^{page 294 note 1} e.g. the well-known story of the sacrifice of an ox on the occasion of the discovery that the angle on a diameter of a circle is a right angle is told about both Thales and Pythagoras (Diog. Laert. 1. 24–25); cf. Schwartz in P.W. s.v. ‘Diogenes Laertios’, col. 741; Pfeiffer, , Callimachus, 1949, i. 168.Google Scholar

^{page 294 note 2} 8th ed. 1956, edited by W. Kranz.

^{page 294 note 3} There are in classical literature at least three mentions of Thales not included by Diels, , viz. Aristophanes, Clouds 180Google Scholar; Birds 1009; Plautus, , Captivi 274Google Scholar; and there are probably more. Cf. Gigon, O., Der Ursprung der griechischen Philosophie, 1945, p. 11Google Scholar, for a plea for a really complete collection of notices regarding the Pre-Socratics.

^{page 295 note 1} Gigon, O., Der Ursprung der griechischen Philosophic, 1945, p. 42.Google Scholar

^{page 295 note 2} Cf. Boll in P.W. s.v. ‘Finsternisse’, col. 2353; Heath, , Aristarchus of Samos, 1913, pp. 13–16Google Scholar; Fotheringham in J.H.S. xxxix [1919], 180 ff.Google Scholar, and in M.N.R.A.S. Ixxxi [1920], 108.Google Scholar

^{page 295 note 3} Cf. Neugebauer, O., The Exact Sciences in Antiquity, 2nd ed. 1957, pp. 141–2.Google Scholar

^{page 295 note 4} Ptolemy mentions it (Synt. math., ed. Heiberg, i. 269. 18 f.) and also the a similar cycle obtained by multiplying the former by 3, making 669 lunar months or 19,756 days, but attributes both to , which refers to Greek astronomers earlier than Hipparchus and not to the Babylonian astronomers, whom Ptolemy always calls .

^{page 295 note 5} Kugler, F. X., Sternkunde und Stemdienst in Babel, ii (1909), 58 f.Google Scholar; Neugebauer, O., Astronomical Cuneiform Texts, i (1956), 68–69, 115, 160 f.Google Scholar

^{page 295 note 6} Ex. Sci., p. 142. As regards the use of the 18-year cycle he says (ibid.), ‘there are certain indications that the periodic recur rence of lunar eclipses was utilised in the preceding period [i.e. before 311 B.C.] by means of a crude 18-year cycle which was also used for other lunar phenomena’ (my italics).

^{page 295 note 7} Diels's suggestion (Antike Technik, 3rd ed. 1924, p. 3, n. 1) that here means ‘solstice’ has nothing to recommend it.

^{page 295 note 8} Ap. Theon. Smyrn., p. 198. 14, ed. Hiller = Diels 17.

^{page 296 note 1} Cf. Kirk, G. S. and Raven, J. E., The Presocratic Philosophers, 1957, p. 78Google Scholar—Kirk's reference to ‘the undoubted fact of Thales’ prediction' is a considerable overstatement.

^{page 296 note 2} Gigon, (op. cit., p. 52Google Scholar) thinks that Herodotus may have taken the story from a poem of Xenophanes, who perhaps expressed incredulity at the report; but it seems much more probable that Herodotus is relating the generally accepted hearsay of his time.

^{page 296 note 3} Revue Archéologique, ix [1864], 170–99.Google Scholar

^{page 296 note 4} Dreyer, J. L. E., A History of Astronomy (originally entitled A History of the Planetary Systems), repr. 1953 (Dover Publications, New York), p. 12.Google Scholar

^{page 296 note 5} Ex. Sci., p. 142. Neugebauer complains of the vagueness of Herodotus' report, but this is somewhat unjust; obviously, what impressed Herodotus was the sudden change from bright daylight to comparative darkness—hence the choice of the words .

^{page 296 note 6} Kirk, and Raven, (op. cit., p. 76Google Scholar) cite this as ‘convincing evidence’ for Thales’ reputation as an engineer—the adjective seems hardly appropriate.

^{page 296 note 7} On this and the scholion (== Diels 3), see below.

^{page 296 note 8} This earliest example of a perennially popular genre of comic story has been subjected to a solemn discussion and analysis by Landmann, M. and Fleckenstein, J. O., ‘Tagesbeobachtung von Sterner in Altertum’, Vierteljakrschr. d. Naturf. Gesch. in Zürich, lxxxviii [1943], 98 f.Google Scholar, in the course of which it is suggested that the story is not ‘echt oder unecht’, but contains a germ of historical truth in that Thales probably observed stars in daylight from the bottom of a well! The article contains an entirely uncritical account of Thales' alleged achievements and discoveries, with the usual imaginary picture of him as the transmitter of Egyptian and Babylonian wisdom.

^{page 297 note 1} Snell, B., ‘Die Nachrichten über die Lehren des Thales und die Anfänge der griechischen Philosophic- und Literatur geschichte’, Philologus xcvi (1944), 170–82.Google Scholar

^{page 297 note 2} Id., op. cit., p. 172.

^{page 297 note 3} Op. cit. pp. 170 and 171 with footnote (1). Thales, of course, was not the only early thinker to be thus treated by Aristotle; Anaxagoras was another—cf. Cornford, F. M., ‘Anaxagoras’ Theory of Matter—II’, C.Q. xxiv [1930], 83–95.Google Scholar

^{page 298 note 1} See Diog. Laert., i. 40 f.

^{page 298 note 2} Werner Jaeger, Aristotle, 2nd ed. 1948 (translated into English by R. Robinson), Appendix II, ‘On the Origin and Cycle of the Philosophic Life’, p. 454, is surely wrong in saying that the reports emphasizing the practical and political activities of the Seven Wise Men were first introduced into the tradition by Dicaearchus in the latter half of the fourth century. In the case of Thales, at any rate, it is the early tradition as exemplified by Herodotus that makes him a practical statesman, while the later doxographers foist on to him any number of discoveries and achievements, in order to build him up as a figure of superhuman wisdom. Jaeger is also wrong in asserting that Plato had made Thales ‘a pure representative of the theoretical life’ (op. cit., p. 453)—he apparently overlooks Rep. 10. 600a, where this is far from being the case, and he takes the well story too seriously. On the other hand, he is undoubtedly right to emphasize the com paratively late origin of the traditional picture of Pre-Socratic philosophy, ‘the whole picture that has come down to us of the history of early philosophy was fashioned during the two or three generations from Plato to the immediate pupils of Aristotle’ (429).

^{page 298 note 3} See especially Plato, Rep. 10. 600a (and Burnet, , Early Greek Philosophy, p. 47 n. 1Google Scholar) where Thales is coupled with Anacharsis, who is said to have invented the potter's wheel and the anchor.

^{page 298 note 4} The single apparent exception (Met. 1. 3. 983^b21 = Diels 12), where Aristotle seems to be more definite, has already been shown to be illusory, in that if the quotation were carried to its proper end we should find the familiar again. Kirk, and Raven, (op. cit., p. 85)Google Scholar also remark on the cautious manner in which Aristotle cites Thales; cf. Snell, , op. cit., pp. 172 and 177Google Scholar— but Snell's insistence that Aristotle is not relying merely on oral tradition but must be using a pre-Platonic written source (which Snell identifies as Hippias) is hardly convincing on the evidence available.

^{page 298 note 5} What Diels (pp. 80–81) prints as ‘Angebliche Fragmente’ of Thales' works are, of course, completely spurious, as Diels himself points out.

^{page 298 note 6} Diog. Laert. 1. 23, cf. Joseph. c.Ap. 1. 2; Simplicius, Phys. 23. 29.

^{page 298 note 7} Cf. Kirk and Raven, p. 218—Aristotle, Plato, and Pythagoras.

^{page 299 note 1} Cf. Diels, , Dox. p. 219; p. 112.Google Scholar

^{page 299 note 2} Oddly enough, this tendency can also be seen in modern times. Earlier writers, like Tannery, are far less prone to exaggerate Thales' achievements than more recent ones, such as van der Waerden—on whom see further below.

^{page 299 note 3} There are summaries in Zeller, , Outlines of the History of Greek Philosophy, 13th ed. repr. 1948, pp. 4–8Google Scholar; Burnet, , Early Greek Philosophy, 4th ed. repr. 1952, pp. 33–38Google Scholar; Kirk, and Raven, , op. cit., pp. 1–7Google Scholar; cf. Michel, P.-H., De Pythagore à Euclide, 1950, pp. 72–167—Google Scholara useful reference section for all the sources relevant to Greek mathematics.

^{page 299 note 4} Dox., p. 101.

^{page 299 note 5} Dox., pp. 45 f.

^{page 300 note 1} Dox., pp. i79f.

^{page 300 note 2} Cf. Schwartz in P.W. s.v. ‘Diogenes Laertios’; Dox., pp. 161 f.

^{page 300 note 3} Op. cit., pp. 170–1, 176.

^{page 300 note 4} Cf. Thomson, J. O., History of Ancient Geography, 1948, pp. 112 and 116.Google Scholar

^{page 300 note 5} Cf. Kirk, G. S., Heraclitus: the Cosmic Fragments, 1954, pp. 20–25.Google Scholar

^{page 300 note 6} What Gigon, (op. cit., pp. 43–44Google Scholar) calls the ‘anekdotische und apophthegmatische Überlieferung’.

^{page 300 note 7} De invent. 2. 2. 6. Further on he mentions Isocrates whose book Cicero knows to exist but which he has not himself found, although he has come across numerous writings by Isocrates’ pupils.

^{page 301 note 1} Cf. Jaeger, , Aristotle, p. 335Google Scholar; in the work of compiling a comprehensive history of human knowledge Menon was allotted the field of medicine, Eudemus that of mathematics and astronomy and perhaps theology, and Theophrastus that of physics and metaphysics.

^{page 301 note 2} Cf. Diels, , Dox., p. 128.Google Scholar

^{page 301 note 3} Dox., pp. 145 f.

^{page 301 note 4} Early Greek Philos., p. 36.

^{page 301 note 5} Snell, , op. cit., pp. 175–6.Google Scholar

^{page 301 note 6} Such as, Cajori, F., A History of Mathematics, 1919, pp. 15 f.Google Scholar; Smith, D. E., History of Mathematics, i (1923), 64 f.Google Scholar; Sarton, G., Introduction to the History of Science, repr. 1950, i. 72Google Scholar; Capelle, W., Die Vorsokratiker, 4th ed. 1953, pp. 67Google Scholar f.; Waerden, B. L. van der, Science Awakening, 1954, pp. 86 f.Google Scholar; Hauser, G., Geometric der Griechen von Thales bis Euklid, 1955, pp. 43–49Google Scholar; Gomperz, , Greek Thinkers, repr. 1955, i. 46–48Google Scholar; Becker, O., Das mathematische Denken der Antike, 1957, pp. 37 fGoogle Scholar.—to name but a few. Even T. L. Heath, who was aware of the flimsiness of the evidence on which our knowledge of Thales is based, is inclined to over-estimate his achievements— cf. History of Greek Mathematics, 1921, i. 128 f.; Manual of Greek Mathematics, 1931, pp. 81 f.

^{page 301 note 7} All three now only extant in meagre fragments, recently edited with a commentary by Wehrli, F., Eudemos von Rhodos (Die Schule des Aristoteles, Heft viii), 1955.Google Scholar

^{page 302 note 1} Cf. Martini in P.W. s.v. ‘Eudemos’; Wehrli, , op. cit., p. 114.Google Scholar

^{page 302 note 2} Cf. Michel, , op. cit., pp. 82–83Google Scholar, quoting Tannery.

^{page 302 note 3} Wehrli, , op. cit., pp. 54–67.Google Scholar

^{page 302 note 4} Id. frag. 133 ad fin.

^{page 302 note 5} Id., frag. 137.

^{page 302 note 6} Id., frag. 140, p. 5g, 1. 24,

^{page 302 note 7} Id., frag. 148. Heath, however, sees no reason to doubt that these late commentators of the fifth and sixth centuries A.D., such as Proclus, Simplicius, and Eutocius, consulted Eudemus at first hand (Hist, of Gk. Maths. ii. 530 f.; cf. The Thirteen Books of Euclid's Elements, 2nd ed. repr. 1956 (Dover Publications, New York), i. 29–38Google Scholar. Heath contradicts Tannery's view (cf. also Martini in P.W. s.v. ‘Eudemos’; Heiberg, , Philol. xliii. 330 f.Google Scholar), but offers no explanation of the passages I have cited above; he does agree that in the case of Oenopodes, for example, Proclus gives a quotation which cannot have been at first hand.

^{page 302 note 8} Heath, , H.G.M. i. 130Google Scholar (cf. Man., p. 83), v. d. Waerden, p. 87, Hauser, p. 45, and Becker, p. 38, give less well-authenticated lists.

^{page 302 note 9} Cf. Heath, , Euclid, p. 36.Google Scholar

^{page 303 note 1} Euclid, , Elements i, Def. 17.Google Scholar

^{page 303 note 2} Cf. Heath, , H.G.M. i. 131.Google Scholar

^{page 303 note 3} Wehrli, frag. 134.

^{page 303 note 4} E.G.P., p. 45; cf. Gigon, , op. cit., p. 55.Google Scholar

^{page 303 note 5} There is an excellent modern example of this type of rationalization in the oft-repeated statement that die Egyptians of the second millennium B.C. knew that a triangle with sides of 3, 4, and 5 units was right-angled, and used this fact in marking out with ropes the base angles of their monuments; hence, it is said, they knew empirically this special case of the general ‘theorem of Pythagoras’. In actual fact, there is no truth in this at all, and the whole story originated in a piece of typical guesswork by Cantor, M. (whose Vorlesungen über Geschkhte der Mathematik, 4 vols., 1880–1908Google Scholar, is probably responsible for more erroneous beliefs in this field than any other book—cf. Neuge-bauer, O., Isis, xlvii [1956], 58Google Scholar, for a just appraisal of it). Because Cantor thought that ropes representing a triangle with sides of 3, 4, and 5 were the simplest means for constructing a right-angle, he assumed that this was die method used by the Egyptians. Unfortunately, there is no evidence that they knew that such a triangle was right-angled; cf. Heath, , Man., p. 96Google Scholar; v. d. Waerden, p. 6.

^{page 303 note 6} Cf. Neugebauer, , Ex. Sci., pp. 147–8.Google Scholar Its beginnings may be dated back to Hippocrates in the last half of the fifth century B.C., if he was really the first to compose a book of ‘Elements’ () as Proclus says (in the ‘Eudemian Summary’—see below— Wehrli, frag. 133, p. 55, 1. 7): cf. v. d. Waerden, pp. 135–6.

^{page 304 note 1} Cf. Heath, , H.G.M. i. II8f.Google Scholar; Euclid, pp.37–38.

^{page 304 note 2} Proclus Diadochus, In primum Euclidis Elementorum librum comment., Prologus II, pp. 64 f. ed. Friedlein; Wehrli, frag. 133, pp. 54–56.

^{page 304 note 3} Wehrli, (op. cit., 115Google Scholar) points out that Eudemus follows Herodotus' view even in the face of a different opinion expressed by Aristotle.

^{page 304 note 4} 2. 109; cf. Diod. Sic. 1. 81. 2; Strabo 757 and 787.

^{page 304 note 5} In fact, a visit of Thales to Babylonia is even less well authenticated than a visit to Egypt—Josephus (c.Ap. 1. 2) seems to be the only writer to mention the former; but since Egyptian astronomy never evolved beyond a very elementary level and did not concern itself with eclipses (cf. Neug., , Ex. Sci., pp. 80–91Google Scholar; 95 ad fin.), some connexion between Thales and Babylonia had to be manufactured. This was made the more plausible by reference to Herodotus' statement (2. 109) that the Greeks learnt about the ‘polos’, the gnomon, and the division of the day into 12 parts (but on this see below) from the Babylonians.

^{page 304 note 6} 2. 20 f.

^{page 304 note 7} Aëtius 4. 1. 1 = Diels 16; cf. Diod. Sic. 1. 38.

^{page 304 note 8} e.g. Gomperz, Gigon, Hölscher, and Hauser accept them all apparently without a qualm; Gigon, (op. cit., p. 87Google Scholar) even accepts Cicero's story (de div. 1. 50. 112) about Anaximander's foretelling an earthquake.

^{page 305 note 1} This was represented as part of the divine teaching of the ancient Egyptian god Thoth (Greek, Hermes) and his interpreters, Nechepso and Petosiris; cf. Festugiére, A.-J., La Révélation d'Hermés Trismégiste, 4 torn. (1944–1954Google Scholar)—especially torn, i, pp. 70 f.

^{page 305 note 2} Cf. Burnet, , Early Greek Philosophy, p. 88Google Scholar; Field, G. C., Plato and His Contemporaries, 2nd ed. 1948, p. 13.Google Scholar

^{page 305 note 3} There is a curious dualism evident in most of the modern accounts of Thales. Even those scholars who profess to recognize the unsatisfactory nature of the evidence on which our knowledge of him depends continue to discuss his alleged achievements as though they are undoubtedly real. Despite the occasional qualifying phrase (e.g. ‘Thales is said to …’, ‘tradition has it that Thales …’, and so on), the desire to believe is so strong that his travels, for example, are now treated as an established fact. One result of this is that the notices about Thales in classical dictionaries and encyclopedias are for the most part uniformly bad; especially misleading are those in P.W., O.C.D., and the Encyclopaedia Britannica—Chambers's is slightly better, while Tannery's in La Grande Encyclopédie, tom. 30 is eminently sensible. It is noteworthy that some American scholars in recent years are at last realizing how little is really known about Thales: cf. Fleming, D. in Isis, xlvii [1956]Google Scholar, reviewing Essays on the Social History of Science (Centaurus 1953); Clagett, M., Greek Science in Antiquity, 1957, p. 56.Google Scholar

^{page 306 note 1} Carpenter, Rhys, Folk Tale, Fiction and Saga in the Homeric Epics, repr. 1956, pp. 39–40.Google Scholar

^{page 306 note 2} See the article by Snell, already quoted.

^{page 307 note 1} Both Egyptian and Babylonian mathematics were already highly developed by the beginning of the second millennium B.C., and both remained largely static until Hellenistic times.

^{page 307 note 2} Excellent accounts are given by Neugebauer, O., The Exact Sciences in Antiquity, 2nd ed. 1957Google Scholar (with full references to the relevant literature), and by Waerden, B. L. van der, Science Awakening, 1954Google Scholar (despite an exaggerated and misleading treatment of Thales).

^{page 307 note 3} The Babylonians commonly used the rough figure π = 3, but one text implies the more accurate value π = 3 ⅛ cf. Neugebauer, , op. cit., p. 47.Google Scholar

^{page 307 note 4} Cf. v. d. Waerden, pp. 63 f.

^{page 307 note 5} Cf. Burnet, , Early Greek Philosophy, p. 17. The passage in Herodotus (2. 154) about ‘interpreters’ significantly mentions only Egyptians sent to the Greek settlements in Egypt to learn the language, and says nothing of Greeks learning Egyptian; nor is there any mention of writing.Google Scholar

^{page 307 note 6} Cf. Neug. p. 73.

^{page 308 note 1} Id., p. 80.

^{page 308 note 2} Van der Waerden (p. 36) is very misleading here. The difference between the classical Greek and the Egyptian methods of multiplication and division is clearly shown by Heath, , Manual, pp. 29 f.Google Scholar

^{page 308 note 3} Neug., p. 80.

^{page 308 note 4} The arguments and the evidence cannot conveniently be presented here, but I hope to discuss them in a further article. Mean while it should be noted that A. Wasserstein's curious paper ‘Thales' Determination of the Diameters of the Sun and Moon’ (as remarkable for its disregard of recent modern work in this field as for its inconclusivcness) in J.H.S. lxxv (1955), 114–16, contains little but unwarrantable assumptions based on unreliable evidence.

^{page 308 note 5} Cf. How, W. W. and Wells, J., A Commentary on Herodotus, repr. 1950, i. 379–80Google Scholar. The only Greek borrowings from the Babylonians that Herodotus mentions are of the ‘polos’ (a portable, hemi-spherical sun-dial), the gnomon, and the division of the day into 12 parts (in this he is only partly correct, as it was the day-and-night period that was divided into 12 parts).

^{page 308 note 6} Cf. Schnabel, P., Berossos und die babylonische-hellenistische Literatur, 1923Google Scholar. It must, however, be said that Schnabel's conclusions regarding Babylonian astronomy are now untenable, and his arguments in support of the great influence of Berossus' writings are very speculative and far from conclusive.

^{page 309 note 1} Kirk, and Raven's, description (op. cit., pp. 81–82Google Scholar) of Thales' astronomical activities is far too optimistic. Some idea of the primitiveness of the astronomical ideas then current may be gained from die peculiar notions of his successors such as Anaximander, Anaximenes, Xenophanes, and Heraclitus, which Heiberg, (Gesch. d. Math, und Naturwiss. im Altert., 1925, p. 50Google Scholar) rightly characterizes as ‘diese Mischung von genialer Intuition und kindlichen Analogien’.