James Adam, The Republic of Plato

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ὅσοι ἂν -- μὴ κτλ.: “who run well from the lower end of the course to the upper, but not from the upper to the lower” etc. (J. and C.). Plato is thinking of the δίαυλος, and calls the outward and homeward journeys respectively ἀπὸ τῶν κάτω and ἀπὸ τῶν ἄνω. We must suppose, although there seems to be no other authority for the supposition, that the end from which the competitors started was spoken of as ‘down’ and the other end as ‘up.’ Schneider suggests that the outward limit may have stood higher, but Greek stadia seem always to have been level. The use of ἄνω and κάτω is as in περιπατεῖν ἄνω κάτω (Ar. Lys. 709), εἷρπ᾽ ἄνω τε καὶ κάτω (Eur. H. F. 953), and other examples quoted in Stephanus-Hase Thes. s.v. ἄνω p. 1063. The subject of ἀποπηδῶσι is not οἱ δρομῆς, but οἱ δεινοί τε καὶ ἄδικοι: so that τὸ μὲν πρῶτον corresponds roughly to ἀπὸ τῶν κάτω, and τελευτῶντες to ἀπὸ τῶν ἄνω. This interpretation is that of Schneider and the other editors. A wholly different view is taken by Riddell (Digest § 111) and Madvig. They understand τὰ κάτω of the lower, and τὰ ἄνω of the upper parts of the body (“who run fairly with their legs, but with the upper part of their bodies—head, neck, arms—in bad form” Riddell l.c. For the use of ἀπό cf. Laws 795 B, 832 E and Xen. Rep. Lac. 5. 9). But an allusion to the physiology of bad running is not in place here, and it is difficult to resist the impression that ἀπὸ τῶν κάτω and ἀπὸ τῶν ἄνω are significant parts of the comparison. On Riddell's view they are not, for there is nothing in the career of the clever and unjust which can well be illustrated by ‘running fairly with their legs’ etc. The point is, as τὸ μὲν πρῶτον—ἀποτρέχοντες expressly states, that they do well at first, but collapse before the end, like runners who run well as far as the καμπτήρ, but break down in the second half of the δίαυλος. For the illustration from the games cf. V 465 D note