We may now readily perceive the difference between the Essence of God, and the Persons, subsisting in the divine essence. By the term, Essence, we are to understand, in reference to this subject, that which the eternal Father, Son, and Holy Spirit are considered, and declared to be, singly and absolutely in themselves, and which is common to the three. By the term, Person, however, we are to understand that which the three persons of the Godhead are considered and declared to be individually and relatively, or as compared with each other, and which they are according to the mode of existence peculiar to each. Or, we may define Essence as the very being of God—the very, eternal, and only Deity—whilst the term Person refers to the mode, or manner, in which the being of God, or the divine essence, subsists in each of these three. God the Father is that Being who is of himself, and not from another. The Son is that self-same Being, or essence, not of himself, but of the Father. The Holy Spirit is in like manner the self-same Being, not of himself, but from the Father and the Son. Thus the Being, or divine essence, of the there persons of the Godhead is one and the same in number. But to be of himself, or from another—from one, or from two; that is, to have this one divine essence of himself, or to have it communicated from another—from one or from two, expresses the mode of existence which is three-fold and distinct; to wit, to be of himself, to be begotten or generated, and to proceed; and hence, the three persons which are expressed by the term, Trinity.
Zacharias Ursinus, The Commentary of Dr. Zacharias Ursinus on the Heidelberg Catechism, trans. G. W. Williard (Cincinnati, OH: Elm Street Printing Company, 1888), 130. (modified)