James Adam, The Republic of Plato

---

ἡ περὶ τὸ αὐτὸ ὄψις. I formerly read αὐτό instead of τὸ αὐτό with Ξ and a few inferior MSS. αὐτό, which Bekker, Schneider and Stallbaum adopt, is easier, but lacking in authority; and τὸ αὐτό is in reality more elegant. The marked antithesis between ἡ περὶ τὸ ἓν μάθησις (‘the intellectual apprehension of the one’) and ἡ περὶ τὸ αὐτὸ ὄψις (‘the visual apprehension of the same’) makes it clear that τὸ αὐτό means ‘the same’ as that with which ἡ μάθησις was concerned (viz. τὸ ἕν), and not (as Hermann imagined) ‘one and the same object of vision’ (like ταὐτόν presently). Plato may have deliberately employed the two forms τὸ αὐτό and ταὐτόν in order to dissociate them from one another.

καὶ ξύμπας ἀριθμὸς κτλ. Because ἀριθμός is τὸ ἐκ μονάδων συγκείμενον πλῆθος (Euclid VII def. 2), or in other words a σύστημα μονάδων (Theo Smyrn. p. 18 ed. Hiller), and thus for example a visible three (i.e. three visible things) presents us with three separate cases of the contrast between ἕν and πολλά.

τοῦτο (see cr. n.) is preferable to τούτῳ, which appears in no MS except A, and would be superfluous after εἴπερ τὸ ἕν. Two MSS do in point of fact omit the word altogether.

λογιστική τε καὶ ἀριθμητική. Greek mathematicians distinguished between ἀριθμητική ‘the science of numbers’ and λογιστική ‘the art of calculation’ (Gow Greek Math. p. 22). It has been doubted whether Plato also held this distinction; but a comparison of Gorg. 451 B, 453 E, Theaet. 198 A (on ἀριθμητική) with Gorg. 451 C, Charm. 166 A, Pol. 259 E (on λογιστική) proves that he did (Rothlauf, l. c. pp. 19—21). Plato does not insist on the distinction here, but we may reasonably suppose that his pupils would begin with λογισμοί (λογιστική) and rise from thence to ἀριθμητική: cf. C, D and Laws 817 E, 819 A ff. See also on λογιστικῷ in B.

ταῦτα: i.e. τὰ τοῦ ἀριθμοῦ.