From John Chrysostom, Baptismal Homily 2:
26. To give you a further lesson that the substance of the Father, the Son and the Spirit is one; baptism is conferred in this form. As the bishop pronounces the words, “N. is baptized in the name of the Father and of the Son and of the Holy Spirit,” he plunges your head into the water and lifts it up again three times, by this sacred rite preparing you to receive the visit of the Holy Spirit. For the bishop is not the only one who touches your head; Christ also touches it with his right hand. This is shown by the actual words of the bishop who baptizes you. He does not say, “I baptize N.,” but rather, “N. is baptized.” This shows that he is only the minister of the grace and merely lends his hand since he has been ordained for this by the Spirit. It is the Father, Son and Holy Spirit, the indivisible Trinity, who bring the whole rite to completion. It is the faith in the Trinity that bestows the grace of remission of sin, and the confession of the Trinity that grants us the adoption of sons (Thomas M. Finn, Early Christian Baptism and the Catechumenate: West and East Syria [Message of the Fathers of the Church 5; Collegeville, Minn.: The Liturgical Press, 1992], 79)