Objection 1. It would seem that the essential names should not be appropriated to the persons. For whatever might verge on error in faith should be avoided in the treatment of divine things; for, as Jerome says, "careless words involve risk of heresy" [In substance Ep. lvii.]. But to appropriate to any one person the names which are common to the three persons, may verge on error in faith; for it may be supposed either that such belong only to the person to whom they are appropriated or that they belong to Him in a fuller degree than to the others. Therefore the essential attributes should not be appropriated to the persons.
Objection 2. Further, the essential attributes expressed in the abstract signify by mode of form. But one person is not as a form to another; since a form is not distinguished in subject from that of which it is the form. Therefore the essential attributes, especially when expressed in the abstract, are not to be appropriated to the persons.
Objection 3. Further, property is prior to the appropriated, for property is included in the idea of the appropriated. But the essential attributes, in our way of understanding, are prior to the persons; as what is common is prior to what is proper. Therefore the essential attributes are not to be appropriated to the persons.
On the contrary, the Apostle says: "Christ the power of God and the wisdom of God" (1 Corinthians 1:24).
I answer that, For the manifestation of our faith it is fitting that the essential attributes should be appropriated to the persons. For although the trinity of persons cannot be proved by demonstration, as was above expounded (32, 1), nevertheless it is fitting that it be declared by things which are more known to us. Now the essential attributes of God are more clear to us from the standpoint of reason than the personal properties; because we can derive certain knowledge of the essential attributes from creatures which are sources of knowledge to us, such as we cannot obtain regarding the personal properties, as was above explained (32, 1). As, therefore, we make use of the likeness of the trace or image found in creatures for the manifestation of the divine persons, so also in the same manner do we make use of the essential attributes. And such a manifestation of the divine persons by the use of the essential attributes is called "appropriation."
The divine person can be manifested in a twofold manner by the essential attributes; in one way by similitude, and thus the things which belong to the intellect are appropriated to the Son, Who proceeds by way of intellect, as Word. In another way by dissimilitude; as power is appropriated to the Father, as Augustine says, because fathers by reason of old age are sometimes feeble; lest anything of the kind be imagined of God.
Reply to Objection 1. The essential attributes are not appropriated to the persons as if they exclusively belonged to them; but in order to make the persons manifest by way of similitude, or dissimilitude, as above explained. So, no error in faith can arise, but rather manifestation of the truth.
Reply to Objection 2. If the essential attributes were appropriated to the persons as exclusively belonging to each of them, then it would follow that one person would be as a form as regards another; which Augustine altogether repudiates (De Trin. vi, 2), showing that the Father is wise, not by Wisdom begotten by Him, as though only the Son were Wisdom; so that the Father and the Son together only can be called wise, but not the Father without the Son. But the Son is called the Wisdom of the Father, because He is Wisdom from the Father Who is Wisdom. For each of them is of Himself Wisdom; and both together are one Wisdom. Whence the Father is not wise by the wisdom begotten by Him, but by the wisdom which is His own essence.
Reply to Objection 3. Although the essential attribute is in its proper concept prior to person, according to our way of understanding; nevertheless, so far as it is appropriated, there is nothing to prevent the personal property from being prior to that which is appropriated. Thus color is posterior to body considered as body, but is naturally prior to "white body," considered as white.
Source: Summa Theologica (New Advent)