non-Euclidean

a prefix used freely in English and meaning "not, lack of," or "sham," giving a negative sense to any word, 14c., from Anglo-French noun-, from Old French non-, from Latin non "not, by no means, not at all, not a," from Old Latin noenum "not one" (*ne oinom, from PIE root *ne- "not" + PIE root *oi-no- "one, unique"). In some cases perhaps from Middle English non "not" (adj.), from Old English nan (see not). "It differs from un- in that it denotes mere negation or absence of the thing or quality, while un- often denotes the opposite of the thing or quality" [Century Dictionary].

1650s, "of or pertaining to Euclid" (Greek Eukleides), c. 300 B.C.E. geometer of Alexandria. Now often used in contrast to alternative models based on rejection of some of his axioms. His name in Greek means "renowned, glorious," from eu "well" (see eu-) + kleos "fame" (see Clio).