Seeing the amazed crowd, the formerly fearful Peter who had denied Jesus, spoke again with the conviction and force he exhibited at Pentecost. Not fully committed to Jesus prior to his death because his human expectation of Jesus restoring the Kingdom of Israel was unfulfilled, Peter now sees things in a different light. The difference was the resurrection and glorification of Jesus which Peter said was by the God of Abraham, Isaac and Jacob. That same God in Exodus 3:6 said to Moses, "I am the God of your father, the God of Abraham, the God of Isaac, and the God of Jacob." Just as God was saying to Moses that Abraham, Isaac and Jacob were alive, so now Peter tells the crowd that God's servant Jesus is alive.
Peter directs the crowd's attention to Jesus, the Author of Life, and says that it is the faith that is through Jesus that restored the man to health. Just as Moses led the Israelites from bondage to freedom, so now Jesus provides a way to freedom from the bondage of sin and to eternal life with God. Probably reflecting on how he failed to understand the ultimate purpose of Jesus' miracles, Peter now uses miracles to point the crowd to the salvation that comes through the risen Jesus Christ. His sole focus now is on promoting God's kingdom on this earth and the eternal life that comes through faith in Jesus.