The Trinity is One. We do not confess three Gods, but one God in three persons, the “consubstantial Trinity”. The divine persons do not share the one divinity among themselves but each of them is God whole and entire: “The Father is that which the Son is, the Son that which the Father is, the Father and the Son that which the Holy Spirit is, i.e. by nature one God.”In the words of the Fourth Lateran Council (1215), “Each of the persons is that supreme reality, viz., the divine substance, essence or nature.”
The divine persons are really distinct from one another. “God is one but not solitary.” “Father”, “Son”, “Holy Spirit” are not simply names designating modalities of the divine being, for they are really distinct from one another: “He is not the Father who is the Son, nor is the Son he who is the Father, nor is the Holy Spirit he who is the Father or the Son.” They are distinct from one another in their relations of origin: “It is the Father who generates, the Son who is begotten, and the Holy Spirit who proceeds.” The divine Unity is Triune.
The divine persons are relative to one another. Because it does not divide the divine unity, the real distinction of the persons from one another resides solely in the relationships which relate them to one another: “In the relational names of the persons the Father is related to the Son, the Son to the Father, and the Holy Spirit to both. While they are called three persons in view of theirrelations, we believe in one nature or substance.” Indeed “everything (in them) is one where there is no opposition of relationship.” “Because of that unity the Father is wholly in the Son andwholly in the Holy Spirit; the Son is wholly in the Father and wholly in the Holy Spirit; the Holy Spirit is wholly in the Father and wholly in the Son.”
St. Gregory of Nazianzus, also called “the Theologian”, entrusts this summary of Trinitarian faith to the catechumens of Constantinople:
Above all guard for me this great deposit of faith for which I live and fight, which I want to take with me as a companion, and which makes me bear all evils and despise all pleasures: I mean the profession of faith in the Father and the Son and the Holy Spirit. I entrust it to you today. By it I am soon going to plunge you into water and raise you up from it. I give it to you as the companion and patron of your whole life. I give you but one divinity and power, existing one in three, and containing the three in a distinct way. Divinity without disparity of substance or nature, without superior degree that raises up or inferior degree that casts down. . . the infinite co-naturality of three infinites. Each person considered in himself is entirely God. . . the three considered together. . . I have not even begun to think of unity when the Trinity bathes me in its splendour. I have not even begun to think of the Trinity when unity grasps me. .
From the Catechism of the Catholic Church 253-256