6. As to the nature and extent of the mathematical knowledge brought back by Thales from Egypt, it seems desirable to point out that many writers have seriously misunderstood the character of the tradition.[73] 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.[74] One of the theorems with which he credits him is that two triangles are equal when they have one side and the two adjacent angles equal. This he must have known, said Eudemos, as otherwise he could not have measured the distances of ships at sea from a watch-tower in the way he was said to have done.[75] Here we see how all these statements arose. Certain remarkable feats in the way of measurement were traditionally ascribed to Thales, and it was assumed that he must have known all the propositions which these imply. But this is quite an illusory method of inference. Both the measurement of the distance of ships at sea, and that of the height of the pyramids, which is also ascribed to him,[76] are easy applications of what Aahmes calls the _seqt_. These rules of mensuration may well have been brought from Egypt by Thales, but we have no ground for supposing that he knew any more about their _rationale_ than did the author of the Rhind papyrus. Perhaps, indeed, he gave them a wider application than the Egyptians had done. Still, mathematics, properly so called, did not come into existence till some time after Thales. Footnote 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). Footnote 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. Footnote 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_. Footnote 76: