early 15c., from Old French indivisible (14c.) and directly from Late Latin indivisibilis "not divisible," from in- "not, opposite of" (see in- (1)) + divisibilis (see divisible). Related: Indivisibly.
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.
"capable of being separated or disunited," early 15c., from Late Latin divisibilis "divisible," from divis-, past-participle stem of Latin dividere "to divide" (see divide (v.)). Related: Divisibility.