1640s, from French coup d'étate, literally "stroke of the state" (see coup). Technically any sudden, decisive political act, especially an important and unexpected change in the form and methods of a government, but in 20c. popularly restricted to the overthrow of a government.
early 15c., crise, crisis, "decisive point in the progress of a disease," also "vitally important or decisive state of things, point at which change must come, for better or worse," from Latinized form of Greek krisis "turning point in a disease, that change which indicates recovery or death" (used as such by Hippocrates and Galen), literally "judgment, result of a trial, selection," from krinein "to separate, decide, judge," from PIE root *krei- "to sieve," thus "discriminate, distinguish."
Transferred non-medical sense is 1620s in English. A German term for "mid-life crisis" is Torschlusspanik, literally "shut-door-panic," fear of being on the wrong side of a closing gate.
1706, "cross-shaped, having the form of an X," from French crucial, a medical term for ligaments of the interior of the knee-joint (which cross each other), from Latin crux (genitive crucis) "cross" (see crux).
The meaning "decisive, critical, finally disproving one of two alternative suppositions" (1830) is extended from a logical term, Instantias Crucis, adopted by Francis Bacon (1620); the notion is of cross fingerboard signposts at forking roads, thus a requirement to choose.
1610s, "occurring at the end," from French conclusif, from Late Latin conclusivus, from conclus-, past participle stem of Latin concludere "to shut up, enclose," from assimilated form of com "together" (see con-) + -cludere, combining form of claudere "to shut" (see close (v.)). Meaning "definitive, decisive, convincing, being so forcible as not to admit of contradiction" (on the notion of "leading to a logical conclusion," and thus putting an end to debate) is from 1640s. Related: Conclusiveness.