James Adam, The Republic of Plato

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τοῦ ἀεὶ ὄντος. Plato held the objects of mathematical study to be ἀΐδια καὶ ἀκίνητα ‘eternal and unchangeable’ (Arist. Met. A 6. 987^{b} 16: cf. VI 510 C ff., VII 526 A note), but not Ideas. The Platonic meaning of τοῦ ἀεὶ ὄντος is certainly not exhausted by the observation that “the truths of every science are always true” (Bosanquet). ὄντος implies substantial existence, independently of our thoughts, and independently also of particulars. The existence of τὰ μαθηματικά as μιμήματα τῶν ὄντων or copies of the Ideas, ‘moving in and out of’ the material substance of the Universe, which they stamp with an infinite diversity of forms and shapes, is a cardinal doctrine of Plato's physics (Tim. 50 C al.), and Bosanquet appears to me to rob the words of Plato of half their significance, in the fruitless attempt to find in his ontology nothing but what commends itself to certain schools of philosophy in the present day. See V 476 E and App. I.

τοῦ ποτέ κτλ.: ‘that which at some particular time is a particular instance of becoming and perishing.’ τι γιγνομένου=ὄντος (the copula) γιγνομένου τινός, but γιγνομένου itself involves the copula, the presence of which would here be intolerable. Cf. V 473 D note and Euthyph. 10 C εἴ τι γίγνεται ἤ τι πάσχει, οὐχ ὅτι γιγνόμενόν ἐστι, γίγνεται, ἀλλ᾽ ὅτι γίγνεται, γιγνόμενόν ἐστι. Here τι is indeclinable like τι in Lach. 200 B, Menex. 247 B (οἰομένῳ τι εἶναι), Euthyd. 303 C (δοκούντων τι εἶναι), οὐδέν, μηδέν etc. tolerably often in tragedy, and the adverbial use of ἀμφότερα and τἀναντία (e.g. Lach. 185 A ὑέων γὰρ που ἢ χρηστῶν ἢ τἀναντία γενομένων κτλ.): cf. also (with Schneider Addit. p. 57) Procl. in Tim. 136 E τοῦ—ἀδιαιρέτως πάντα ὄντος et al. The indeclinable form adds to the emphasis, and indeed τινὸς (if placed after ποτέ) could hardly stand at all. Schneider translates “des etwas werdenden und vergehenden,” apparently taking τι predicatively with γιγνομένου. But the expression ‘that which becomes something’ suggests a substratum underlying γιγνόμενον, whereas the only correct antithesis to ὄν (τοῦ ἀεὶ ὄντος) is γιγνόμενον itself. Stallbaum wrongly explains τι as “aliqua ratione.” A few inferior MSS omit the word. I believe the text is sound, though possibly τι should be accented, as in the exactly similar Aristotelian usage of τις “ad significandam τὴν ἀτομότητα” (Bonitz Ind. Ar. p. 763) e.g. ὁ τὶς ἄνθρωπος. The use of ποτέ also reminds us of the ποτέ of the Categories.

γεωμετρική is an adjective (Schneider).

σχεῖν. The tense is inchoative or ingressive, as usual: see 516 E note