Objection 1. It would seem that the accomplishment of Christ's conception should not be attributed to the Holy Ghost, because. as Augustine says (De Trin. i), "The works of the Trinity are indivisible, just as the Essence of the Trinity is indivisible." But the accomplishment of Christ's conception was the work of God. Therefore it seems that it should not be attributed to the Holy Ghost any more than to the Father or the Son.
Objection 2. Further, the Apostle says (Galatians 4:4): "When the fulness of time was come, God sent His Son, made of a woman"; which words Augustine expounds by saying (De Trin. iv): "Sent, in so far as made of a woman." But the sending of the Son is especially attributed to the Father, as stated in I, 43, 8. Therefore His conception also, by reason of which He was "made of a woman," should be attributed principally to the Father.
Objection 3. Further, it is written (Proverbs 9:1): "Wisdom hath built herself a house." Now, Christ is Himself the Wisdom of God; according to 1 Corinthians 1:24: "Christ the Power of God and the Wisdom of God." And the house of this Wisdom is Christ's body, which is also called His temple, according to John 2:21: "But He spoke of the temple of His body." Therefore it seems that the accomplishment of Christ's conception should be attributed principally to the Son, and not, therefore, to the Holy Ghost.
On the contrary, It is written (Luke 1:35): "The Holy Ghost shall come upon Thee."
I answer that, The whole Trinity effected the conception of Christ's body: nevertheless, this is attributed to the Holy Ghost, for three reasons. First, because this is befitting to the cause of the Incarnation, considered on the part of God. For the Holy Ghost is the love of Father and Son, as stated in I, 37, 1. Now, that the Son of God took to Himself flesh from the Virgin's womb was due to the exceeding love of God: wherefore it is said (John 3:16): "God so loved the world as to give His only-begotten Son."
Secondly, this is befitting to the cause of Incarnation, on the part of the nature assumed. Because we are thus given to understand that human nature was assumed by the Son of God into the unity of Person, not by reason of its merits, but through grace alone; which is attributed to the Holy Ghost, according to 1 Corinthians 12:4: "There are diversities of graces, but the same Spirit." Wherefore Augustine says (Enchiridion xl): "The manner in which Christ was born of the Holy Ghost... suggests to us the grace of God, whereby man, without any merits going before, in the very beginning of his nature when he began to exist was joined to God the Word, into so great unity of Person, that He Himself should be the Son of God."
Thirdly, because this is befitting the term of Incarnation. For the term of Incarnation was that that man, who was being conceived, should be the Holy one and the Son of God. Now, both of these are attributed to the Holy Ghost. For by Him men are made to be sons of God, according to Galatians 4:6: "Because you are sons, God hath sent the Spirit of His Son into your [Vulgate: 'our'] hearts, crying: Abba, Father." Again, He is the "Spirit of sanctification," according to Romans 1:4. Therefore, just as other men are sanctified spiritually by the Holy Ghost; so as to be the adopted sons of God, so was Christ conceived in sanctity by the Holy Ghost, so as to be the natural Son of God. Hence, according to a gloss on Romans 1:4, the words, "Who was predestinated the Son of God, in power," are explained by what immediately follows: "According to the Spirit of sanctification, i.e. through being conceived of the Holy Ghost." And the Angel of the Annunciation himself, after saying, "The Holy Ghost shall come upon thee," draws the conclusion: "Therefore also the Holy which shall be born of thee shall be called the Son of God."
Reply to Objection 1. The work of the conception is indeed common to the whole Trinity; yet in some way it is attributed to each of the Persons. For to the Father is attributed authority in regard to the Person of the Son, who by this conception took to Himself (human nature). The taking itself (of human nature) is attributed to the Son: but the formation of the body taken by the Son is attributed to the Holy Ghost. For the Holy Ghost is the Spirit of the Son, according to Galatians 4:6: "God sent the Spirit of His Son." For just as the power of the soul which is in the semen, through the spirit enclosed therein, fashions the body in the generation of other men, so the Power of God, which is the Son Himself, according to 1 Corinthians 1:24: "Christ, the Power of God," through the Holy Ghost formed the body which He assumed. This is also shown by the words of the angel: "The Holy Ghost shall come upon thee," as it were, in order to prepare and fashion the matter of Christ's body; "and the Power of the Most High," i.e. Christ, "shall overshadow thee--that is to say, the incorporeal Light of the Godhead shall in thee take the corporeal substance of human nature: for a shadow is formed by light and body," as Gregory says (Moral. xviii). The "Most High" is the Father, whose Power is the Son.
Reply to Objection 2. The mission refers to the Person assuming, who is sent by the Father; but the conception refers to the body assumed, which is formed by the operation of the Holy Ghost. And therefore, though mission and conception are in the same subject; since they differ in our consideration of them, mission is attributed to the Father, but the accomplishment of the conception to the Holy Ghost; whereas the assumption of flesh is attributed to the Son.
Reply to Objection 3. As Augustine says (QQ. Vet. et Nov. Test., qu. 52): "This may be understood in two ways. For, first, Christ's house is the Church, which He built with His blood. Secondly, His body may be called His house, just as it is called His temple... and what is done by the Holy Ghost is done by the Son of God, because Theirs is one Nature and one Will."
Source: Summa Theologica (New Advent)