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Socrates' Diagram in the Meno of Plato, Pp. 86e–87a.1

Published online by Cambridge University Press:  11 February 2009

A. S. L. Farquharson
A. S. L. Farquharson
Affiliation:
University College, Oxford
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Extract

I desire to invite the attention of students of Plato and of Greek mathematics to a solution of a passage which has long been a field of controversy for critics. For brevity's sake I shall take for granted an acquaintance with the two solutions which at present dispute the field, and further adopt certain positions which previous enquirers have established beyond reasonable doubt.

Type
Research Article
Information
The Classical Quarterly , Volume 17 , Issue 1 , January 1923 , pp. 21 - 26
Copyright
Copyright © The Classical Association 1923

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References

Page 22 note 1 λèγω ბ τბ ξ ὐπоθỏωω ὣბε, ὢσπερ οἰ γεωμბρα πολλáκις σκοŭναι ἐπειδν ις ρνται αǔσοον περιομ, εბ οბῖν τε ές τῖνῖε τῖν τῖςε τῖ ϰѡρ τρλνν νταθναι ει αν τισ ορπ ωισα εστι το το τοιοῠτον, λλ', ὣσπερ μν τια ὺπθεσιν προὔργοὑ οἲμαἱ ϰειν πρἆμα τοιμςε. εἱ μμ στι τοτο τ ϰωρἱομ τοιỦτομ οἲομ παρ τημ σοθεισαν αủτοι γραμμημ παρατειμαμτα ελλείπειμ τοιοὐτῳ ϰωρί ῳ οίον αὑτ τ παρατεταμνον λλο τι σνṷβαίνειν ṷοι παθειν ṷοι ςοκεῖ, καί λλο εί ςὑνατατόν στι ταὑτα παθεῖν ὑποθμεν οὐν θλω είπε σοι σν περω τς ντσεω αủτοὗ εἰς τν–κὐκλον εἳτε δὑνανον εἲτε μἠ (Plato, Mίno, pp. 86E–87A).

Page 22 note 2 The rival modern theories are to be found in two pamphlets: August, E. F., Zur Kenntniss der geometrischen Methode der Alten, Berlin, 1854Google Scholar ; Benecke, A., Ueber die geomeirische Hypothesis in Platons Menon, Elbing, 1867Google Scholar . An epitome of the question is given in SirHeath, T., A History of Greek Mathematics, Vol. I., pp. 298–303Google Scholar. Cantor and M. Paul Tannery accept Benecke's solution.

Page 24 note 1 This is clear from Aristophanes' jest about Socrates' map of Negropont, which had been ‘laid simulout’ by Pericles:

M. δ λ' Εὔβοι', ὡς ρᾷς,

δ παρατταται μακρ πρρω πνυ.

S. οἶδ', ὑπò γρ μν παρετθη—κα περικλους.

(Nubes 211). Galen also uses the word of the hand applied to the ear and transformed simultaneously to make an improvised ear-trumpet, de usu partium, Vol. II. (Helmreich), p. 151, K.III.895.

page 24 note 2 Proclus, in Eucl. Elem. I., pp. 419–20 (Friedlein); Eudemus (Spengel), Fr. LXXXIX.

page 25 note 1 I need, perhaps, hardly remind the beginner that γν δοθ εῖσαν γραμμν in Euclid is, in English idiom, ‘a given line,’ not ‘the given line.’

page 25 note 2 παραβλλειν. The word παρατενειν disappears from geometry after the time of Plato.