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].
1660s, from French toxique and directly from Late Latin toxicus "poisoned," from Latin toxicum "poison," from Greek toxikon (pharmakon) "(poison) for use on arrows," from toxikon, neuter of toxikos "pertaining to arrows or archery," and thus to a bow, from toxon "bow," probably from a Scythian word that also was borrowed into Latin as taxus "yew." Watkins suggests a possible source in Iranian taxša- "bow," from PIE *tekw- "to run, flee." As a noun from 1890. Toxic waste is by 1888 in medicine, "toxin;" by 1955 as "chemical or radioactive waste."