John Calvin on the Distinction of Persons in the Trinity

"By person, then, I mean a subsistence [a state of existence] in the divine essence [inward nature]- a subsistence which, while related to the other two [that is, the other two persons of the Trinity], is distinguished from them by incommunicable properties.  By subsistence we wish something else to be understood than essence.  For if the Word [Jesus] 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, the 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 own properties.  Here relation is distinctly expressed, because, when God is mentioned simply and indefinitely the same 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 [incapable of being shared], because nothing can apply or be transferred to the Son which 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.' -Tertullian, Adversus Praxeam" (John Calvin, Institutes of the Christian Religion, 1.13.6).