The Godhead versus the Trinity
The current Orthodox Christian belief of the Trinity, three gods-in-one, came about due to the concern of many Christians and Jewish-Christians, that the early Christian doctrine of plurality of the Godhead sounded like polytheism. Many fought the idea, particularly Bishop Athanasius, who changed the concept to fit his belief.
Athanasius (4th century) essentially believed what the Greek Orthodox Church has believed for centuries. A christian may become "deified" in the sense that he "participates in" God's nature, but that doesn't mean that hewill have the same nature as God. According to Davies, Athanasius drew a distinction between the deity of men, who can only be divine by participation in the "Divine Substance", and that of the Godhead, who ARE the "Divine Substance". (Davies, _The Early Christian Church_, p. 192). "Thus He is Son of God by nature, and we by grace." Athanasius, in Kelly,_Early Christian Doctrines_.
This may seem strange to Latter-day Saints unless we remember that the Nicene doctrine of the Trinity, which Athanasius fought for his whole life, defines the Godhead as an eternal, indivisible, unchangeable "substance", analogous to one of Plato's "Forms". Thus, the "Divine Substance" CANNOT be added to, and deified Christians have to settle for "participating".
The doctrine of deification, however, goes back much farther than the Council of Nicea and any Christian historian will tell you that none of the Christians we know of believed anything remotely similar to the doctrine behind the Nicene Creed before about 200 A.D., and even then there were essential differences.
So how did the pre-Nicene Fathers view deification?
Several of them directly repudiated Athanasius' distinction between deification by nature and by grace. For example, Clement of Alexandria (late second and early third centuries) wrote, "Heraclitus, then, rightly said, 'Men are gods, and gods are men.'" (Clement of Alexandria, The Instructor 3:1, in _The Ante-Nicene Fathers_ 2:271). Origen (third century) taught that we "will be wholly God...." (Origen, De Principiis 3:6:3, in ANF 4:345.) And he insisted that anyone who "participates" in anything is of one nature with it! "Every one who participates in anything, is unquestionably of one essence and nature with him who is partaker of the same thing." (Origen, De Principiis 4:1:36, in ANF 4:381.)
Here's a killer from Lactantius (third century): "In the same strain Lactantius affirms that the chaste man will become 'identical in all respects with God.'" (Angus, _The Mystery-Religions_, pp. 106-107.)
In fact, during the Council of Nicea, there were actually THREE doctrines on the Godhead that were debated, but only two came to the forefront. The two better known doctrines were of Athanasius: trinitarian three-in-one god of spirit, and that of Arius: all members of Godhead are separate beings, and since there is only one God, Christ can't be a god.
The third belief was known as Origenism, after the great Christian scholar, Origen. His belief was that of three separate Gods in the Godhead, with God the Father as the supreme God over the other two members of the Godhead. He taught that the unity of Father and Son resides in the unity of will; it is in virtue of the "one will" that the Son says, "I and the Father are one." The Christian author, Tertullian, also taught such a Godhead, as well.
The great Church historian, Eusebius, also believed in Origenism, but when Athanasius took control of the Council of Nicea (where only 300 bishops out of thousands were invited, and most were Athanasius' allies) and used excommunication and exile to enforce their Trinitarian belief; many were forced to go along.
Arius was excommunicated and exiled for refusing to accept the Athanasius creed, and Eusebius was exiled for reluctantly going along with the others.
So, we see that the LDS belief in a separate beings in the Godhead, and that man can become as God is, are ancient beliefs held by the early Christian Church. Any other belief, including those beliefs held by most Christian churches today, seem to be interpolations placed upon the Christian faith by Athanasius and others who refused to believe in the early teachings of the Church.