But when they believed Philip's message. Note that: (1) Philip preached to them; (2) the Good News of the Kingdom of God and the name of Jesus Christ; (3) faith came from hearing the message (Romans 10:17); (4) when they believed, they were baptized. This is the pattern found throughout Acts, including the special case of Cornelius. Both men and women. There is no mention of children.

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Old Testament