ‘filled with unmixed fire’ there come ‘bands filled with night and wth them (μετά, which Diels translates by ‘between’) is spread (or is set in motion, ferac) a share of fire’. _ And this line itself may mean either that the bands of night have a portion of fire mixed in them, or that each of the bands of night has a stream of fire (its ‘share of fire’) coursing through it. If the fire were enclosed in the darkness as under the second alternative, we should have a fairly exact reproduction of Anaximander’s tubes containing fire; but there is nothing in the fragment to suggest that fire shines out of vents in the dark covering ; hence the mixture of light and dark, with light shining out at certain points (without enclosure in tubes), as assumed by Diels, seems to be the safer interpretation.
Tannery and Diels differ fundamentally about the inner band | of fire. According to the former, it is the atmosphere round the earth, and, if the ‘atmosphere’ be taken to include the empty space outside the actual atmosphere as far as the nearest of the mixed bands, this seems quite possible. Diels, however, (reading ὑφ᾽ 4, ‘under which’, instead of περὶ 6,‘ round which’), makes it a kernel _ of fire zzside the earth and concludes that ‘ Parmenides is for us the - first who stated the truth not only as regards the form of the earth but also as regards its constitution, whether he guessed the latter or inferred it correctly from indications such as volcanoes and hot springs’. But it seems to me that there are great difficulties in
' Diels, Parmenides Lehrgedicht, pp. 105, 106.
72, PARMENIDES PARTI
the way of Diels’ interpretation. First, it is difficult to regard a kernel of fire, which ‘would presumably be a solid mass of fire, spherical in shape, as satisfying the description of a wreath or band. Secondly, whereas Fr. 12 speaks of the narrower bands as filled with unmixed fire and then of the mixed bands being ‘next to these’ (ai δ᾽ ἐπὶ ταῖς νυκτός ...), the mixed bands would, on Diels’ interpretation, be next to only one of the bands of fire (the outer one) and would not be next to the inner one but would be separated from it by the earth’s crust. Diels seems to have anticipated this objection, for he explains that it is doth the unmixed kinds of bands (i.e. those made of unmixed fire and those of unmixed earth, and not only the former, the ‘narrower’ bands) on which the mixed bands follow, in the inward direction starting from the outside envelope and in the outward direction starting from the centre ;! but ταῖς would much more naturally mean the narrower bands only. Thirdly, it seems to me to be difficult to assume that there is no band intervening between the surface of the earth and the nearest of the mixed bands; if there were no intervening band, the nearest mixed band, say that of the moon, would have to be in contact with the earth, and therefore the moon also, shining out of it, must practically touch the earth. Therefore there must be some intervening band. But, if there is an intervening band, it must be one of three kinds, dense, mixed, or fiery. It cannot be a dense band, for, if it were, the sun, moon and stars would never be visible; if it were a mixed band, there would again be some heavenly body or bodies in the same position of virtual contact with the earth; therefore the intervening band can only be a band of fire. I am disposed, therefore, to accept Tannery’s view that the inner band of fire is our atmosphere with the empty space beyond it reaching to the mixed bands.
If the above arguments are right, the order would be, starting from the outside: (1) the solid envelope like a wall; (2) a band of fire =the aether-fire; (3) mixed bands, in which are included the Milky Way, the planets, the sun, and the moon; (4) a band of fire, the inner side of which is our atmosphere, touching the earth; (5) the earth itself; which is Diels’ solution except as regards (4).
1 Parmenides Lehrgedicht, p. τοῦ.
ctx PARMENIDES 73
Berger! has an ingenious theory as regards the inner band of fire round the earth. If I understand him rightly, he argues that ' the bands in the heaven containing the stars were described in one part of Parmenides’ poem, and the zones of the earth in another, and that Fr. 12 refers to the zones; that the two descriptions then got confused in the Dorographi, and that the inner band of fire is really nothing but the ‘orrid zone, which has no business in the description at all. Diels has shown that this cannot be correct.? Gilbert * disagrees with Diels’ view of the inner band of fire as _ a kernel of fire inside the earth; he himself.thinks that there was not a band of fire about the earth, but that πυρώδης (with στεφάνη understood), ‘a band of fire’, is a mistake for mip,‘ fire’, or πυρῶδες in the neuter, and that the meaning is a fire or a fiery space _ connected with the earth (περί in that sense being possible) ‘ down- wards’, which fire or fiery space he says we must suppose to embrace the under surface of the earth’s sphere.
Lastly, there is a difficulty as to the position occupied by the ‘ goddess who steers all things’, Justice or Necessity. This mytho- logical personification of Necessity and Justice is, of course, after the Pythagorean manner,* and reminds us of the similar introduction _ of Necessity in Plato’s Myth of Er, which has so many other points of resemblance to Parmenides’ theory. Fragment 12 says that this _ Deity is ‘in the middle of these’, i.e. presumably ‘these dands’, and _ Aétius, that is to say Theophrastus, took this to mean in the midst _ of the ‘ bands filled with night but with a share of fire in them’. _ Simplicius, on the other hand, takes it to mean ‘in the middle of the _ whole system (ἐν μέσῳ πάντων)᾽,5 i.e. in the middle of the whole world, clearly identifying the goddess with the central fire or hearth of the _Pythagoreans. Diels seems to favour Simplicius’s view, taking the centre of the universe to be the centre of the earth,® without, how-
* Berger, Geschichte der wissenschaftlichen Erdkunde der Griechen, p. 204 sq. 3 Parmenides Lehrgedicht, p.104. Since the torrid zone, as viewed by Par- menides, is twice the size of the zone between the tropics, the ‘ narrower’ zones _must be the temperate zones, which requires the impossible reading ἀκρίτοιο ; with the true reading dxpyrow, the torrid zone would be ‘broader’, not _ ‘narrower’, Besides, Aétius’s paraphrase agrees so closely with the fragment, ᾿ς especially in the striking introduction of the Deity, that it cannot be regarded __as being anything else than Theophrastus’s paraphrase of the verses. __ ® Gilbert, ‘ Die δαίμων des Parmenides’, in Archiv fiir Gesch. der Philosophie, ᾿ Χχ, 1906, pp. 25-45. * Tannery, loc, cit. 5 Simpl. iz Phys. p. 34. 15 ( Vors. 15, p. 123. 16). ® Diels, Parmenides Lehrgedicht, pp. 107-8.
74 PARMENIDES PART I
ever, attempting to reconcile this with Aétius’s statement that she is placed in the middle of the mixed bands. It is in any case difficult to suppose that Parmenides treated his goddess who ‘guides the encircling heaven and compels it to hold fast the bounds of the stars’ as shut up within a solid spherical earth with no outlet ; the difficulty is even greater than in the Myth of Er, where at all events there is ‘a straight light like a pillar which extends from above through all the heaven and earth’, and which accordingly passes through the place where Necessity is assumed to be seated. The statement of Aétius that she is placed in the middle of the mixed bands suggested to Berger! the possibility that her place was in the sun, in view of the pre-eminent position commonly assigned to the sun in the celestial system.? Gilbert holds that the goddess had her abode in the fiery space under the earth above mentioned; he quotes from other poets, Hesiod, Heraclitus, Aeschylus and Sophocles, references to Diké as con- nected with the gods of the lower world, his object being to show that, in connecting Justice or Necessity with the earth, night, and the under-world, Parmenides was only adopting notions generally current.*. Gilbert (like Diels) is confronted with the difficulty of Aétius’s location of the goddess ‘in the middle of the mixed bands,’ and he disposes of this objection by assuming that the words were interpolated by some one who wished to find her in the sun.*. This, however, seems too violent.
Both Tannery and Diels specially mention the planets, and Tannery makes Parmenides arrange the heavenly bodies in the following order, starting from the earth: moon, sun, planets, fixed stars. There is, however, nothing in the texts about the bands which distinguishes the planets from the fixed stars or indicates their relative distances.
1 Berger, op. cit., pp. 204, 205.
2 e.g. Cleanthes (Aét. 11. 4.16) saw in the sun the seat of authority in the universe (τὸ ἡγεμονικὸν τοῦ κόσμου) : cf. also such passages as Theon of Smyrna, pp. 138. 16, 140. 7, 187. 16; Plut. De fac. in orbe lunae 30, 945 C; Proclus, zn Timaeum 258 A, ‘The sun, where the justice ordering the world is placed.’
8 Gilbert, loc. cit., p. 36.
* The text in Diels’ Doxographi (p. 335. 10 sq.) being καὶ τὸ μεσαίτατον πασῶν περὶ ὃ πάλιν πυρώδης" τῶν δὲ συμμιγῶν τὴν μεσαιτάτην ἁπάσαις τοκέα πάσης κινήσεως καὶ γενέσεως ὑπάρχειν, ἥντινα καὶ δαίμονα κιτ.ἑ., Gilbert would reject τῶν δὲ συμμιγῶν τὴν μεσαιτάτην as an interpolation, leaving καὶ τὸ μεσαίτατον πασῶν, περὶ ὃ πάλιν πυρώδης (ἢ στεφάνη), ἁπάσαις τοκέα πάσης κινήσεως καὶ γενέσεως ὑπάρχειν κιτ.ἕ,
.
ΠΘΗΟΙΧ PARMENIDES 75
i
| The only passage in the Doxographi throwing light on the matter _ is a statement that
᾿ς *Parmenides places the Morning Star, which he thinks the same 85 the Evening Star, first in the aether; then, after it, the sun, and _ under it again the stars in the fiery (thing) which he calls heaven.’ ὦ
Tannery thinks that, if Parmenides distinguished Venus, and if it was from the first Pythagoreans that he learnt to do so, the other planets must equally have been known to the Pythagoreans and therefore to Parmenides. Tannery’s view, however, of Parmenides’ arrangement of the stars can hardly be reconciled with the distinct statement of Aétius that, while Venus is outside the sun, the other stars are below it; this, except as regards Venus, ‘agrees with Anaximander’s order, according to which both the planets and the other stars are all placed below the sun and moon. Tannery is therefore obliged to assume that Aétius’s remark is an ‘error based on a too rigorous interpretation of the terms aether _and heaven ; this, however, seems somewhat arbitrary.
_ It remains to deal with the statement of the Doxographi that _Parmenides held the moon to be illuminated by the sun:
_ *The moon Parmenides declared to be equal to the sun; for indeed it is illuminated by it.’ ?
This is the more suspicious because in another place Aétius attributes the first discovery of this fact to Thales, and adds that Pythagoras, Parmenides, and Empedocles, as well as Anaxagoras and Metrodorus, held the same view.* Parmenides was doubtless credited with the discovery on the ground of two lines from his poem.* The first is quoted by Plutarch : ὃ
‘For even if a man says that red-hot iron is not fire, or that the moon is not a sun because, as Parmenides has it, the moon is
“a night-shining foreign light wandering round the earth”,
he does not get rid of the use of iron or of the existence of the moon.’
? Aét. ii. 15. 7 (2. G. p. 345).
® Aet. ii. 26. 2 (D. G. "ἢ 357; Vors. i, P- 111. 32).
3. Aét. ii. 28. 5 (D. G. p. 358; Vors. i*, p. 111. 33).
4 Fr. 14 and 15 (Vors. 15, p. 124. 6, το).
5. Plutarch, Adv. Colot. 15, p. 1116 A (Vors. i*, p. 124, 4-7).
76 ὶ PARMENIDES PARTI
But, even if the verse is genuine, ‘foreign’ (ἀλλότριον) need not have meant ‘ borrowed’; the expression ἀλλότριον φῶς is, as Diels says, a witty adaptation of Homer’s ἀλλότριος φῶς used of persons, ‘a stranger’.2 Tannery thinks that the line is adapted from one of Empedocles’, and was probably interpolated in Parmenides’ poem by some Neo-Pythagorean who was anxious to refer back to the Master the discovery which gives Anaxagoras his greatest title to fame.
Boll,* on the other hand, considers it absolutely certain that Parmenides knew of the illumination of the moon by the sun. He admits, however, that we cannot suppose Parmenides to have discovered the. fact for himself, and that we cannot be certain whether he got it from Anaximenes or the Pythagoreans. We have seen (p. 19) good reason for thinking that it was not Anaximenes who made the discovery; and the only support that Boll can find for the alternative hypothesis is the statement of Aétius that Pythagoras considered the moon to be a ‘ mirror-like _body’ (κατοπτροειδὲς σῶμα). But-this is an uncertain phrase to build upon, especially when account is taken of the tendency to attribute to Pythagoras himself the views of later Pythagoreans ; and indeed the evidence attributing the discovery to Anaxagoras is so strong that it really excludes all other hypotheses.
The other line speaks of the moon as ‘always fixing its gaze on the beams of the sun’. This remark is certainly important, but is far from explaining the cause of the observed fact. But we have positive evidence against the attribution of the discovery of the opacity of the moon to Parmenides or even to Pythagoras. It is part of the connected prose description of Parmenides’ system® that the moon is a mixture of air and fire;’ in other passages we are told that Parmenides held the moon to be of fire®
? Diels, Vors. 112, τ, p. 675 ; Parmenides Lehrgedicht, p. 110.
3 Homer, ας v. 2143 Od. xviii. 219, &c.
8 Tannery, op. cit., p. 210. The lines are respectively—
Νυκτιφαὲς περὶ γαῖαν ἀλώμενον ἀλλότριον φῶς (Parm.). Κυκλοτερὲς περὶ γαῖαν ἑλίσσεται ἀλλότριον φῶς (Emped.).
* Boll, art. ‘Finsternisse’ in Pauly-Wissowa’s Real-Encyclopadie der classischen Altertumswissenschaft, vi. 2, 1909, p. 2342.
5 Aét. ii. 25. 14 (D. G. p. 357).
5 Aét. ii, 7. 1 (D.G. p. 335; Vors. ἴδ, p. 111. 5 sqq.).
7 Ibid. (D. G. p. 335; Vors. i®, p. 111. 13). 8. Aét. ii. 25. 3 (D. G. p. 356; Vors. 13, p. 111. 31).
CHIX PARMENIDES 77
_ and to be an excretion from the denser part of the mixture in the . Milky Way; which itself (like the sun) is an exspiration of fire.? - More important still is the evidence of Plato, who speaks of ‘the fact which Anaxagoras lately asserted, that the moon has its light from the sun’.* It seems impossible that Plato should have spoken in such terms if the fact had been stated for the first time by -Parmenides or the Pythagoreans.
1 Aét. ii. 20.8 a (D. G. p. 349; Vors. i*, p. 111. 35). 5 Aét. ii. 7. 1 (2. σ. p. 335; Vors. #, p. 111. 13). 3 Plato, Cratylus 409 A.
Χ ANAXAGORAS
ANAXAGORAS was born at Clazomenae in the neighbourhood of Smyrna about 500B.c. He neglected his possessions, which were considerable, in order to devote himself to science. Some one once asked him what was the object of being born, to which he replied, ‘The investigation of sun, moon, and heaven.’? He seems to have been the first philosopher to take up his abode at Athens, where he enjoyed the friendship of Pericles, who had probably induced him to come thither. When Pericles became unpopular shortly before the outbreak of the Peloponnesian war, he was attacked through his friends, and Anaxagoras was accused of impiety for holding that the sun was a red-hot stone and the moon earth. According to one account he was fined five talents and banished ;* another account says that he was put in prison and it was intended to put him to death, but Pericles got him set at liberty ;° there are other variations of the story. He went and lived at Lampsacus, where he died at the age of 72.
A great man of science, Anaxagoras enriched astronomy by one epoch-making discovery. This was nothing less than the discovery of the fact that the moon does not shine by its own light but receives its light from the sun. As a result, he was able to give (though not without an admixture of error) the true explanation of eclipses. I quote the evidence, which is quite conclusive :
‘, . . the fact which he (Anaxagoras) recently asserted, namely that the moon has its light from the sun.’ ὃ
‘Now when our comrade, in his discourse, had expounded that proposition of Anaxagoras, that “the sun places the brightness in the moon”, he was greatly applauded.’ *
1 Plato, Hippias Major 283 A. 3 Diog. L. ii. 10 (Vors. i*, p. 294. 17). 8 Plato, Apology 26 D. 4 Diog. L. ii. 12 (Vors. i*, p. 294. 32). δ᾽ Ibid. ii. 13 (Vors. i*, p. 294. 42). 5 Plato, Cratylus, p. 409 A.
7 Plutarch, De facie in orbe lunae 16, p. 929 B (Vors. i*, p. 321. 5-7).
ANAXAGORAS "9
‘The moon has a light which is not its own, but comes from the sun.’?
‘The moon is eclipsed through the interposition of the earth, sometimes also of the bodies below the moon’? [i.e. the ‘ bodies below the stars which are carried round along with the sun and the moon but are invisible to us’.*]
‘The sun is eclipsed at the new moon through the interposition of the moon.’* ‘He was the first to set out distinctly the facts about eclipses and illuminations.’®
‘For Anaxagoras, who was the first to put in writing, most clearly and most courageously of all men, the explanation of the moon's illumination and darkness, did not belong to ancient times, and even his account was not common property but was still a secret, current only among a few and received by them with caution or simply on trust. For in those days they refused to tolerate the physicists and star-gazers as they were called, who presumed to fritter away the deity into unreasoning causes, blind forces, and necessary properties. Thus Protagoras was exiled, and Anaxa- _ goras was imprisoned and with difficulty saved by Pericles.’ ὃ ‘ Anaxagoras, in agreement with the mathematicians, held that _ the moon’s obscurations month by month were due to its following _the course of the sun by which it is illuminated, and that the _ eclipses of the moon were caused by its falling within the shadow
_ of the earth, which then comes between the sun and the moon,
_ while the eclipses of the sun were due to the interposition of the / moon,’?
_ ‘Anaxagoras, as Theophrastus says, held that the moon was _ also sometimes eclipsed by the interposition of the (other) bodies below the moon.’ ὃ
Here, then, we have the true explanation of lunar and other eclipses, though with the unnecessary addition that, besides the earth, there are other dark bodies invisible to us which sometimes
1 Hippolytus, Refuz. i. 8.8 (from Theophrastus: see D.G. p. 562; Vors. i?,
Σ 46).
5 Ibid. i. 8. 9. (D. G. p. 562; Vors. i, p. 301. 47).
5 Tbid. i. 8. 6 (D.G. p. 562; Vors. i*, p. 301. 41).
4 Ibid. i. 8. 9 (D. G. p. 562; Vors. i*, p. 301. 48).
5 Ibid. i. 8. 10 (D. G. p. 562; Vors. 15, p. 302. 3).
§ Plutarch, Vic. 23 (Vors. i?, p. 297. 40-6).
7 A&t. ii. 29. 6 (D. G. p. 360; Vors. 13, p. 308.17). I have in the last phrase _ translated Diels’ conjecturally emended reading ἥλιον δὲ τῆς σελήνης instead of
᾿ς μᾶλλον δὲ τῆς σελήνης ἀντιφραττομένης (D.G. pp. 53-4). The difficulty, however,
| is that, according to the heading, the passage deals with the eclipses of the _ moon only. 8 Aét. ii. 29. 7 (2. G. p. 360; Vors. i*, p. 308. 20).
80.” ANAXAGORAS PARTI
obscure the moon and cause eclipses. In this latter hypothesis, as in much else, Anaxagoras followed Anaximenes.!
Whether Anaxagoras reached the true explanation of the phases of the moon is much more doubtful. It is true that Parmenides had observed that the moon has its bright portion always turned in the direction of the sun; when to this was added Anaxagoras’s discovery that the moon derived its light from the sun, the explana- tion of the phases was ready to hand. But it required that the moon should be spherical in shape; Anaxagoras, however, held that the earth, and doubtless the other heavenly bodies also, were
1 The same idea is attributed by Aristotle (De caelo ii. 13, 293 Ὁ 21-25) to certain persons whom he does not name: ‘Some think it is possible that more bodies of the kind [i.e. such as the Pythagorean counter-earth] may move about the centre but may be invisible to us owing to the interposition of the earth. This, they say, is the reason why more eclipses of the moon occur than of the sun, for each of the bodies in question obscures the moon, and it is not only the earth which does so.’ An interesting suggestion has been made (by Boll in art. ‘Finsternisse’ in Pauly-Wissowa’s Real-Encyclopadie d. class. Altertumsw, vi. 2, p- 2351), which furnishes a conceivable explanation of the persistence of the idea that lunar eclipses are sometimes caused by the interposition of dark bodies other than the earth. Cleomedes (De motu circulari ii. 6, Ὁ. 218. 8. sqq.) mentions that there were stories of extraordinary eclipses which ‘the more ancient of the mathematicians’ had vainly tried to explain; the supposed ‘ paradoxical’ case was that in which, while the sun seems to be still above the horizon, the ec/ifsed moon rises in the east. The phenomenon appeared to be inconsistent with the explanation of lunar eclipses by the entrance of the moon into the earth’s shadow; how could this be if both bodies were above the © horizon at the same time? The ‘more ancient’ mathematicians tried to argue that it was possible that a spectator standing on an eminence of the spherical earth might see along the generators of a cone, i.e. a little downwards on all sides, instead of merely in the A/ane of the horizon, and so might see both the sun and the moon even when the latter was in the earth’s shadow. Cleomedes denies this and prefers to.regard the whole story of such cases as a fiction designed merely for the purpose of plaguing astronomers and philosophers ; no Chaldean, he says, no Egyptian, and no mathematician or philosopher has recorded such a case. But we do not need the evidence of Pliny (V.H. ii, c. 57, § 148) to show that the phenomenon is possible; and Cleomedes himself really gives the explanation (pp. 222. 28-226. 3), namely, that it is due to atmospheric refraction. Observing that such cases of atmospheric refraction were especially noticeable in the neighbourhood of the Black Sea, he goes on to say that it is possible that the visual rays going out from our eyes are refracted through falling on wet and damp air, and so reach the sun though it is already below the horizon ; and he compares the well-known experiment of the ring at the bottom of a jug, where the ring, just out of sight when the jug is empty, is brought into view when water is poured in. Unfortunately there is nothing to indicate the date of the ‘more ancient mathematicians’ who gave the somewhat primitive explanation which Cleomedes refutes; but was it the observation of the phe- nomenon, and their inability to explain it otherwise, which made Anaxagoras and others adhere to the theory that there are other bodies besides the earth which sometimes, by their interposition, cause lunar eclipses ?
CH. X ANAXAGORAS 81
flat, and accordingly his explanation of the phases could hardly have been correct.?
Anaxagoras’s cosmology contained other fruitful ideas. Accord- ing to him the formation of the world began with a vortex set up, in a portion of the mixed mass in which ‘all things were together’, by his deus ex machina, Nous.2. This rotatory movement began at one point and then gradually spread, taking in wider and wider circles. The first effect was to separate two great masses, one _ consisting of the rare, hot, light, dry, called the ‘aether’, and the other of the opposite categories and called ‘air’. The aether or fire took the outer position, the air the inner.2 The next step is the successive separation, out of the air, of clouds, water, earth, and stones. The dense, the moist, the dark and cold, and all the heaviest things collect in the centre as the result of the circular motion ; and it is from these elements when consolidated that the earth is formed.® But, after this, ‘in consequence of the violence of the whirling motion, the surrounding fiery aether tore stones away from the earth and kindled them into stars.’ Reading this with the remark that stones ‘rush outwards more than water’,’ we see ' that Anaxagoras conceived the idea of