1620s, "without coherence" (of immaterial or abstract things, especially thought or language), from in- (1) "not, opposite of" + coherent. As "without physical coherence" from 1690s. Related: Incoherently.
word-forming element meaning "not, opposite of, without" (also im-, il-, ir- by assimilation of -n- with following consonant, a tendency which began in later Latin), from Latin in- "not," cognate with Greek an-, Old English un-, all from PIE root *ne- "not."
In Old French and Middle English often en-, but most of these forms have not survived in Modern English, and the few that do (enemy, for instance) no longer are felt as negative. The rule of thumb in English has been to use in- with obviously Latin elements, un- with native or nativized ones.
1550s, "harmonious;" 1570s, "sticking together," also "connected, consistent" (of speech, thought, etc.), from French cohérent (16c.), from Latin cohaerentem (nominative cohaerens), present participle of cohaerere "cohere," from assimilated form of com "together" (see co-) + haerere "to adhere, stick" (see hesitation).