That Peter entered (tou eiselthein ton Petron). This is a difficult construction, for the subject of egeneto (it happened) has to be the articular genitive infinitive tou eiselthein with the accusative of general reference ton Petron. Most commentators consider it inexplicable. It is probably an extension of the ordinary articular infinitive under the influence of the Hebrew infinitive construct without regard to the case, regarding it as a fixed case form and so using it as nominative. Precisely this construction of tou and the infinitive as the subject of a verb occurs in the lxx (2 Chronicles 6:7, etc.). See Robertson, Grammar, pp. 1067f. for full discussion of this obvious Hebraism. Somewhat similar examples appear in Act 20:3; Act 27:1. But the Codex Bezae avoids this awkward idiom by the genitive absolute (proseggizontos tou Petrou) and some additional details (one of the servants ran forward and announced that he was come).
Worshipped him (prosekunēsen). “Cornelius was not an idolator and would not have honoured Peter as a god” (Furneaux). The word probably means here reverence like old English usage (Wycliff) and not actual worship, though Peter took it that way (Act 10:26). Jesus accepted such worship (Mat 8:2; Luk 5:8 by Peter).