James Adam, The Republic of Plato

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θέαν -- αὐτῇ. The ‘nature of numbers’ cannot be fully seen except in their connexion with the Good and with all other νοητά (VI 511 B—D notes). Plato does not of course imply that ἀριθμητική by itself will achieve this result (although it may be doubted whether some of his successors did not exalt the science to something like this dignity: see e.g. the Epinomis): neither ἀριθμητική nor all the propaedeutic studies taken together will ever carry us so far. He only means that the student, having once set foot on the ladder, must not redescend until he reaches the Good. Then and then only will he understand the ‘nature of numbers’ i.e. the Ideas of 1, 2, etc., because only then will he know Numbers dialectically (VI 511 B). On the use of φύσις see X 597 B note

τῇ νοήσει αὐτῇ: ‘by thought alone.’ αὐτῇ is ‘by itself’ i.e. (in this case) unadulterated with αἴσθησις: cf. 525 D note and supra IV 437 E, 438 B, VI 510 B, D notes

ῥᾳστώνης. A few inferior MSS add καί after this word: A alone has ῥᾳστώνης τε. I agree with Schneider in holding that the conjunctions are interpolated to avoid the concurrence of genitives, in which there is, however, no difficulty at all: cf. V 449 A note

νῦν καὶ ἐννοῶ. Cf. (with J. and C.) II 370 A ἐννοῶ γὰρ καὶ αὐτὸς εἰπόντος σοῦ.

λογισμούς: see on λογιστικῷ in B.