Early Greek Philosophy by John Burnet, with Burnet's notes
5. Thales in Egypt 7. Thales as a Politician

From Chapter I., The Milesian School

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.23 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,24 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.25 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. But this is quite illusory. Both the measurement of the distance of ships at sea, and that of the height of the pyramids, which is also ascribed to him,26 are easy applications of the rule given by Aahmes for finding the seqt.27 What the tradition really points to is that Thales applied this empirical rule to practical problems which the Egyptians had never faced, and that he was thus the originator of general methods. That is a sufficient title to fame.

Burnet's Notes


23. See Cantor, Vorlesungen über Geschichte der Mathematik, vol. i. pp. 12 sqq.; Allman, "Greek Geometry from Thales to Euclid" (Hermathena, iii. pp. 164-174).

24. 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.

25. 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.

26. 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 reflexion that the shadows of all objects will 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.

27. See Gow, Short History of Greek Mathematics, § 84.

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