1680s, with reference to leaves, petals, teeth, etc., "falling off at a certain stage of existence," from Latin deciduus "that which falls down," from decidere "to fall off, fall down," from de "down" (see de-) + combining form of cadere "to fall," from PIE root *kad- "to fall." Of trees and bushes, "losing foliage every year" (opposed to evergreen), from 1778. The Latin adjective was used of shooting stars and testicles, but it seems not to have been used of trees or leaves (the phenomenon in Italy seems to be restricted to the mountain regions). Related: Deciduousness.
1705, "be identical in substance or nature;" 1715, "occupy the same space, agree in position," from Medieval Latin coincidere (used in astrology), literally "to fall upon together," from assimilated form of Latin com "with, together" (see com-) + incidere "to fall upon" (from in- "upon" + combining form of cadere "to fall," from PIE root *kad- "to fall"). From 1809 as "occur at the same time." Related: Coincided; coinciding. Latin coincidere was used as a verb in English from 1640s.
It forms all or part of: accident; cadaver; cadence; caducous; cascade; case (n.1); casual; casualty; casuist; casus belli; chance; cheat; chute (n.1); coincide; decadence; decay; deciduous; escheat; incident; occasion; occident; recidivist.
It is the hypothetical source of/evidence for its existence is provided by: Sanskrit sad- "to fall down;" Latin casus "a chance, occasion, opportunity; accident, mishap," literally "a falling," cadere "to fall, sink, settle down, decline, perish;" Armenian chacnum "to fall, become low;" perhaps also Middle Irish casar "hail, lightning."