Would you please help me to understand why, in Acts 10:37,KJV,Peter says, "That word, I say, ye know." It sounds as if Peter is aware that Cornelius, and maybe some of the others, had already heard the word, and been baptized with John's baptism. Although they were the first Gentiles to receive the Holy Spirit, was Cornelius' situation the same as those at Ephesus,in Acts 19:3? Thank you very very much, I can not thank you enough for your help.
Giving the context of the phrase in question; Peter is speaking to Cornelius and states, "The word which God sent to the children of Israel, preaching peace through Jesus Christ -- He is Lord of all -- that word you know, which was proclaimed throughout all Judea, and began from Galilee after the baptism which John preached: how God anointed Jesus of Nazareth with the Holy Spirit and with power, who went about doing good and healing all who were oppressed by the devil, for God was with Him" (Acts 10:36-38).
Peter reminds Cornelius and those with him that they were aware of the recent events in Judea. The "word" Peter refers to is the preaching of Jesus Christ (John 1:14). The preaching started when Jesus was baptized by John (Mark 1:1), starting in Galilee and then spreading through all of Judea. That teaching was upheld by God when God anointed Jesus with the Holy Spirit at his baptism and by the power God showed through Jesus in the miracles that Jesus did (John 20:30-31; Hebrews 2:3-4). It is not John's teaching that Peter is discussing, but Jesus' teaching. The baptism referred to is Jesus' baptism by John and not the general baptisms John was doing.
The reason for mentioning this is quite clear. To effectively teach someone, you need to start with common ground. For example, when Paul spoke to the Athenians on Mars Hill, he started with mention of their worship of the unknown God (Acts 17:22-23). Peter started Cornelius with the things he had heard concerning Jesus. This served as the foundation for the message which Peter then delivered to Cornelius. Peter did not need to prove that Jesus existed or that Jesus had done miracles by the power of God because Cornelius was aware of these things. Hence, Peter started on common ground to then introduce Cornelius to the things he and those he knew needed to do.
While Cornelius and his friends were aware of the events surrounding Jesus' ministry, there is nothing in this passage to indicate whether they had interacted with John.