1560s, "exactly corresponding, having the same nature or character;" 1590s, "happening at the same time, concurrent," from French coincident, from coincider,from Medieval Latin coincidere, 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").
1725, American English, "fall of water" (earlier shoot, 1610s), from French chute "fall," from Old French cheoite "a fall," fem. past participle of cheoir "to fall," from Latin cadere"to fall," from PIE root *kad- "to fall." Meaning "inclined tube, trough" is from 1804; that of "narrow passage for cattle, etc." first recorded 1871. In North America, absorbing some senses of similar-sounding shoot (n.1).
"relapsed criminal," 1863, from French legal term récidiviste (by 1847), from récidiver "to fall back, relapse," from Medieval Latin recidivare "to relapse into sin," from Latin recidivus "falling back," from recidere "fall back," from re- "back, again" (see re-) + combining form of cadere "to fall" (from PIE root *kad- "to fall"). As an adjective by 1883.
"reproductive body in flowerless plants corresponding to the seeds of flowering ones," 1836, from Modern Latin spora, from Greek spora "a seed, a sowing, seed-time," related to sporas "scattered, dispersed," sporos "a sowing," from PIE *spor-, variant of root *sper- "to spread, sow" (see sparse).