Etymology
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Words related to *kad-

chance (n.)

c. 1300, "something that takes place, what happens, an occurrence" (good or bad, but more often bad), especially one that is unexpected, unforeseen, or beyond human control, also "one's luck, lot, or fortune," good or bad, in a positive sense "opportunity, favorable contingency;" also "contingent or unexpected event, something that may or may not come about or be realized," from Old French cheance "accident, chance, fortune, luck, situation, the falling of dice" (12c., Modern French chance), from Vulgar Latin *cadentia "that which falls out," a term used in dice, from neuter plural of Latin cadens, present participle of cadere "to fall," from PIE root *kad- "to fall."

In English frequently in plural, chances. The word's notions of "opportunity" and "randomness" are as old as the record of it in English and now all but crowd out its original notion of "mere occurrence." Meaning "fortuity, absence of any cause why an event should happen or turn out as it does, variability viewed as a real agent" is from c. 1400.

Chance is equivalent to the mathematical concept of probability, which is a precisely measurable factor enabling the accurate prediction of average outcomes over long runs of random events — the longer the run, the more accurate the predictions. Luck is at best a platitude and at worst a superstition. [David Partlett, "A History of Card Games"]

Main chance "probability that offers greatest advantage," hence "thing of most importance" is from 1570s. Mathematical sense "probability, likelihood of a certain outcome" is from 1778, hence the odds-making sense "balanced probability of gain or loss." To stand a chance (or not) is from 1796. To take (one's) chances "accept what happens" (early 14c.) is from the old, neutral sense; to take a chance/take chances is originally (by 1814) "participate in a raffle or lottery or game;" extended sense of "take a risk" is by 1826.

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cheat (v.)

mid-15c., "to escheat, to seize as an escheat," a shortening of Old French escheat, legal term for revision of property to the state when the owner dies without heirs, literally "that which falls to one," past participle of escheoir "happen, befall, occur, take place; fall due; lapse (legally)," from Late Latin *excadere "fall away, fall out," from Latin ex- "out" (see ex-) + cadere "to fall" (from PIE root *kad- "to fall").

Also compare escheat. The royal officers who had charge of  escheats evidently had a reputation for unscrupulousness, and the meaning of the verb evolved through "confiscate" (mid-15c.) to "deprive unfairly" (1580s), to "deceive, impose upon, trick" (1630s). Intransitive sense "act dishonestly, practice fraud or trickery" is from 1630s. To cheat on (someone) "be sexually unfaithful" is attested by 1934. Related: Cheated; cheating.

chute (n.1)

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).

coincide (v.)

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.

decadence (n.)

1540s, "deteriorated condition, decay," from French décadence (early 15c.), from Medieval Latin decadentia "decay," from decadentem (nominative decadens) "decaying," present participle of decadere "to decay," from Latin de- "apart, down" (see de-) + cadere "to fall" (from PIE root *kad- "to fall"). Meaning "process of falling away from a better or more vital state" is from 1620s. Used of periods in art since 1852, on French model.

decay (v.)

late 15c., "to decrease," also "to decline, deteriorate, lose strength or excellence," from Anglo-French decair, Old North French decair (Old French decheoir, 12c., Modern French déchoir) "to fall, set (of the sun), weaken, decline, decay," from Vulgar Latin *decadere "to fall off," from de "off" (see de-) + Latin cadere "to fall" (from PIE root *kad- "to fall").

Transitive sense of "cause to deteriorate, cause to become unsound or impaired" is from 1530s. Sense of "decompose, rot" is from 1570s. Related: Decayed; decaying.

deciduous (adj.)

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.

escheat (n.)
the reverting of land to a king or lord in certain cases, early 14c., from Anglo-French eschete (late 13c.), Old French eschete "succession, inheritance," literally "that which falls to one," noun use of fem. past participle of escheoir "happen, befall, occur, take place; fall due; lapse (legally)," from Late Latin *excadere "to fall out," from Latin ex "out, away" (see ex-) + cadere "to fall" (from PIE root *kad- "to fall"). As a verb, from late 14c. Related: Escheated; escheating. Late Latin *excadere represents a restored form of excidere, which yielded excise.
incident (n.)
early 15c., "something which occurs casually in connection with something else," from Old French incident (13c.), and directly from Latin incidentem (nominative incidens), present participle of incidere "to fall in, fall, find the way; light upon, fall in with; fall upon, occur; happen, befall," from in- "on" (from PIE root *en "in") + -cidere, combining form of cadere "to fall" (from PIE root *kad- "to fall"). Broader sense of "an occurrence viewed as a separate circumstance" is from mid-15c. Euphemistic meaning "event that might trigger a crisis or political unrest" first attested 1913.
occasion (n.)

late 14c., occasioun, "opportunity; grounds for action or feeling; state of affairs that makes something else possible; a happening, occurrence leading to some result," from Old French ochaison, ocasion "cause, reason, excuse, pretext; opportunity" (13c.) or directly from Latin occasionem (nominative occasio) "opportunity, appropriate time," in Late Latin "cause," from occasum, occasus, past participle of occidere "fall down, go down," from ob "down, away" (see ob-) + -cidere, combining form of cadere "to fall" (from PIE root *kad- "to fall"). The notion is of a "falling together," or juncture, of circumstances. The sense of "the time or a time at which something happens" is from 1560s.

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