Vincent's NT Word Studies
34. I perceive. See on ch. iv. 13.Respecter of persons (proswpolhmpthv). See on respect of persons, Jas. ii. 1. Only here in New Testament.
Robertson's NT Word Studies
10:34 {Opened his mouth} (anoixas to stoma). Solemn formula for beginning his address (#8:35; 18:14; Mt 5:2; 13:35). But also good elocution for the speaker. {I perceive} (katalambanomai). Aoristic present middle of katalambanw, to take hold of, the middle noting mental action, to lay hold with the mind (#Ac 4:13; 10:34; 25:25; Eph 3:18). It had been a difficult thing for Peter to grasp, but now "of a truth" (ep' aleqeias) the light has cleared away the fogs. It was not until Peter had crossed the threshold of the house of Cornelius in the new environment and standpoint that he sees this new and great truth. {Respecter of persons} (proswpolemptes). this compound occurs only here and in Chrysostom. It is composed of proswpon face or person (pros and oy, before the eye or face) and lambanw. The abstract form pros"polmpsia occurs in #Jas 2:1 (also #Ro 2:11; Eph 6:9; Col 3:25) and the verb pros"polempte" in #Jas 2:9. The separate phrase (lambanein proswpon) occurs in #Lu 20:21; Ga 2:6. The phrase was already in the LXX (#De 10:17; 2Ch 19:7; Ps 82:6). Luke has simply combined the two words into one compound one. The idea is to pay regard to one's looks or circumstances rather than to his intrinsic character. The Jews had come to feel that they were the favorites of God and actually sons of the kingdom of heaven because they were descendants of Abraham. John the Baptist rebuked them for this fallacy.