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γοητείας οὐδὲν ἀπολείπει: ‘leaves no magic art untried.’ τὸ μετρεῖν -- ἱστάναι. Cf. Euthyph. 7 B, C, Prot. 356 B, Phil. 55 E, [περὶ δικαίου] 373 A and Xen. Mem. I 1. 9 ἃ ἔξεστιν ἀριθμήσαντας ἢ μετρήσαντας ἢ στήσαντας εἰδέναι. See also on IX 587 B. ἐφάνησαν: ‘were discovered’ ‘were invented’=ηὑρέθησαν: cf. φανῆναι VII 528 D. The meaning is not ‘were found by us to be’ etc., as Liebhold supposes (Fleck. Jb. 1884 p. 522), and even Krohn, who actually thinks ἐφάνησαν may possibly contain a reference to some ‘lost fragment’ of the Republic (Pl. St. p. 252). Grimmelt, in his reply to Krohn, takes nearly the right view (de comp. et unit. etc. p. 90 note). τὸ φαινόμενον -- βαρύτερον. ‘The apparently larger’ rules in us when we believe the nearer and smaller of two objects to be larger than a more distant object which measurement shews to be larger. Similarly in the other cases. There is no good reason for adding ἢ κουφότερον after βαρύτερον, as Madvig proposes to do: cf. IV 433 D note τὸ λογισάμενον κτλ.: ‘that which has counted’ etc. For ἢ καί=‘or if you like’ see on 599 A.
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