The day following (tēi epiousēi hēmerāi). Locative case, “on the following day” (from epeimi, to come upon, to approach, present active participle epiōn ̇ousa, ̇on). Common phrase in old Greek both with hēmera (day) as here and without as Act 16:11. Only in Acts in the N.T.
Appeared (ōphthē). First aorist passive indicative of horaō not with idea that only a vision but rather that it was sudden or unexpected.
As they strove (machomenois). Present middle participle of machomai, actually fighting.
Would have set them at one again (sunēllassen autous eis eirēnen). Better, he tried to reconcile them (or change them into peace). It is the conative imperfect active as in Mat 3:14 of sunallassō, only here in the N.T. though common in the old Greek. Vulgate has reconciliabat. The usual word in the N.T. for reconcile is katallassō.
Do ye wrong one to another (adikeite allēlous). The same word used in Act 7:24of the wrong done one of the Hebrews by the Egyptian, but here both are “brethren.”