What was the purpose of the ministry of Peter in the house of Cornelius?
We must note some things that are not true in order to appreciate that which is true. Nothing is said about Cornelius attending temple or synagogue. All we know is that he was a centurion at the head of an Italian band of soldiers and that he was devout, feared God, gave alms to poor Jews, and prayed to God always. This sums up all we know about him. Even after his experience at the preaching of Peter there is nothing said about him, whether he went to the temple or synagogue or whether he ever joined with the band of Christians at Jerusalem or elsewhere. With that out of the way, we can see that this was a preparation for Paul and his ministry to Gentiles during the Acts period of time.