[264] Xen. _Banquet_, iv. 27. School friendships are also mentioned in Aristot. _Eth._ viii. 12; Aristoph. _Clouds_, 1006. [265] Athen. 242 d. [266] The translation is free, and I omit a good deal that is less relevant. [267] For a picture of such a flogging see p. 599 of Bury’s _Roman Empire_. [268] Plato, _Laws_, 809 C. [269] The distinction between λογιστική [logistikê], reckoning up and comparing numbers, chiefly in bills and the like, practical arithmetic, and ἀριθμητική [arithmêtikê], theory of numbers, is noted in Plato, _Gorg._ 451 B. [270] Plato, _Laws_, 643 B.C. [271] Plato, _Protag._ 318 D. [272] So Theodoros in the _Theaitetos_. [273] Xen. _Econ._ viii. 14. [274] Xen. _Mem._ iv. 4. 7. [275] Aristoph. _Wasps_, 656. [276] In Diogenes Laertius, i. 2. 10. [277] Alexis (in Athen. 117 e). [278] An abacus of a very similar sort is still in use in China and Japan, even in banks. The “pebbles” are pushed to and fro, not in grooves, but on wires passing through the middle of them. Calculations can be made by this means with marvellous rapidity.] [279] e.g. _Polit._ 299 D. πεττείαν ἢ ξύμπασαν ἀριθμητικήν [petteian ê xympasan arithmêtikên]. [280] Plato, _Phaid._ 274. [281] Plato, _Laws_, 819 B. [282] The restoration of this process rests on Athen. 671; the other two are purely conjectural. [283] Suggests at once Hellenic, not Egyptian customs. [284] Plato, _Rep._ 526 B. [285] Plato, _Laws_, 747. [286] Technically speaking, this was λύρα [lyra], the κιθάρα [kithara] being a professional instrument which was not taught at school. [287] Illustr. Plate I. B. [288] Plato, _Lusis_, 209 B. On Inscriptions there are separate prizes for the two methods. [289] Xen. _Econ._ ii. 13. [290] _Ibid._ xvii. 7. [291] Cp. British Museum Vase E 57, on which a man is leading a leopard by a string. [292] Plato, _Protag._ 326 B. [293] Aristoph. _Clouds_, 1356. [294] Aristoph. fragment of _Banqueters_. [295] Aristoph. _Knights_, 526. [296] Plut. _Solon_, iii. [297] Hermippos (in Athen. 619 b). [298] Aristoph. _Wasps_, 959. [299] _Ibid._ 989. [300] Aristot. _Pol._ viii. 6. 11. [301] For this reason it was opposed to _Dorian_ influences by Pratinas. It was excluded from the Pythian games (Pausan. 10. vii. 5). Pratinas bids it be content to “lead drunk young men in their carousals and brawls.” [302] Telestes, in his defence of the flute, could only retort that Athena, being condemned to eternal spinsterhood, ought not to be particular about her looks (Athen. 617). [303] Aristot. _Pol._ viii. 6. 11.