But to say nothing more of words, let us now attend to the thing signified. By person, then, I mean a subsistence in the divine essence—a subsistence which, while related to the other two, is distinguished from them by incommunicable properties. By subsistence, we wish something else to be understood than essence. For if the Word were God simply and had not some property peculiar to Himself, John could not have said correctly that He had always been with God. When he adds immediately after, that the Word was God, He calls us back to the one essence. But because He could not be with God without dwelling in the Father, hence arises that subsistence, which, though connected with the essence by an indissoluble tie, being incapable of separation, yet has a special mark by which it is distinguished from it. Now, I say that each of the three subsistences while related to the others is distinguished by its properties. Here relation is distinctly expressed, because, when God is mentioned simply and indefinitely the name belongs not less to the Son and Spirit than to the Father. But whenever the Father is compared with the Son, the peculiar property of each distinguishes the one from the other. Again, whatever is proper to each I affirm to be incommunicable, because nothing can apply or be transferred to the Son that is attributed to the Father as a mark of distinction. I have no objections to adopt the definition of Tertullian, provided it is properly understood, “that there is in God a certain arrangement or economy, which makes no change on the unity of essence.” 

God The Creator (Book 1 of the Institutes) - John Calvin