[30]. For the possibility that Indian philosophy came from Greece, see Weber, Die Griechen in Indien (Berl. Sitzb. 1890, pp. 901 sqq.), and Goblet d’Alviella, Ce que l’Inde doit à la Grèce (Paris, 1897).
[31]. I am indebted for most of the information which follows to Cantor’s Vorlesungen über Geschichte der Mathematik, vol. i. pp. 46-63. See also Gow’s Short History of Greek Mathematics, §§ 73-80; and Milhaud, La science grecque, pp. 91 sqq. The discussion in the last-named work is of special value because it is based on M. Rodet’s paper in the Bulletin de la Société Mathématique, vol. vi., which in some important respects supplements the interpretation of Eisenlohr, on which the earlier accounts depend.
[32]. Plato, Laws, 819 b 4, μήλων τέ τινων διανομαὶ καὶ στεφάνων πλείοσιν ἄμα καὶ ἐλάττοσιν ἁρμοττόντων ἀριθμῶν τῶν αὐτῶν, καὶ πυκτῶν καὶ παλαιστῶν ἐφεδρείας τε καὶ συλλήξεως ἐν μέρει καὶ ἐφεξῆς καὶ ὡς πεφύκασι γίγνεσθαι. καὶ δὴ καὶ παίζοντες, φιάλας ἅμα χρυσοῦ καὶ χαλκοῦ καὶ ἀργύρου καὶ τοιούτων τινῶν ἄλλων κεραννύντες, οἱ δὲ καὶ ὅλας πως διαδιδόντες. In its context, the passage implies that no more than this could be learnt in Egypt.
[33]. Herod. ii. 109; Arist. Met. Α, 1. 981 b 23.
[34]. For a fuller account of this method, see Gow, Short History of Greek Mathematics, pp. 127 sqq.; and Milhaud, Science grecque, p. 99.
[35]. R. P. 188.
[36]. The real meaning of ἁρπεδονάπτης was first pointed out by Cantor. The gardener laying out a flower-bed is the true modern representative of the “harpedonapts.”
[37]. See Milhaud, Science grecque, p. 103.
[38]. The word πυραμίς is often supposed to be derived from the term piremus used in the Rhind papyrus, which does not mean pyramid, but “ridge.” It is really, however, a Greek word too, and is the name of a kind of cake. The Greeks called crocodiles lizards, ostriches sparrows, and obelisks meat-skewers, so they may very well have called the pyramids cakes. We seem to hear an echo of the slang of the mercenaries that carved their names on the colossus at Abu-Simbel.
[39]. Three different positions of the equinox are given in three different Babylonian tablets, namely, 10°, 8° 15′, and 8° 0′ 30″ of Aries. (Kugler, Mondrechnung, p. 103; Ginzel, Klio, i. p. 205.) Given knowledge of this kind, and the practice of formulating recurrences in cycles, it is scarcely conceivable that the Babylonians should not have invented a cycle for precession. It is equally intelligible that they should only have reached a rough approximation; for the precessional period is really about 27,600 years and not 36,000. It is to be observed that Plato’s “perfect year” is also 36,000 solar years (Adam’s Republic, vol. ii. p. 302), and that it is probably connected with the precession of the equinoxes. (Cf. Tim. 39 d, a passage which is most easily interpreted if referred to precession.) This suggestion as to the origin of the “Great Year” was thrown out by Mr. Adam (op. cit. p. 305), and is now confirmed by Hilprecht, The Babylonian Expedition of the University of Pennsylvania (Philadelphia, 1906).