Chrysostom: It is moreover an allusion to ancient history; for in the deluge this creature appeared bearing an olive branch, and tidings of rest to the world. All which things were a type of things to come. For now also a dove appears pointing out to us our liberator, and for an olive branch bringing the adoption of the human race.
Aug., de Trin., ii, 5: It is easy to understand how the Holy Ghost should be said to be sent, when as it were a dove in visible shape descended on the Lord; that is, there was created a certain appearance for the time in which the Holy Spirit might be visibly shewn. And this operation thus made visible and offered to mortal view, is called the mission of the Holy Spirit, not that His invisible substance was seen, but that the hearts of men might be roused by the external appearance to contemplate the unseen eternity.
Yet this creature in the shape of which the Spirit appeared, was not taken into unity of person, as was that human shape taken of the Virgin. For neither did the Spirit bless the dove, nor unite it with Himself for all eternity, in unity of person. Further, though that dove is called the Spirit, so far as to shew that in this dove was a manifestation of the Spirit, yet can we not say of the Holy Spirit that He is God and dove, as we say of the Son that He is God and man; and yet it is not as we say of the Son that He is "the Lamb of God," as not only has John Baptist declared, but as John the Evangelist saw the vision of the Lamb slain in the Apocalypse. For this was a prophetic vision, not put before the bodily eyes in bodily shape, but seen in the Spirit in spiritual images.
But concerning this dove none ever doubted that is was seen with the bodily eye; not that we say the Spirit is a dove as we say Christ is a Rock; (for "that Rock was Christ.) [[1Co 10:10]] For that Rock already existed as a creature, and from the resemblance of its operation was called by the name of Christ, (whom it figured;) not so this dove, which was created at the moment for this single purpose.
It seems to me to be more like the flame which appeared to Moses in the bush, or that which the people followed in the wilderness, or to the thunderings and lightnings which were when the Law was given from the mount. For all these were visible objects intended to signify something, and then to pass away. For that such forms have been from time to time seen, the Holy Spirit is said to have been sent; but these bodily forms appeared for the time to shew what was required, and then ceased to be.
Jerome: It sat on the head of Jesus, that none might suppose the voice of the Father spoken to John, and not to the Lord.
Ver. 17. And lo a voice from heaven, saying, "This is my beloved Son, in whom I am well pleased."
Aug., non occ.: Not as before by Moses and the Prophets, neither in type or figure did the Father teach that the Son should come, but openly shewed Him to be already come, "This is my Son."
Hilary: Or, that from these things thus fulfilled upon Christ, we might learn that after the washing of water the Holy Spirit also descends on us from the heavenly gates, on us also is shed an unction of heavenly glory, and an adoption to be the sons of God, pronounced by the Father’s voice.
Jerome: The mystery of the Trinity is shewn in this baptism. the Lord is baptized; the Spirit descends in the shape of a dove; the voice of the Father is heard giving testimony to the Son.
Ambrose, Ambrosiaster, Serm. 10. 1: And no wonder that the mystery of the Trinity is not wanting to the Lord’s laver, when even our laver contains the sacrament of the Trinity. The Lord willed to shew in His own case what He was after to ordain for men.
Pseudo-Aug., Fulgent. de Fide ad Petrum. c. 9: Though Father, Son, and Holy Ghost are one nature, yet do thou hold most firmly that They be Three Persons; that it is the Father alone who said, "this is my beloved Son;" the Son alone over whom that voice of the Father was heard; and the Holy Ghost alone who in the likeness of a dove descended on Christ at His baptism.
Aug., de Trin. 4. 21: Here are deeds of the whole Trinity. In their own substance indeed Father, Son, and Holy Spirit are One without interval of either place or time; but in my mouth they are three separate words, and cannot be pronounced at the same time, and in written letters they fill each their several places. By this comparison may be understood how the Trinity in Itself indivisible may be manifested dividedly in the likeness of a visible creation. That the voice is that of the Father only is manifest from the words, "This is my Son."
Hilary, de Trin. iii. 11: He witnesses that He is His Son not in name merely, but in very kindred. Sons of God are we many of us; but not as He is a Son, a proper and true Son, in verity, not in estimation, by birth, not adoption.
Aug., in Joann. tr. 14. 11: The Father loves the Son, but as a father should, not as a master may love a servant; and that as an own Son, not an adopted; therefore He adds, "in whom I am well-pleased."
Remigius: Or if it be referred to the human nature of Christ, the sense is, I am pleased in Him, whom alone I have found without sin. Or according to another reading, "It hath pleased me" to appoint Him, by whom to perform those things I would perform, i.e. the redemption of the human race.
Aug., de Cons. Evan., ii, 14: These words Mark and Luke give in the same way; in the words of the voice that came from Heaven, their expression varies though the sense is the same. For both the words as Matthew gives them, "This is my beloved Son," and as the other two, "Thou art my beloved Son," express the same sense in the speaker; (and the heavenly voice, no doubt, uttered one of these,) but one shews an intention of addressing the testimony thus borne to the Son to those who stood by; the other of addressing it to Himself, as if speaking to Christ He had said, "This is my Son." Not that Christ was taught what He knew before, but they who stood by heard it, for whose sake the voice came.
Again, when one says, "in whom I am well-pleased;" another, "in thee it hath pleased me," if you ask which of these was actually pronounced by that voice; take which you will, only remembering that those who have not related the same words as were spoken have related the same sense. That God is well-pleased with His Son is signified in the first; that the Father is by the Son pleased with men is conveyed in the second form, "in thee it hath well-pleased me."
Or you may understand this to have been the one meaning of all the Evangelists, In Thee have I put My good pleasure, i.e. to fulfil all My purpose.