What did Peter preach in Cornelius's house about Jesus?
Peter preached about Jesus of Nazareth, expounding how He had come to be Israel's Messiah, Redeemer, and King. He delivered this message in Cornelius's house, though he wondered why he was giving it to Gentiles, not realizing God was then moving to reach the Gentile world.
Les explains that as Peter was in Cornelius's house, he was preaching and probably expounding about Jesus of Nazareth—how He had come to be Israel's Messiah, Redeemer, and King. Peter had gone contrary to his own desires, because God forced him to go to the house of Cornelius. As he laid this out, Peter wondered why he was giving this to Gentiles. He did not yet realize that something was moving in God's purposes, that He was now going to go out to the Gentile world. The context shows this had a distinct divine purpose, just as at Pentecost the purpose was that mankind might hear the plan of salvation.
Then Peter opened his mouth, and said, Of a truth I perceive that God is no respecter of persons:
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Did Peter preach about the cross and Jesus' shed blood to Cornelius?
When Peter preached at Cornelius' house he had not said a word about the work of the cross for salvation by Jesus' shed blood, the way Paul would have done.
What was Peter preaching about in Cornelius's house?
While preaching in Cornelius's house, Peter expounded that Jesus of Nazareth had come to be Israel's Messiah, Redeemer, and King.