Theandrosic Vocabulary
"Ho logos egeneto sarx." (Greek for "The word became flesh".)
John's Gospel 1:14
The fact or beginning of God's human life has usually been called "the incarnation" (from Latin incarnatio) in English (and similarly in other Western European languages) and ensarkosis (Greek) in the East (both meaning "in flesh" or "into flesh"), but this is misleading because it suggests an inhabiting of flesh, a being in flesh (where "flesh" means, roughly, "animal life").
For God to become a man does not mean beginning to inhabit a human body (which he has always done, being always involved in all his creatures), but to be a human body, to become fully human as well as fully divine. He does not enter flesh, but becomes flesh.
So it is better to speak of "carnification" (from Latin carnificatio, "being made flesh") or sarkosis (Greek "becoming flesh").
However, we can do better, for two reasons.
Human life is more than flesh. It may sometimes be worth focussing on flesh to clarify what is being asserted (which to some might seem shocking), as the above quotation does, but it is not a complete picture.
And it may be misleading, for it may suggest a hostility to God's purposes, and God's original and unchanging purpose had no reference to hostility (whatever may have occured later).
So it is better to speak of anthroposis (Greek for "becoming a human").
And (more fully) theanthroposis ("God becoming a human").
And more precisely, theandrosis ("God becoming a man").
The re-founding of Humanity, which is what theandrosis achieves rather than what it is, is traditionally called "recapitulation" (from the Latin for "re-heading"). This sees the man who is God as a second "head" of Humanity, the first being "Adam" (the Hebrew word for "man"), that is, mere human nature.
Whatever we call it, none of this is to be confused with the supposed "reincarnation" (Greek metempsychosis, Indian punarjanman or samsara) in which human souls are supposed to flit between bodies.