ἡμῖν: “for let us all make the examination together.” Prodicus and Hippias had been invited at the outset 317 d, but Socrates repeats particularly 343 c ἐπισκεψώμεθα δὴ αὐτὸ κοινῇ ἅπαντες and 358 d συνεδόκει ἅπασιν ἡμῖν. By taking the others along with Protagoras, Socrates makes it the more difficult for the latter to break away again before the consummation of the argument, cf. 360 d.
διαίρεσιν: see on 337 a, l. 26.