mid-14c., "of the doctrines of the ancient Church" (before the East/West schism), literally "universally accepted," from French catholique, from Church Latin catholicus "universal, general," from Greek katholikos, from phrase kath' holou "on the whole, in general," from kata "about" + genitive of holos "whole" (from PIE root *sol- "whole, well-kept").
Medieval Latin catholicus was practically synonymous with Christian and meant "constituting or conforming to the church, its faith and organization" (as opposed to local sects or heresies). With capital C-, applied by Protestants to the Church in Rome c. 1554, after the Reformation began. General sense of "embracing all, universal" in English is from 1550s. Meaning "not narrow-minded or bigoted" is from 1580s. The Latin word was rendered in Old English as eallgeleaflic.
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].
also noncom, by 1817, short for non-commissioned(officer).
The "non-coms" — non-commissioned, meaning, not non compos; though evil-minded high privates declare it might well mean that — have assigned to them an upper cabin, with staterooms, over the quarters of the officers, in the after-part of the ship. [James K. Hosmer, "The Color-Guard," Boston, 1864]
"lack of access," 1745, from non- + access (n.). Especially in law, "impossibility of access for sexual intercourse," as when a husband is out of the country in military service or at sea longer than the time of gestation of a child. "[W]hen a husband could not, in the course of nature, by reason of his absence, have been the father of his wife's child, the child is a bastard" ["Wharton's Law Lexicon," London, 1883].