Objection 1. It would seem that nativity regards the nature rather than the person. For Augustine [Fulgentius] says (De Fide ad Petrum): "The eternal Divine Nature could not be conceived and born of human nature, except in a true human nature." Consequently it becomes the Divine Nature to be conceived and born by reason of the human nature. Much more, therefore, does it regard human nature itself.
Objection 2. Further, according to the Philosopher (Metaph. v), "nature" is so denominated from "nativity." But things are denominated from one another by reason of some likeness. Therefore it seems that nativity regards the nature rather than the person.
Objection 3. Further, properly speaking, that is born which begins to exist by nativity. But Christ's Person did not begin to exist by His nativity, whereas His human nature did. Therefore it seems that the nativity properly regards the nature, and not the person.
On the contrary, Damascene says (De Fide Orth. iii): "Nativity regards the hypostasis, not the nature."
I answer that, Nativity can be attributed to someone in two ways: first, as to its subject; secondly, as to its terminus. To him that is born it is attributed as to its subject: and this, properly speaking, is the hypostasis, not the nature. For since to be born is to be generated; as a thing is generated in order for it to be, so is a thing born in order for it to be. Now, to be, properly speaking, belongs to that which subsists; since a form that does not subsist is said to be only inasmuch as by it something is: and whereas person or hypostasis designates something as subsisting, nature designates form, whereby something subsists. Consequently, nativity is attributed to the person or hypostasis as to the proper subject of being born, but not to the nature.
But to the nature nativity is attributed as to its terminus. For the terminus of generation and of every nativity is the form. Now, nature designates something as a form: wherefore nativity is said to be "the road to nature," as the Philosopher states (Phys. ii): for the purpose of nature is terminated in the form or nature of the species.
Reply to Objection 1. On account of the identity of nature and hypostasis in God, nature is sometimes put instead of person or hypostasis. And in this sense Augustine says that the Divine Nature was conceived and born, inasmuch as the Person of the Son was conceived and born in the human nature.
Reply to Objection 2. No movement or change is denominated from the subject moved, but from the terminus of the movement, whence the subject has its species. For this reason nativity is not denominated from the person born, but from nature, which is the terminus of nativity.
Reply to Objection 3. Nature, properly speaking, does not begin to exist: rather is it the person that begins to exist in some nature. Because, as stated above, nature designates that by which something is; whereas person designates something as having subsistent being.
Source: Summa Theologica (New Advent)