Chapter 14

242. The verb ὑποτείνειν is, of course, used intransitively. The explanation suggested in the text seems to me much simpler than that of Max C. P. Schmidt (Kulturhistorische Beiträge, Heft i. pp. 64 sqq.). He explains the hypotenuse as the longest string in a triangular harp; but my view seems more in accordance with analogy. So ἡ κάθετος is, literally, a plumb-line.

243. The statement comes from Eudemos; for it is found in Proclus’s commentary on Euclid i. 47. Whether historical or not, it is no Neopythagorean fancy.

244. Arist.An. Pr.Α, 23. 41 a 26, ὅτι ἀσύμμετρος ἡ διάμετρος διὰ τὸ γίγνεσθαι τὰ περιττὰ ἴσα τοῖς ἀρτίοις συμμέτρου τεθείσης. The proofs given at the end of Euclid’s Tenth Book (vol. iii. pp. 408 sqq., Heiberg) turn on this very point. They are not Euclidean, and may be substantially Pythagorean. Cf. Milhaud,Philosophes géomètres, p. 94.

245. Plato,Theaet.147 d 3 sqq.

246. How novel these consequences were, is shown by the fact that inLaws, 819 d 5, the Athenian Stranger says that he had only realised them late in life.

247. This version of the tradition is mentioned in Iamblichos,V. Pyth.247, and looks older than the other, which we shall come to later (§ 148). Hippasos is theenfant terribleof Pythagoreanism, and the traditions about him are full of instruction.

248. Plato (Tim.36 a 3) defines the harmonic mean as τὴν ... ταὐτῷ μέρει τῶν ἄκρων αὐτῶν ὑπερέχουσαν καὶ ὑπερεχομένην. The harmonic mean of 12 and 6 is therefore 8; for 8 = 12 - 12/3 = 6 + 6/3.

249. For these stories and a criticism of them, see Max C. P. Schmidt,Kulturhistorische Beiträge, i. pp. 78 sqq. The smith’s hammers belong to the region ofMärchen, and it is not true either that the notes would be determined by the weight of the hammers, or that, if they were, the weights hung to equal strings would produce the notes. These inaccuracies were pointed out by Montucla (Martin,Études sur le Timée, i. p. 391).

250. Arist.Met.Μ, 4. 1078 b 21 (R. P. 78); Zeller, p. 390, n. 2. TheTheologumena Arithmetica, wrongly attributed to Nikomachos of Gerasa, is full of fanciful doctrine on this subject (R. P. 78 a). Alexanderin Met.p. 38, 8, gives a few definitions which may be old (R. P. 78 c).

251. Arist.Phys.Δ, 6. 213 b 22 (R. P. 75).

252. Diog. ix. 19 (R. P. 103 c). It is true that Diogenes is here drawing from a biographical rather than a doxographical source (Dox.p. 168), but this touch can hardly be an invention.

253. Arist.Met.Μ, 3. 1091 a 13 (R. P. 74).

254. Arist.Phys.Δ, 6. 213 b 23 (R. P. 75 a). The words διορίζει τὰς φύσεις have caused unnecessary difficulty, because they have been supposed to attribute the function of limiting to the ἄπειρον. Aristotle makes it quite clear that his meaning is that stated in the text. Cf. especially the words χωρισμοῦ τινος τῶν ἐφεξῆς καὶ διορίσεως. The term διωρισμένον is the proper antithesis to συνεχές. In his work on the Pythagorean philosophy, Aristotle used instead the phrase διορίζει τὰς χώρας (Stob. i. p. 156, 8; R. P. 75), which is also quite intelligible if we remember what the Pythagoreans meant by χώρα (cf. p. 115,n.240).

255. Cf. Arist.Phys.Δ, 6. 213 a 27, οἱ δ’ ἄνθρωποι ... φασὶν ἐν ᾦ ὅλως μηδέν ἐστι, τοῦτ’ εἶναι κενόν, διὸ τὸ πλῆρες ἀέρος κενὸν εἶναι;de Part. An.Β, 10. 656 b 15, τὸ γὰρ κενὸν καλούμενον ἀέρος πλῆρές ἐστι;de An.Β, 10 419 b 34, δοκεῖ γὰρ εἶναι κενὸν ὁ ἀήρ.

256. Arist.Met.Α, 3. 984 a 7 (R. P. 56 c).

257. See Chap. IV.§ 91.

258. Arist.Met.Α, 5. 986 a 25 (R. P. 66).

259. Plato,Tim.58 d 2.

260. This is quoted by Plutarch,de def. orac.422 b, d, from Phanias of Eresos, who gave it on the authority of Hippys of Rhegion. If we may follow Wilamowitz (Hermes, xix. p. 444) in supposing that this really means Hippasos of Metapontion (and it was in Rhegion that the Pythagoreans took refuge), this is a very valuable piece of evidence.

261. Plato,Tim.55 c 7 sqq.

262. This will be found in Chap. IV.§ 93.

263. For a clear statement of this view (which was still that of Demokritos), see Lucretius, v. 621 sqq. The view that the planets had an orbital motion from west to east is attributed by Aetios, ii. 16, 3, to Alkmaion (§ 96), which certainly implies that Pythagoras did not hold it. As we shall see (§ 152), it is far from clear that any of the Pythagoreans did. It seems rather to be Plato’s discovery.

264. See Chap. IV.§§ 92-93, and Chap. VII.§§ 150-152.

265. See fr. 7 (= 18 Karst.),ap.Diog. viii. 36 (R. P. 88).

266. Diog. ix. 18 (R. P. 97). We know that Xenophanes referred to the prediction of an eclipse by Thales (Chap. I. p. 41,n.62). We shall see that his own view of the sun was hardly consistent with the possibility of such a prediction, so it may have been in connexion with this that he opposed him.

267. Timaiosap.Clem.Strom.i. p. 533 (R. P. 95). There is only one anecdote which actually represents Xenophanes in conversation with Hieron (Plut.Reg. apophth.175 e), but it is natural to understand Arist.Met.Γ, 5. 1010 a 4 as an allusion to a remark made by Epicharmos to him. Aristotle has more than one anecdote about Xenophanes, and it seems most likely that he derived them from the romance of which Xenophon’sStrom.is an echo.

268. Clem.,loc. cit.; Sext.Strom.i. 257. The mention of Cyrus is confirmed by Hipp.Strom.i. 94. Diels thinks that Dareios was mentioned first for metrical reasons; but no one has satisfactorily explained why Cyrus should be mentioned at all, unless the early date was intended. On the whole subject, see Jacoby, pp. 204 sqq., who is certainly wrong in supposing that ἄχρι τῶν Δαρείου καὶ Κύρου χρόνων can mean “during the times of Dareios and Cyrus.”

269.Strom.xxxi. p. 22. He assumes an early corruption of N into M. As Apollodoros gave the Athenian archon, and not the Olympiad, we might with more probability suppose a confusion due to two archons having the same name.

270. As Elea was founded by the Phokaians six years after they left Phokaia (Herod. i. 164 sqq.) its date is just 540-39B.C.Cf. the way in which Apollodoros dated Empedokles by the era of Thourioi (§ 98).

271. Bergk (Litteraturgesch.ii. p. 418, n. 23) took φροντίς here to mean the literary work of Xenophanes, but it is surely an anachronism to suppose that at this date it could be used like the Latincura.

272. It was certainly another poem; for it is in hexameters while the preceding fragment is in elegiacs.

273. Xenophanes, fr. 7 (above, p. 124,n.265); Herakleitos, frs.16,17(below, p.147).

274. Diog. ix. 21 (R. P. 96 a).

275. Diog. ix. 18 (R. P. 96). The use of the old name Zankle, instead of the later Messene, points to an early source for this statement—probably the elegies of Xenophanes himself.

276. Diog. ix. 18 (R. P. 97) says αὐτὸς ἐρραψῴδει τὰ ἑαυτοῦ, which is a very different thing. Nothing is said anywhere of his reciting Homer, and the word ῥαψῳδεῖν is used quite loosely for “to recite.” Gomperz’s imaginative picture (Greek Thinkers, vol. i. p. 155) has no further support than this single word. Nor is there any trace of Homeric influence in the fragments. They are in the usual elegiac style.

277. The statement is justly suspected by Hiller (Rh. Mus.xxxiii. p. 529) to come from Lobon of Argos, who provided the Seven Wise Men, Epimenides, etc., with stichometric notices, all duly recorded in Diogenes. Even if true, however, it proves nothing.

278. Arist.Rhet.Β, 26. 1400 b 5 (R. P. 98 a). Anecdotes like this are really anonymous. Plutarch transfers the story to Egypt (P. Ph. Fr.p. 22, § 13), and others tell it of Herakleitos. It is hardly safe to build on such a foundation.

279. Diog. ix. 18 (R. P. 97). The word ἐπικόπτων is a reminiscence of Timon, fr. 60; Diels, Ξεινοφάνης ὑπάτυφος Ὁμηραπάτης ἐπικόπτης.

280. The oldest reference to a poem Περὶ φύσεως is in the Geneva scholium onIl.xxi. 196 (quoting fr. 30), and this goes back to Krates of Mallos. We must remember, however, that such titles are of later date than Xenophanes, and he had been given a place among philosophers long before the time of Krates. All we can say, therefore, is that the Pergamene librarians gave the title Περὶ φύσεως to some poem of Xenophanes.

281. Simpl.de Caelo, p. 522, 7 (R. P. 97 b). It is true that two of our fragments (25 and 26) are preserved by Simplicius, but he got them from Alexander. Probably they were quoted by Theophrastos; for it is plain that Alexander had no first-hand knowledge of Xenophanes either. If he had, he would not have been taken in byM.X.G.(See p. 138,n.305.)

282. Three fragments (27,31,33) come from theHomeric Allegories, two (30,32) are from Homeric scholia.

283. Cf. Wilamowitz, Progr. Gryphiswald. 1880.

284. I formerly, with Zeller, preferred Theodoret’s reading αἴσθησιν, but both Clement and Eusebios have ἐσθῆτα, and Theodoret is entirely dependent on them.

285. Reading ἠέρι for καὶ ῥεῖ with Diels.

286. This fragment has been recovered in its entirety from the Geneva scholia on Homer (seeArch.iv. p. 652). The words in brackets are added by Diels. See also Praechter,“Zu Xenophanes”(Philol.xviii. p. 308).

287. The word is ὑπεριέμενος. This is quoted from theAllegoriesas an explanation of the name Hyperion, and doubtless Xenophanes so meant it.

288. Reading δεδοξάσθω with Wilamowitz.

289. As Diels suggests, this probably refers to the stars, which Xenophanes held to be clouds.

290. Cf. Dielsad loc.(P. Ph. Fr.p. 44),“ut Sol et cetera astra, quae cum in nebulas evanescerent, deorum simul opinio casura erat.”Cf.Arch.x. p. 533.

291. Aet. ii. 18, 1 (Dox.p. 347), Ξενοφάνης τοὺς ἐπὶ τῶν πλοίων φαινομένους οἷον ἀστέρας, οὓς καὶ Διοσκούρους καλοῦσί τινες, νεφέλια εἶναι κατὰ τὴν ποιὰν κίνησιν παραλάμποντα.

292. The passages from Aetios are collected inP. Ph. Fr.pp. 32 sqq. (Vors.p. 42).

293. Aet. ii. 20, 3 (Dox.p. 348), Ξενοφάνης ἐκ νεφῶν πεπυρωμένων εἶναι τὸν ἥλιον. Θεόφραστος ἐν τοῖς Φυσικοῖς γέγραφεν ἐκ πυριδίων μὲν τῶν συναθροιζομένων ἐκ τῆς ὑγρᾶς ἀναθυμιάσεως, συναθροιζόντων δὲ τὸν ἥλιον.

294. Aet. ii. 24, 9 (Dox.p. 355). πολλοὺς εἶναι ἡλίους καὶ σελήνας κατὰ κλίματα τῆς γῆς καὶ ἀποτομὰς καὶ ζώνας, κατὰ δέ τινα καιρὸν ἐμπίπτειν τὸν δίσκον εἴς τινα ἀποτομὴν τῆς γῆς οὐκ οἰκουμένην ὑφ’ ἡμῶν καὶ οὕτως ὥσπερ κενεμβατοῦντα ἔκλειψιν ὑποφαίνειν· ὁ δ’ αὐτὸς τὸν ἥλιον εἰς ἄπειρον μὲν προιέναι, δοκεῖν δὲ κυκλεῖσθαι διὰ τὴν ἀπόστασιν. It is clear that in this notice ἔκλειψινἕκλειψιν has been erroneously substituted for δύσιν, as it has also in Aet. ii. 24, 4 (Dox.p. 354).

295. That this is the meaning of ὥσπερ κενεμβατοῦντα appears sufficiently from the passages referred to in Liddell and Scott.

296. Aet. ii. 13, 14 (Dox.p. 343), ἀναζωπυρεῖν νύκτωρ καθάπερ τοὺς ἄνθρακας.

297. Aet. ii. 30, 8 (Dox.p. 362), τὸν μὲν ἥλιον χρήσιμον εἶναι πρὸς τὴν τοῦ κόσμου καὶ τὴν τῶν ἐν αὐτῷ ζῴων γένεσίν τε καὶ διοίκησιν, τὴν δὲ σελήνην παρέλκειν, The verb παρέλκειν means “to cork.” Cf. Aristophanes,Pax, 1306.

298. There is an interesting note on these in Gomperz’sGreek Thinkers(Eng. trans. i. p. 551). I have translated his conjecture φυκῶν instead of the MS. φωκῶν, as this is said to involve a palæontological impossibility, and impressions of fucoids are found, not indeed in the quarries of Syracuse, but near them. It is said also that there are no fossils in Paros, so the anchovy must have been an imaginary one.

299. Aet. ii. 1, 2 (Dox., p. 327); Diog. ix. 19 (R. P. 103 c). It is true, of course, that this passage of Diogenes comes from the biographical compendium (Dox.p. 168); but, for all that, it is a serious matter to deny the Theophrastean origin of a statement found in Aetios, Hippolytos, and Diogenes.

300. Arist.Met.Α, 5. 986 b 23 (R. P. 101), οὐδὲν διεσαφήνισεν.

301. This is given as an inference by Simpl.Phys.p. 23, 18 (R. P. 108 b), διὰ τὸ πανταχόθεν ὅμοιον. It does not merely come fromM.X.G.(R. P. 108), πάντῃ δ’ ὅμοιον ὄντα σφαιροειδῆ εἶναι. Hippolytos has it too (Ref.i. 14; R. P. 102 a), so it goes back to Theophrastos. Timon of Phleious understood Xenophanes in the same way; for he makes him call the One ἴσον ἁπάντῃ (fr. 60, Diels = 40 Wachsm.; R. P. 102 a).

302. Arist.de Caelo, Β, 13. 294 a 21 (R. P. 103 b).

303. I take δαψιλός as an attribute and ἀπείρονα as predicate to both subjects.

304.Il.viii. 13-16, 478-481, especially the words οὐδ’ εἴ κε τὰ νείατα πείραθ’ ἵκηαι | γαίης καὶ πόντοιο κ.τ.λ.Iliadviii. must have seemed a particularly bad book to Xenophanes.

305. In Bekker’s edition this treatise bears the title Περὶ Ξενοφάνους, περὶ Ζήνωνος, περὶ Γοργίου, but the best MS. gives as the titles of its three sections: (1) Περὶ Ζήνωνος, (2) Περὶ Ξενοφάνους, (3) Περὶ Γοργίου. The first section, however, plainly refers to Melissos, so the whole treatise is now entitledDe Melisso, Xenophane, Gorgia(M.X.G.). It has been edited by Apelt in the Teubner Series, and more recently by Diels (Abh. der k. Preuss. Akad.1900), who has also given the section dealing with Xenophanes inP. Ph. Fr.pp. 24-29 (Vors.pp. 36 sqq.). He has now withdrawn the view maintained inDox.p. 108 that the work belongs to the third centuryB.C., and holds that it wasa Peripatetico eclectico(i.e.sceptica, platonica, stoica admiscente) circa Christi natalem conscriptum. If that is so, there is no reason to doubt, as I formerly did, that the second section is really meant to deal with Xenophanes. The writer would have no first-hand knowledge of his poems, and the order in which the philosophers are discussed is that of the passage in theMetaphysicswhich suggested the whole thing. It is possible that a section on Parmenides preceded what we now have.

306.Met.Α, 5. 986 b 21 (R. P. 101), πρῶτος τούτων ἑνίσας. The verb ἑνίζειν occurs nowhere else, but is plainly formed on the analogy of μηδίζειν, φιλιππίζειν, and the like. It is not likely that it means “to unify.” Aristotle could easily have said ἑνώσας if he had meant that.

307.Tht.181 a 6, τοῦ ὅλου στασιῶται. The noun στασιῶτης has no other meaning than “partisan.” There is no verb στασιοῦν “to make stationary,” and such a formation would be against all analogy. The derivation στασιώτας ... ἀπὸ τῆς στάσεως appears first in Sext.Math.x. 46, from which passage we may infer that Aristotle used the word, not that he gave the derivation.

308.Soph.242 d 5 (R. P. 101 b). If the passage implies that Xenophanes settled at Elea, it equally implies this of his predecessors. But Elea was not founded till Xenophanes was in the prime of life.

309.Tht.179 e 3, τῶν Ἡρακλειτείων ἤ, ὥσπερ σὺ λέγεις Ὁμηρείων καὶ ἔτι παλαιοτέρων. In this passage, Homer stands to the Herakleiteans in exactly the same relation as Xenophanes does to the Eleatics in theSophist.

310.Met.981 b 24. The words cannot mean “gazing up at the whole heavens,” or anything of that sort. They are taken as I take them by Bonitz (im Hinblicke auf den ganzen Himmel) and Zeller (im Hinblick auf das Weltganze). The word ἀποβλέπειν had become much too colourless to bear the other meaning, and οὐρανός, as we know, means what was later called κόσμος.

311. See above, p. 137,n.301.

312. Diog. ix. 19 (R. P. 103 c), ὅλον δ’ ὁρᾶν καὶ ὅλον ἀκούειν, μὴ μέντοι ἀναπνεῖν. See above, p. 120,n.252.

313. [Plut.]Strom.fr. 4, ἀποφαίνεται δὲ καὶ περὶ θεῶν ὡς οὐδεμιᾶς ἡγεμονίας ἐν αὐτοῖς οὔσης· οὐ γὰρ ὅσιον δεσπόζεσθαί τινα τῶν θεῶν, ἐπιδεῖσθαί τε μηδενὸς αὐτῶν μηδένα μηδ’ ὅλως, ἀκούειν δὲ καὶ ὁρᾶν καθόλου καὶ μὴ κατὰ μέρος.

314.Gesch. des Alterth.ii. § 466.

315. Freudenthal,Die Theologie des Xenophanes.

316. Xenophanes calls his god “greatest among gods and men,” but this is simply a case of “polar expression,” to which parallels will be found in Wilamowitz’s note to theHerakles, v. 1106. Cf. especially the statement of Herakleitos (fr.20) that “no one of gods or men” made the world.

317.Griechische Literatur, p. 38.

318.Parmenides Lehrgedicht, p. 9.

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