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Hippias compares himself and the rest of the company to arbitrators, umpires, freely chosen by the contending parties. It is the office of these umpires to persuade both parties (here, Socrates and Protagoras) to moderate their demands and to unite upon some intermediate course. συμβαίνειν and συμβιβάζειν are here the technical expressions (cf. Thuc. ii. 29 ξυνεβίβασε δὲ καὶ τὸν Περδίκκαν τοῖς Ἀθηναίοις). ὑπό is used because συμβῆναι has a pass. sense. See H. 820. — The peculiar transposition of the words, for ὑφ᾽ ἡμῶν ὥσπερ ὑπὸ διαιτητῶν, is very freq. in Plato in such comparisons. Cf. Rep. iii. 414 e δεῖ ὡς περὶ μητρὸς καὶ τροφοῦ τῆς χώρας ἐν εἰσὶ βουλεύεσθαι, vii. 520 e ὡς ἐπ᾽ ἀναγκαῖον αὐτῶν ἕκαστος εἶσι τὸ ἄρχειν (will take office), viii. 545 e ὡς πρὸς παῖδας ἡμᾶς παιζούδας (viz. τὰς Μούσας), Theaet. 170 a ὥσπερ πρὸς θεοὺς ἔχειν τοὺς ἐν ἑκἀστοις ἄρχοντας look up to their commanders in such peril as to gods. — As συμβῆναι in this sense almost always stands absolutely, εἰς τὸ μέσον is most simply connected with συμβιβαζόντων.

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