+------+---------+ | | | M +------+---------+ | o | o | C +------+---------+ | | o o o o | X +------+---------+ | o | o o o | +------+---------+ +------+---------+ This abacus was ascribed to Pythagoras, but was in all probability older, and derived from Egypt, where elementary science was well and widely taught from very early times. When initial letters were used for numbers, as Π for πέντε, and Δ for δέκα, combinations such as IΔI meant 50. Last of all, we find in our MSS. a system of using the letters of the alphabet for numbers, preserving ϛ (ἐπίσημον) for 6, and thus reaching 10 with ι, proceeding by tens through κ (20), λ (30), etc., to ρ (100), σ (200), and for 900 using Ϡ. This notation must not be confused with the marking of the twenty-four books of the Homeric epics by the simple letters of the alphabet. Further details as to the technical terms for arithmetical operations, and the amount to be attributed to a nation using so clumsy a notation, must be sought in professed hand-books of antiquity.[40] As regards geometry, all we can say is that in the days of Plato and Aristotle both these philosophers recognize not only its extraordinary value as a mental training, but also the fact that it can be taught to young boys as yet unfit for political and metaphysical studies. § 40. Having thus disposed of the severer side of school education, we will turn to the artistic side, one very important to the Greeks, and suggestive to us of many instructive problems. FOOTNOTES: [24] Διδασκάλιον is the thing learned. [25] vi. 27. [26] The Greek form of our word school, though in common use, meant _leisure_, and only passed through its application to the leisurely discussions of philosophers into its new and opposite sense. There is some difficulty about the word παιδαγωγεῖον, which some have imagined to be a waiting-room for the pædagogue slaves--absurdly enough. It is probably a mere synonym for the schoolroom. [27] Grasberger, ii. 224. [28] [ὦ φίλε παῖ] Θεωδώρηον μάθε τάξιν Ὁμήρου ὄφρα δαεὶς πάσης μέτρον ἔχῃς σοφίας. [29] All our evidence, with every possible surmise about it, may be found in Welcker’s “Kleine Schriften,” vol. i. p. 371 sq. [30] This assumption may perhaps hardly seem surprising when it still prevails among the English public as regards girls. Accordingly, a vast amount of time and brain power is wasted in the endeavor to make them play and sing, though nature has peremptorily precluded it in most cases. [31] The objections of the Eleatics and Platonists to the moral side of Homer and the other epic poets will be discussed in connection with the philosophic attempts at reform in higher education. [32] Plutarch (“Life of Demosth.,” 2) laments his inability to master Latin, and the difficulties it presents when not acquired very early. [33] iii. 4, 19.