"constant, uniform, unchanging," early 15c., from Old French invariable (14c.) and directly from Medieval Latin invariabilis, from in- "not, opposite of" (see in- (1)) + variabilis "changeable" (see variable). Related: Invariably.
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.
late 14c., of persons, "apt to change, fickle," from Old French variable "various, changeable, fickle," from Late Latin variabilis "changeable," from variare "to change" (see vary). Of weather, seasons, etc., attested from late 15c.; of stars, from 1788.