Objection 1. It would seem that the union of the Word Incarnate did not take place in the suppositum or hypostasis. For Augustine says (Enchiridion xxxv, xxxviii): "Both the Divine and human substance are one Son of God, but they are one thing [aliud] by reason of the Word and another thing [aliud] by reason of the man." And Pope Leo says in his letter to Flavian (Ep. xxviii): "One of these is glorious with miracles, the other succumbs under injuries." But "one" [aliud] and "the other" [aliud] differ in suppositum. Therefore the union of the Word Incarnate did not take place in the suppositum.
Objection 2. Further, hypostasis is nothing more than a "particular substance," as Boethius says (De Duab. Nat.). But it is plain that in Christ there is another particular substance beyond the hypostasis of the Word, viz. the body and the soul and the resultant of these. Therefore there is another hypostasis in Him besides the hypostasis of the Word.
Objection 3. Further, the hypostasis of the Word is not included in any genus or species, as is plain from [I, 3, 5]. But Christ, inasmuch as He is made man, is contained under the species of man; for Dionysius says (Div. Nom. 1): "Within the limits of our nature He came, Who far surpasses the whole order of nature supersubstantially." Now nothing is contained under the human species unless it be a hypostasis of the human species. Therefore in Christ there is another hypostasis besides the hypostasis of the Word of God; and hence the same conclusion follows as above.
On the contrary, Damascene says (De Fide Orth. iii, 3,4,5): "In our Lord Jesus Christ we acknowledge two natures and one hypostasis."
I answer that, Some who did not know the relation of hypostasis to person, although granting that there is but one person in Christ, held, nevertheless, that there is one hypostasis of God and another of man, and hence that the union took place in the person and not in the hypostasis. Now this, for three reasons, is clearly erroneous. First, because person only adds to hypostasis a determinate nature, viz. rational, according to what Boethius says (De Duab. Nat.), "a person is an individual substance of rational nature"; and hence it is the same to attribute to the human nature in Christ a proper hypostasis and a proper person. And the holy Fathers, seeing this, condemned both in the Fifth Council held at Constantinople, saying: "If anyone seeks to introduce into the mystery of Incarnation two subsistences or two persons, let him be anathema. For by the incarnation of one of the Holy Trinity, God the Word, the Holy Trinity received no augment of person or subsistence." Now "subsistence" is the same as the subsisting thing, which is proper to hypostasis, as is plain from Boethius (De Duab. Nat.). Secondly, because if it is granted that person adds to hypostasis something in which the union can take place, this something is nothing else than a property pertaining to dignity; according as it is said by some that a person is a "hypostasis distinguished by a property pertaining to dignity." If, therefore, the union took place in the person and not in the hypostasis, it follows that the union only took place in regard to some dignity. And this is what Cyril, with the approval of the Council of Ephesus (part iii, can. 3), condemned in these terms: "If anyone after the uniting divides the subsistences in the one Christ, only joining them in a union of dignity or authority or power, and not rather in a concourse of natural union, let him be anathema." Thirdly, because to the hypostasis alone are attributed the operations and the natural properties, and whatever belongs to the nature in the concrete; for we say that this man reasons, and is risible, and is a rational animal. So likewise this man is said to be a suppositum, because he underlies [supponitur] whatever belongs to man and receives its predication. Therefore, if there is any hypostasis in Christ besides the hypostasis of the Word, it follows that whatever pertains to man is verified of some other than the Word, e.g. that He was born of a Virgin, suffered, was crucified, was buried. And this, too, was condemned with the approval of the Council of Ephesus (part iii, can. 4) in these words: "If anyone ascribes to two persons or subsistences such words as are in the evangelical and apostolic Scriptures, or have been said of Christ by the saints, or by Himself of Himself, and, moreover, applies some of them to the man, taken as distinct from the Word of God, and some of them (as if they could be used of God alone) only to the Word of God the Father, let him be anathema." Therefore it is plainly a heresy condemned long since by the Church to say that in Christ there are two hypostases, or two supposita, or that the union did not take place in the hypostasis or suppositum. Hence in the same Synod (can. 2) it is said: "If anyone does not confess that the Word was united to flesh in subsistence, and that Christ with His flesh is both--to wit, God and man--let him be anathema."
Reply to Objection 1. As accidental difference makes a thing "other" [alterum, so essential difference makes "another thing" [aliud]. Now it is plain that the "otherness" which springs from accidental difference may pertain to the same hypostasis or suppositum in created things, since the same thing numerically can underlie different accidents. But it does not happen in created things that the same numerically can subsist in divers essences or natures. Hence just as when we speak of "otherness" in regard to creatures we do not signify diversity of suppositum, but only diversity of accidental forms, so likewise when Christ is said to be one thing or another thing, we do not imply diversity of suppositum or hypostasis, but diversity of nature. Hence Gregory Nazianzen says in a letter to Chelidonius (Ep. ci): "In the Saviour we may find one thing and another, yet He is not one person and another. And I say 'one thing and another'; whereas, on the contrary, in the Trinity we say one Person and another (so as not to confuse the subsistences), but not one thing and another."
Reply to Objection 2. Hypostasis signifies a particular substance, not in every way, but as it is in its complement. Yet as it is in union with something more complete, it is not said to be a hypostasis, as a hand or a foot. So likewise the human nature in Christ, although it is a particular substance, nevertheless cannot be called a hypostasis or suppositum, seeing that it is in union with a completed thing, viz. the whole Christ, as He is God and man. But the complete being with which it concurs is said to be a hypostasis or suppositum.
Reply to Objection 3. In created things a singular thing is placed in a genus or species, not on account of what belongs to its individuation, but on account of its nature, which springs from its form, and in composite things individuation is taken more from matter. Hence we say that Christ is in the human species by reason of the nature assumed, and not by reason of the hypostasis.
Source: Summa Theologica (New Advent)