34: Then Peter opened his mouth, and said, Of a truth I perceive that God is no respecter of persons: 35: But in every nation he that feareth him, and worketh righteousness, is accepted with him. 36: The word which God sent unto the children of Israel, preaching peace by Jesus Christ: (he is Lord of all:) 37: That word, I say, ye know, which was published throughout all Judaea, and began from Galilee, after the baptism which John preached; 38: How God anointed Jesus of Nazareth with the Holy Ghost and with power: who went about doing good, and healing all that were oppressed of the devil; for God was with him. 39: And we are witnesses of all things which he did both in the land of the Jews, and in Jerusalem; whom they slew and hanged on a tree: 40: Him God raised up the third day, and shewed him openly; 41: Not to all the people, but unto witnesses chosen before of God, even to us, who did eat and drink with him after he rose from the dead. 42: And he commanded us to preach unto the people, and to testify that it is he which was ordained of God to be the Judge of quick and dead. 43: To him give all the prophets witness, that through his name whosoever believeth in him shall receive remission of sins. 44: While Peter yet spake these words, the Holy Ghost fell on all them which heard the word. 45: And they of the circumcision which believed were astonished, as many as came with Peter, because that on the Gentiles also was poured out the gift of the Holy Ghost. 46: For they heard them speak with tongues, and magnify God. Then answered Peter, 47: Can any man forbid water, that these should not be baptized, which have received the Holy Ghost as well as we? 48: And he commanded them to be baptized in the name of the Lord. Then prayed they him to tarry certain days.
The stage is set (or should l say pulpit.) for Peter to preach the Gospel to Cornelius. Firstly Peter says that now he understands that God has no prejudice on the basis of race, because in every nation he that fears God and lives righteously is accepted with him. In other words Gentiles who live according to the Mosaic Law are as acceptable as Jews in the flesh. Then Peter goes on to tell Cornelius that God sent his word to the children of Israel through the preaching of peace by Jesus Christ. That Gospel of peace was preached throughout all Judea and Galilee you know. It followed the preaching John the Baptist. That message was that Jesus of Nazareth was anointed by God with the Holy Spirit and with power to go about doing good and healing all that were possessed. Then Peter said, we are witnesses of all these things which he did in Judea and in Jerusalem. But the people of Jerusalem crucified him, but God raised him from the dead on the third day and shewed him openly to us who were appointed to be witnesses of the resurrection. We ate and drank with him after he had risen from the dead. Jesus of Nazareth commanded us to preach to the people and to testify that he has been ordained to be the Judge of the living and the dead. Cornelius had heard of John and Christ’s life, ministry and death but they had never heard of his resurrection. The OT prophets testified that through his name whosoever believes in him will receive remission of sins. While Peter spoke these words the assembled company believed in Christ resurrection and the Holy Spirit came upon them. The Jews that were there were astonished, that the Holy Spirit came on Gentiles. Those that believed testified in languages given to them by the Holy Spirit to those Gentiles who were unconvinced. Peter took charge and asked if anyone could deny baptism? So he ordered them to be baptised in the name of the Lord. Peter stayed a while with them for a few days.