Today, whenever one hears the term “Trinity,” one immediately thinks of the post-biblical formulation that the persons of the Father, Son, and Spirit are one in “essence”; furthermore, it contains later theological baggage such as the Hypostatic Union and communicatio idiomatum, etc. As a result of this, some have read the early Patristic writers rather anachronistically. For instance, Tertullian of Carthage used the term trinitas to describe the relationship of the Father, Son, and Spirit. Some rather ignorant Trinitarian apologists, both historically and in modern times, have latched onto this term, citing it as evidence, if not “proof,” that Tertullian was a “Trinitarian” in the modern understanding thereof. However, as Dr. Dale Tuggy and others have shown, Tertullian used the term trinitas to denote a “triad,” with this triad being composed of the “one true God,” the Son, and the Spirit—for Tertullian, only the person of the Father was the “one true God.” Indeed, Tertullian (as well as Origen) used the term “second God” to denote Jesus. Furthermore, when one reads Tertullian’s writings, and not just selective “proof-texts” thereof, one finds that he was most definitely not a Trinitarian; for instance, contra Trinitarian theology, Tertullian taught and believed:
That the person of the Father is the only true God (Answer to the Jews ch. 1)
That the true God was the “common Father” (the person of the Father [Apology ch. 39])
That Jesus did not exist eternally (Against Hermogenes ch 3)
That the Son’s relationship to the Father can be understood as that of a beam to the sun, a rather “Arian” understanding of the relationship between Jesus and the Father (Against Praxeas 8)
The Father is older than the Son (Against Praxeas 9)
Interestingly, early Latter-day Saints used the term “Trinity” in a positive manner to describe the LDS belief in “the Godhead” wherein the three persons, while being truly separate persons from one another, are still united in a powerful way through “perichorsis”; as Blake Ostler described it in a comment responding to Ben Witherington III:
The Father, Son and Holy Ghost are distinct but decidedly not separate. The Father, Son and Holy Ghost are one in the same sense that Social Trinitarians have suggested — they are united in perichoretic unity of spirit and purpose, in shared omniscience and glory. There is only one sovereign of the universe in Mormon thought — the Trinity or Godhead of three divine persons united as one in unity of thought, purpose, knowledge, power, act and glory. It is true that Mormons deny metaphysical simplicity, but so have many that you undoubtedly consider Christian including Alvin and Cornelius Plantinga.
Here are some examples from early LDS sources:
Journal of Discourses, Vol. 6, p.95
With regard to this particular point, I will say that you shall judge the matter and be my witnesses. Have we not learned enough with regard to the character of the Father, Son, and Holy Ghost, to at once believe, admit, and affirm that the Holy Ghost always has and always will operate precisely according to the suggestion of the Father? Not a desire, act, wish, or thought does the Holy Ghost indulge in contrary to that which is dictated by the Father. We all sense this in a degree, because it has always been taught to us. It is taught in the Bible, in the revelations given through Joseph, and in the preaching by the Elders of Israel. It is our tradition, education, and experience in the kingdom of God. The Holy Ghost, we believe, is one of the characters that form the Trinity, or the Godhead. Not one person in three, nor three persons in one; but the Father, Son, and Holy Ghost are one in essence, as the hearts of three men who are united in all things. He is one of the three characters we believe in, whose office it is to administer to those of the human family who love the truth. I have stated that they are one, as the hearts of three men might be one. Lest you should mistake me, I will say that I do not wish you to understand that the Holy Ghost is a personage having a tabernacle, like the Father and the Son; but he is God's messenger that diffuses his influence through all the works of the Almighty. (Brigham Young, November 29, 1857)
Journal of Discourses Vol. 14, p.92
Well, where is the harm in this I wish the world, or any scientific men in it, would detail the error in a people being one; and I will go still further, and say, being one in the Lord, as we are commanded and recommended to be. Even in the wicked world, where there is so much confusion, where is the good that arises from contention and opposition? I have not seen it, and, as I have said, I cannot see the point. But here in Utah that "one-man power" is such a terrible thing. I would ask: Who is that man, and where is the power, and what is the power? It is the power of him who brought us into existence, and he is the MAN who wields it, and he is the Father of us all, and the God and Father of our Lord Jesus Christ. He is the Maker and Possessor of this earth that we inhabit, and is the Producer of all things upon it. Is he one? Yes. Is his trinity one? Yes. Is his organization one? Are the heavens one? Yes. (Brigham Young, April 8, 1871)
Joseph F. Smith, Gospel Doctrine Ch.2, p.37
Even in the five distinctive and characteristic topics generally considered by commentators original in the teachings of Jesus, we find little if anything new, except the enlargement. These are named as, the Fatherhood of God, the Kingdom of God; subjects or members of the Kingdom; the Messiah, the Holy Ghost; and the Trinity of God.
Joseph F. Smith, Gospel Doctrine Ch.5, p.73
HOLY GHOST, HOLY SPIRIT, COMFORTER. The Holy Ghost, who is a member of the Trinity in the Godhead, has not a body of flesh and bones, like the Father and the Son, but is a personage of Spirit. (Doc. and Cov., Sec. 130:22.)
When discussing theology or any related field, one should make sure that they do not hoist an anachronistic meaning onto a term; the term “Trinity” is one such term that should be defined from the get-go.