1670s, "exist at the same time as another," from co- + exist. Of political/economic systems, "to exist peaceably at the same time" (especially with reference to communism and the West) from 1931. Related: Coexisted; coexisting.
in Latin, the form of com- "together, with" in compounds with stems beginning in vowels, h-, and gn-; see com-. Taken in English from 17c. as a living prefix meaning "together, mutually, in common," and used promiscuously with native words (co-worker) and Latin-derived words not beginning with vowels (codependent), including some already having it (co-conspirator).
"to have actual being of any kind, actually be at a certain moment or throughout a certain period of time," c. 1600, from French exister (17c.), from Latin existere/exsistere "to step out, stand forth, emerge, appear; exist, be" (see existence). "The late appearance of the word is remarkable" [OED]. Middle English often used ibēn, ibeon (based on be) for "to exist." Related: Existed; existing.