Gonzalez Lodge, Commentary on Plato: Gorgias

ὀψοποιική: is not attributive to κολακεία, but the latter is predicate with ὑπόκειται, as flattery. Hence the point of the following κατὰ λόγον.

ὑπόκειται (equiv. to ὑποτέθειται): is not used in the sense which we elsewhere find, lie at the foundation of, as in Prot. 349 b ἑκάστῳ τῶν ὀνομάτων ὑπόκειταί τις ἴδιος οὐσία, but like ὑποδέδυκεν above, 464 d.

κακοῦργος κτἑ.: these four adjectives go in pairs. The two first describing the nature of κολακεία per se, contain the κακόν of it; the first is more general, the second adds the special (Kr. 69, 32, 2), at the same time emphasizing the result for the world at large. The second pair contains the αἰσχρόν, the verdict on the value of such skill. The following participle, with its datives, defines more narrowly ἀπατηλή.

οἱ γεωμέτραι: the word denotes “mathematicians” in general. So i.e. Theodorus of Cyrene is continually called γεωμέτρης in the Theaetetus. Higher arithmetic also is included under geometry, because the Greeks employed geometrical methods to represent the higher relations of numbers. In the following proportion, we are reminded at once of an arithmetical formula; while the Greeks were reminded of the due proportion of lines and figures, in accordance with the development of mathematical science among them. The relations of the ideas can, by means of this threefold division into pairs, be brought into a simple but complete scheme. See on 464 a above.

ἤδη γὰρ κτἑ.: mathematics was looked upon by Plato as a preparation for ‘dialectic.’

ὃ κομμωτικὴ πρὸς γυμναστικήν: in this formula ἐστί is always wanting.