"unthinkable, inconceivable," 1520s, from Late Latin incogitabilis "unthinking; unthinkable," from in- "not" (see in- (1)) + cogitabilis "thinkable, conceivable," from stem of cogitare "to think" (see cogitation).
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.
c. 1200, cogitacioun, "thought, idea, notion, that which is thought out; act of thinking, earnest reflection," from Old French cogitacion "thought, consideration, reflection," from Latin cogitationem (nominative cogitatio), noun of action from past participle stem of cogitare "to think, reflect, consider, turn over in the mind," which is apparently a contraction of co-agitare, from assimilated form of com "together" (see co-) + agitare, here in a sense of "to turn over in the mind," literally "to put in constant motion, drive, impel," frequentative of agere "to move, drive" (from PIE root *ag- "to drive, draw out or forth, move").
<a href="https://www.etymonline.com/word/incogitable">Etymology of incogitable by etymonline</a>
Harper, D. (n.d.). Etymology of incogitable. Online Etymology Dictionary. Retrieved $(datetime), from https://www.etymonline.com/word/incogitable