Acts 13:3

3Then, after they had fasted
The three aorist participles νηστεύσαντες (nēsteusantes), προσευξάμενοι (proseuxamenoi), and ἐπιθέντες (epithentes) are translated as temporal participles. Although they could indicate contemporaneous time when used with an aorist main verb, logically here they are antecedent. On fasting and prayer, see Matt 6:5, 16; Luke 2:37; 5:33; Acts 14:23.
and
Normally English style, which uses a coordinating conjunction between only the last two elements of a series of three or more, would call for omission of “and” here. However, since the terms “fasting and prayer” are something of a unit, often linked together, the conjunction has been retained here.
prayed and placed their hands
The placing of hands on Barnabas and Saul (traditionally known as “the laying on of hands”) refers to an act picturing the commission of God and the church for the task at hand.
on them, they sent them off.

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