Etymology
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befall (v.)
Old English befeallan "to deprive of; fall to, occur to, be assigned to," from be- "by, about" + feallan (see fall). Compare Old Frisian bifalla, Old Saxon, Old High German bifallan, German befallen. Intransitive sense of "to happen, come to pass" is from c. 1300. Related: Befell; befalling.
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misbefall (v.)

mid-13c., of events, "to turn out badly;" early 15c., of persons, "suffer harm, come to grief;" from mis- (1) "badly, wrongly" + befall. Related: Misbefell; misbefalling.

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happen (v.)
late 14c., happenen, "to come to pass, occur, come about, be the case," literally "occur by hap, have the (good or bad) fortune (to do, be, etc.);" extension (with verb-formative -n) of the more common hap (v.). Old English used gelimpan, gesceon, and Middle English also had befall. In Middle English fel it hap meant "it happened." Related: Happened; happening. Phrase happens to be as an assertive way to say "is" is from 1707.
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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.

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incident (adj.)

late 15c., "likely to happen," from Latin incidentem (nominative incidens), present participle of incidere "to happen, befall" (see incident (n.)). From 1620s as "occurring as a subordinate;" 1660s in literal sense "falling or striking upon."

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incidence (n.)

early 15c., "incidental matter," from Old French incidence (15c.), from Late Latin incidentia, from incidere "to happen, befall" (see incident (n.)). Meaning "act of coming into contact with or affecting" is from 1650s. In physics, of rays of light, etc., considered with reference to direction, from 1620s.

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become (v.)
Old English becuman "happen, come about, befall," also "meet with, fall in with; arrive, approach, enter," from Proto-Germanic *bikweman (source also of Dutch bekomen, Old High German biqueman "obtain," German bekommen, Gothic biquiman). A compound of the sources of be- and come.

Meaning "change from one state of existence to another" is from 12c. Older sense preserved in what has become of it? It drove out Old English weorðan "to befall." Meaning "to look well, suit or be suitable to" is early 14c., from earlier sense of "to agree with, be fitting or proper" (early 13c.).
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time (v.)
Old English getimian "to happen, befall," from time (n.). Meaning "to appoint a time" (of an action, etc.) is attested from c. 1300; sense of "to measure or record the time of" (a race, event, etc.) is first attested 1660s. Related: Timed; timing.
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worth (v.)
"to come to be," now chiefly, if not solely, in the archaic expression woe worth the day, present subjunctive of Old English weorðan "to become, be, to befall," from Proto-Germanic *werthan "to become" (source also of Old Saxon, Old Dutch werthan, Old Norse verða, Old Frisian wertha, Old High German werdan, German werden, Gothic wairþan "to become"), literally "to turn into," from PIE root *wer- (2) "to turn, bend."
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occur (v.)

1520s, "meet, meet in argument," from French occurrer "happen unexpectedly" or directly from Latin occurrere "run to meet, run against, befall, present itself," from ob "against, toward" (see ob-) + currere "to run" (from PIE root *kers- "to run"). Sense development is from "meet" to "present itself" to "appear" to "happen" ("present itself in the course of events"). Meaning "to come into one's mind" is from 1620s. Related: Occurred; occurring.

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