many later writers. Now, this comes from a treatise on the Rise of the Nile attributed to Aristotle and known to the Greek commentators, but extant only in a Latin epitome of the thirteenth century.[1] In this the first of the theories mentioned by Herodotos is ascribed to Thales, the second to Euthymenes of Massalia, and the third to Anaxagoras. Where did Aristotle, or whoever wrote the book, get these names? We think naturally of Hekataios; and this conjecture is strengthened when we find that Hekataios mentioned Euthymenes.[2] We may conclude that Thales really was in Egypt; and, perhaps, that Hekataios, in describing the Nile, took account, as was natural, of his fellow-citizen's views.
6.Thales and geometry. As to the nature and extent of the mathematical knowledge brought back by Thales from Egypt, it must be pointed out that most writers have seriously misunderstood the character of the tradition.[3] In his commentary on the First Book of Euclid, Proclus enumerates, on the authority of Eudemos, certain propositions which he says were known to Thales,[4] one of which is that two triangles are equal when they have one side and the two adjacent angles equal. This he must have known, as otherwise he could not have measured the distances of ships at sea in the way he was said to have done.[5] Here we see how all these statements arose. Certain feats in the way of measurement were traditionally ascribed to Thales, and Eudemos assumed that he must have known all the propositions these imply.
- ↑ Dox. pp. 226-229. The Latin epitome will be found in Rose's edition of the Aristotelian fragments.
- ↑ Hekataios, fr. 278 (F.H.G. i. p. 19).
- ↑ See Cantor, Vorlesungen über Geschichte der Mathematik, vol. i. pp. 12 sqq.; Allman, "Greek Geometry from Thales to Euclid" (Hermathena, iii. pp. 164-174).
- ↑ Proclus, in Eucl. pp. 65, 7; 157, 10; 250, 20; 299, 1; 352, 14 (Friedlein). Eudemos wrote the first histories of astronomy and mathematics, just as Theophrastos wrote the first history of philosophy.
- ↑ Proclus, p. 352, 14, Εὔδημος δὲ ἐν ταῖς γεωμετρικαῖς ἱστορίαις εἰς Θαλῆν τοῦτο ἀνάγει τὸ θεώρημα (Eucl. 1.26) τὴν γὰρ τῶν ἐν θαλάττῃ πλοίων ἀπόστασιν δι' οὗ τρόπου φασὶν αὐτὸν δεικνύναι τούτῳ προσχρῆσθαί φησιν ἀναγκαῖον.
