ἐπὶ τέχνῃ: cf. 315 a; to practise it as an art, to make it a profession.
ἐπὶ παιδείᾳ: for the sake of general culture. Cf. Gorg. 485 a φιλοσοφίας μὲν ὅσον παιδείας χάριν καλὸν μετέχειν.
τόν, τόν: generic arts. See H. 659.
ἰδιώτην: here contrasted with δημιουργός (one who pursues the art, cf. 327 c), elsewhere with ποιητής, ἰατρός etc. Cf. 322 c, 327 c, 344 c, 345 a; ἰδιωτεύειν 327 a.
ἐλεύθερον: liberalis, superior in dignity to the moneygetting class. See on 311 b.
πάνυ μὲν οὖν: emphatic form of assent.
It seems, then, that Hippocrates does not know what he wishes to obtain from Protagoras. The question naturally follows, what a sophist is, essentially; whether he has anything of value to impart, and whether it is a safe experiment to throw oneself precipitately (cf. 313 b) under his instruction, without previously ascertaining its precise nature.
τοῦ [τίνος] πέρι: sc. λανθάνει με.—
ὅτι μέλλεις κτἑ.: ὅτι depends upon λανθάνει, but with θαυμάζοιμ᾽ ἄν the discourse abandons the depend. const.