Etymology
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Words related to *kad-

accident (n.)

late 14c., "an occurrence, incident, event; what comes by chance," from Old French accident (12c.), from Latin accidentem (nominative accidens) "an occurrence; chance; misfortune," noun use of present participle of accidere "happen, fall out, fall upon," from ad "to" (see ad-) + combining form of cadere "to fall" (from PIE root *kad- "to fall").

The sense has had a tendency since Latin to extend from "something that happens, an event" to "a mishap, an undesirable event." Latin si quid cui accidat, "if anything should happen to one," was a euphemism for "if one should die." In Middle English the word is met usually in theology (in reference to the material qualities in the sacramental bread and wine), medicine ("something out of the ordinary, disease, injury"), or philosophy ("non-essential characteristic of a thing").

From late 15c. as "the operations of chance." Meaning "an unplanned child" is attested by 1932. Accident-prone is from 1926.

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cadaver (n.)
"a dead body, a corpse," late 14c., from Latin cadaver "dead body (of men or animals)," probably from a perfective participle of cadere "to fall, sink, settle down, decline, perish," from PIE root *kad- "to fall." Compare Greek ptoma "dead body," literally "a fall" (see ptomaine); poetic English the fallen "those who have died in battle."
cadence (n.)

late 14c., "flow of rhythm in prose or verse," from French cadence, from Old Italian cadenza "conclusion of a movement in music," literally "a falling," from Vulgar Latin *cadentia, from neuter plural of Latin cadens, present participle of cadere "to fall" (from PIE root *kad- "to fall"). A doublet of chance (n.).

The notion is of a "fall" in the voice in reading aloud or speaking, as at the end of a sentence, also the rising and falling in modulation of tones in reciting. Later (1590s) extended to music, in reference to a sequence of chords expressing conclusion at the end of a phrase and resolving to the key in which the piece was written. Also the measure or beat of any rhythmic movement (c. 1600). In 16c., sometimes used literally for "an act of falling." Related: Cadential.

caducous (adj.)
"having a tendency to fall or decay," 1797, in botany, from Latin caducus "falling, fallen, fleeting," from cadere "to fall, decline, perish," from PIE root *kad- "to fall." Related: Caducity.
cascade (n.)
"a fall or flow of water over a cliff, a waterfall," 1640s, from French cascade (17c.), from Italian cascata "waterfall," from cascare "to fall," from Vulgar Latin *casicare, frequentative of Latin casum, casus, past participle of cadere "to fall" (from PIE root *kad- "to fall").
case (n.1)

early 13c., "what befalls one; state of affairs," from Old French cas "an event, happening, situation, quarrel, trial," from Latin casus "a chance, occasion, opportunity; accident, mishap," literally "a falling," from cas-, past-participle stem of cadere "to fall, sink, settle down, decline, perish" (used widely: of the setting of heavenly bodies, the fall of Troy, suicides), from PIE root *kad- "to fall."

The notion is of "that which falls" as "that which happens" (compare befall). From its general nature, the word has taken on widespread extended and transferred meanings. Meaning "instance, example" is from c. 1300. Meaning "actual state of affairs" is from c. 1400. In law, "an instance of litigation" (late 14c.); in medicine, "an instance of a disease" (late 14c.).

The grammatical sense, "one of the forms which make up the inflections of a noun" (late 14c.) also was in Latin, translating Greek ptōsis "declension," literally "a falling." "A noun in the nominative singular ..., or a verb in the present indicative ...,

is conceived as standing straight. Then it falls, or is bent, or

declines into various positions" [Gilbert Murray, "Greek Studies"]

U.S. slang meaning "person" (especially one peculiar or remarkable in any way) is from 1848. Meaning "incident or series of events requiring police investigation" is from 1838. In case "in the event" is recorded from mid-14c. Case-history is from 1879, originally medical; case-study "study of a particular case" is from 1879, originally legal; case-law "law as settled by previous court cases" is from 1861.

casual (adj.)

late 14c., casuel, "subject to or produced by chance," from Old French casuel (15c.), from Late Latin casualis "by chance," from Latin casus "chance, occasion, opportunity; accident, event" (see case (n.1)).

Of persons, in the sense of "not to be depended on, unmethodical," it is attested from 1883 (from the notion of "without regularity," hence "uncertain, unpredictable"); meaning "showing lack of interest" is from 1916. Of clothes, "informal," from 1891. Related: Casually.

casualty (n.)

early 15c., casuelte, caswelte, "chance, accident; incidental charge," from casual (adj.) on model of royalty, penalty, etc. From the earliest use especially of untoward events or misfortunes. Meaning "losses in numbers from a military or other troop" is from late 15c. Meaning "an individual killed, wounded, or lost in battle" is from 1844. Casuality had some currency 16c.-17c. in the sense "chance, a chance occurrence," especially an unfortunate one, but now is obsolete.

casuist (n.)

c. 1600, "one who studies and resolves cases of conscience," from French casuiste (17c.) or Spanish casuista (the French word also might be from Spanish), Italian casista, all from Latin casus "case" (see case (n.1)) in its Medieval Latin sense "case of conscience." Often since 17c. in a sinister or contemptuous sense "over-subtle reasoner, sophist." Related: Casuistic; casuistical; casuistically.

casus belli (n.)

an act justifying war, 1840, from Latin casus "case" (see case (n.1)) + belli, genitive of bellum "war" (see bellicose).