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αὐτῶν τῶν ἀριθμῶν: ‘numbers themselves,’ e.g. 1, 2, 3, 4 etc., in other words individual mathematical numbers and nothing more. αὐτῶν means ‘by themselves,’ ‘alone,’ i.e. with nothing αἰσθητόν about them, such as is present in the ὁρατὰ ἁπτὰ σώματα ἔχοντας ἀριθμούς (=Aristotle's αἰσθητικοὶ or σωματικοὶ ἀριθμοί: v. Bonitz Ind. Arist. s. v. ἀριθμός), e.g. one man, two men etc. These mathematical numbers are not Ideas, but (like τὰ μαθηματικά generally) a half-way house between sensibles and Ideas, and for this reason valuable as a προπαιδεία to Dialectic: cf. 526 A note and see on VI 510 D and App. I. For αὐτῶν in this sense cf. αὐτὸ τὸ ἕν in E, αὐτῇ τῇ νοήσει 526 B and ἀριθμῶν αὐτῶν ἀλλ᾽ οὐ σώματα ἐχόντων [Epin.] 990 C.

δεινούς. The word δύο, which was originally written after δεινούς (see cr. n.) in Α and Π, is probably due to a marginal adscript on the words ἐάν τις αὐτὸ τὸ ἓν ἐπιχειρῇτέμνειν. Burnet neatly conjectures δεινοὺς αὖ, but αὖ is inappropriate here.

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