Objection 1. It would seem that equality is not becoming to the divine persons. For equality is in relation to things which are one in quantity as the Philosopher says (Metaph. v, text 20). But in the divine persons there is no quantity, neither continuous intrinsic quantity, which we call size, nor continuous extrinsic quantity, which we call place and time. Nor can there be equality by reason of discrete quantity, because two persons are more than one. Therefore equality is not becoming to the divine persons.
Objection 2. Further, the divine persons are of one essence, as we have said (39, 2). Now essence is signified by way of form. But agreement in form makes things to be alike, not to be equal. Therefore, we may speak of likeness in the divine persons, but not of equality.
Objection 3. Further, things wherein there is to be found equality, are equal to one another, for equality is reciprocal. But the divine persons cannot be said to be equal to one another. For as Augustine says (De Trin. vi, 10): "If an image answers perfectly to that whereof it is the image, it may be said to be equal to it; but that which it represents cannot be said to be equal to the image." But the Son is the image of the Father; and so the Father is not equal to the Son. Therefore equality is not to be found among the divine persons.
Objection 4. Further, equality is a relation. But no relation is common to the three persons; for the persons are distinct by reason of the relations. Therefore equality is not becoming to the divine persons.
On the contrary, Athanasius says that "the three persons are co-eternal and co-equal to one another."
I answer that, We must needs admit equality among the divine persons. For, according to the Philosopher (Metaph. x, text 15,16, 17), equality signifies the negation of greater or less. Now we cannot admit anything greater or less in the divine persons; for as Boethius says (De Trin. i): "They must needs admit a difference [namely, of Godhead] who speak of either increase or decrease, as the Arians do, who sunder the Trinity by distinguishing degrees as of numbers, thus involving a plurality." Now the reason of this is that unequal things cannot have the same quantity. But quantity, in God, is nothing else than His essence. Wherefore it follows, that if there were any inequality in the divine persons, they would not have the same essence; and thus the three persons would not be one God; which is impossible. We must therefore admit equality among the divine persons.
Reply to Objection 1. Quantity is twofold. There is quantity of "bulk" or dimensive quantity, which is to be found only in corporeal things, and has, therefore, no place in God. There is also quantity of "virtue," which is measured according to the perfection of some nature or form: to this sort of quantity we allude when we speak of something as being more, or less, hot; forasmuch as it is more or less, perfect in heat. Now this virtual quantity is measured firstly by its source--that is, by the perfection of that form or nature: such is the greatness of spiritual things, just as we speak of great heat on account of its intensity and perfection. And so Augustine says (De Trin. vi, 18) that "in things which are great, but not in bulk, to be greater is to be better," for the more perfect a thing is the better it is.
Secondly, virtual quantity is measured by the effects of the form. Now the first effect of form is being, for everything has being by reason of its form. The second effect is operation, for every agent acts through its form. Consequently virtual quantity is measured both in regard to being and in regard to action: in regard to being, forasmuch as things of a more perfect nature are of longer duration; and in regard to action, forasmuch as things of a more perfect nature are more powerful to act. And so as Augustine (Fulgentius, De Fide ad Petrum i) says: "We understand equality to be in the Father, Son and Holy Ghost, inasmuch as no one of them either precedes in eternity, or excels in greatness, or surpasses in power."
Reply to Objection 2. Where we have equality in respect of virtual quantity, equality includes likeness and something besides, because it excludes excess. For whatever things have a common form may be said to be alike, even if they do not participate in that form equally, just as the air may be said to be like fire in heat; but they cannot be said to be equal if one participates in the form more perfectly than another. And because not only is the same nature in both Father and Son, but also is it in both in perfect equality, therefore we say not only that the Son is like to the Father, in order to exclude the error of Eunomius, but also that He is equal to the Father to exclude the error of Arius.
Reply to Objection 3. Equality and likeness in God may be designated in two ways--namely, by nouns and by verbs. When designated by nouns, equality in the divine persons is mutual, and so is likeness; for the Son is equal and like to the Father, and conversely. This is because the divine essence is not more the Father's than the Son's. Wherefore, just as the Son has the greatness of the Father, and is therefore equal to the Father, so the Father has the greatness of the Son, and is therefore equal to the Son. But in reference to creatures, Dionysius says (Div. Nom. ix): "Equality and likeness are not mutual." For effects are said to be like their causes, inasmuch as they have the form of their causes; but not conversely, for the form is principally in the cause, and secondarily in the effect.
But verbs signify equality with movement. And although movement is not in God, there is something that receives. Since, therefore, the Son receives from the Father, this, namely, that He is equal to the Father, and not conversely, for this reason we say that the Son is equalled to the Father, but not conversely.
Reply to Objection 4. In the divine persons there is nothing for us to consider but the essence which they have in common and the relations in which they are distinct. Now equality implies both --namely, distinction of persons, for nothing can be said to be equal to itself; and unity of essence, since for this reason are the persons equal to one another, that they are of the same greatness and essence. Now it is clear that the relation of a thing to itself is not a real relation. Nor, again, is one relation referred to another by a further relation: for when we say that paternity is opposed to filiation, opposition is not a relation mediating between paternity and filiation. For in both these cases relation would be multiplied indefinitely. Therefore equality and likeness in the divine persons is not a real relation distinct from the personal relations: but in its concept it includes both the relations which distinguish the persons, and the unity of essence. For this reason the Master says (Sent. i, D, xxxi) that in these "it is only the terms that are relative."
Source: Summa Theologica (New Advent)