[71]. Dox. pp. 226-229. The Latin epitome will be found in Rose’s edition of the Aristotelian fragments.
[72]. Hekataios, fr. 278 (F.H.G. i. p. 19).
[73]. See Cantor, Vorlesungen über Geschichte der Mathematik, vol. i. pp. 112 sqq.; Allman, “Greek Geometry from Thales to Euclid” (Hermathena, iii. pp. 164-174).
[74]. 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.
[75]. Proclus, p. 352, 14, Εὔδημος δὲ ἐν ταῖς γεωμετρικαῖς ἱστορίαις εἰς Θαλῆν τοῦτο ἀνάγει τὸ θεώρημα (Eucl. i. 26)· τὴν γὰρ τῶν ἐν θαλάττῃ πλοίων ἀπόστοσιν δι’ οὗ τρόπου φασὶν αὐτὸν δεικνύναι τούτῳ προσχρῆσθαί φησιν ἀναγκαῖον. For the method adopted by Thales, see Tannery, Géométrie grecque, p. 90. I agree, however, with Dr. Gow (Short History of Greek Mathematics, § 84) that it is very unlikely Thales reproduced and measured on land the enormous triangle which he had constructed in a perpendicular plane over the sea. Such a method would be too cumbrous to be of use. It is much simpler to suppose that he made use of the Egyptian seqt.
[76]. The oldest version of this story is given in Diog. i. 27, ὁ δὲ Ἱερώνυμος καὶ ἐκμετρῆσαί φησιν αὐτὸν τὰς πυραμίδας, ἐκ τῆς σκιᾶς παρατηρήσαντα ὅτε ἡμῖν ἰσομεγέθης ἐστίν. Cf. Pliny, H. Nat. xxxvi. 82, mensuram altitudinis earum deprehendere invenit Thales Milesius umbram metiendo qua hora par esse corpori solet. (Hieronymos of Rhodes was contemporary with Eudemos.) This need imply no more than the simple reflexion that the shadows of all objects will probably be equal to the objects at the same hour. Plutarch (Conv. sept. sap. 147 a) gives a more elaborate method, τὴν βακτηρίαν στήσας ἐπὶ τῷ πέρατι τῆς σκιᾶς ἣν ἡ πυραμὶς ἐποίει, γενομένων τῇ ἐπαφῇ τῆς ἀκτῖνος δυοῖν τριγώνων, ἔδειξας ὃν ἡ σκιὰ πρὸς τὴν σκιὰν λόγον εἶχε, τὴν πυραμίδα πρὸς τὴν βακτηρίαν ἔχουσαν. This, as Dr. Gow points out, is only another calculation of seqt, and may very well have been the method of Thales.
[77]. Herod. i. 170 (R. P. 9 d).
[78]. The story of Thales falling into a well (Plato, Tht. 174 a) is nothing but a fable teaching the uselessness of σοφία; the anecdote about the “corner” in oil (Ar. Pol. Α, 11. 1259 a 6) is intended to inculcate the opposite lesson.
[79]. See R. P. 9 e.
[80]. R. P. ib.