Tertullian’s Formula was never used for much of the 4th century Christological debates, surprisingly enough. It was, however, redefined by Damasus in the late 4th century to mesh with the Eastern viewpoint. Personally, I like Tertullian in the Greek.
“tres Personae, una Substantia” – Three Persons, One Substance
For the Father is the entire substantia, but the Son is a derivation and portion of the whole. Against Praxeas 9
I wonder if you can make the argument that had Tertullian written in Greek, at least this formula, what difference it would have made in later debates, and even the debates today?
God, who made the world out of nothing through his Son, the Word, has corporeity though he is a spirit (De praescriptione, vii.; Adv. Praxeam, vii.). In the statement of the Trinity, Tertullian was a forerunner of the Nicene doctrine, approaching the subject from the standpoint of the Logos doctrine, though he did not fully state the immanent Trinity. In his treatise against Praxeas, who taught patripassianism in Rome, he used the words, ” Trinity and economy, persons and substance.” The Son is distinct from the Father, and the Spirit from both the Father and the Son (Adv. Praxeam, xxv.). “These three are one substance, not one person; and it is said, ‘I and my Father are one’ in respect not of the singularity of number but the unity of the substance.” The very names “Father” and “Son” indicate the distinction of personality. The Father is one, the Son is one, and the Spirit is one (Adv. Praxeam, ix.). The question whether the Son was coeternal with the Father Tertullian does not set forth in full clearness; and though he did not fully state the doctrine of the immanence of the Trinity, he went a long distance in the way of approach to it (B. B. Warfield, in Princeton Theological Review, 1906, pp. 56, 159).
In Praxeas 8.5-7, Tertullian uses the image of a Spring (Father), River (Son) and Canal (Spirit) as a typology of the Godhead. There is but one divine substance (the water) and the Son and Spirit are emanations from it.
Although it seems that many wish to act as if Tertullian only taught their version of the trinity, The Catholic Encyclopedia admits this about Tertullian’s understanding of the Godhead:
He says that from all eternity there was reason (ratio) in God, and in reason the Word (Sermo), not distinct from God, but in vulva cordis. For the purpose of creation the Word received a perfect birth as Son. There was a time when there was no Son and no sin, when God was neither Father nor Judge. In his Christology Tertullian has had no Greek influence, and is purely Roman. Like most Latin Fathers he speaks not of two Natures but of two Substances in one Person, united without confusion, and distinct in their operations (Chapman J. Transcribed by Lucy Tobin. Tertullian. The Catholic Encyclopedia, Volume XIV. Copyright © 1912 by Robert Appleton Company. Online Edition Copyright © 2003 by K. Knight. Nihil Obstat, July 1, 1912. Remy Lafort, S.T.D., Censor. Imprimatur. +John Cardinal Farley, Archbishop of New York).
While Tertullian himself also wrote:
The simple…are constantly throwing out against us that we are preachers of two gods and three gods…
Now, from this one passage of the epistle of the inspired apostle, we have been already able to show that the Father and the Son are two separate Persons, not only by the mention of their separate names as Father and the Son, but also by the fact that He who delivered up the kingdom, and He to whom it is delivered up — and in like manner, He who subjected (all things), and He to whom they were subjected — must necessarily be two different Beings. But since they will have the Two to be but One, so that the Father shall be deemed to be the same as the Son…For the Father is the entire substance, but the Son is a derivation and portion of the whole, as He Himself acknowledges: “My Father is greater than I.” In the Psalm His inferiority is described as being “a little lower than the angels.” Thus the Father is distinct from the Son, being greater than the Son (Tertullian. Against Praxeas, Chapters 3,4-5,9. Translated by Peter Holmes. Excerpted from Ante-Nicene Fathers, Volume 3. Edited by Alexander Roberts and James Donaldson. American Edition, 1885. Online Edition Copyright © 2004 by K. Knight).
“For the word ‘person’ seems to be borrowed from a different source, namely from the masks (personae) which in comedies and tragedies used to represent the people concerned…The Greeks, too, call these masks ‘prosopa‘ from the fact that they are placed over the face and conceal the countenance in front of the eyes: παρα του προς τους ωπας τιθεσθαι (from being put up against the face). But since, as we have said, it was by the masks they put on that actors respresented the individual concerned in a tragedy or comedy – Hecuba or Medea or Simo or Chremes, – so also of all other men who could be clearly recognized by their appearance the Latins used the name ‘persona‘, the Greeks ‘prosopa‘.” (Anicius Manlius Severinus Boethius, Contra Eutychen, III).