Etymology
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cave (n.)

"a hollow place in the earth, a natural cavity of considerable size and extending more or less horizontally," early 13c., from Old French cave "a cave, vault, cellar" (12c.), from Latin cavea "hollow" (place), noun use of neuter plural of adjective cavus "hollow," from PIE root *keue- "to swell," also "vault, hole." Replaced Old English eorðscrafu.

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cave (v.)

early 15c., caven, "to hollow something out," from cave (n.). Modern sense "to collapse in or down" is 1707, American English, presumably from East Anglian dialectal calve "collapse, fall in and leave a hollow," which is perhaps from Flemish and subsequently was influenced by cave (n.). Transitive sense by 1762. Related: Caved; caving. Figurative sense of "yield to pressure" is from 1837.

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cave-dweller (n.)

"prehistoric human or animal who lived in natural caves," 1857, from cave (n.) + dweller.

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cave-bear (n.)

Ice Age vegetarian bear of Europe and western Asia (extinct from c. 10.000 years ago), known from fossil remains found in caves, 1826, from cave (n.) + bear (n.).

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caveman (n.)

also cave-man, "prehistoric human dwelling in a natural cave," 1865, from cave (n.) + man (n.). Related: Cave-woman (1904).

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cage (n.)
"box-like receptacle or enclosure, with open spaces, made of wires, reeds, etc.," typically for confining domesticated birds or wild beasts, c. 1200, from Old French cage "cage, prison; retreat, hideout" (12c.), from Latin cavea "hollow place, enclosure for animals, coop, hive, stall, dungeon, spectators' seats in the theater" (source also of Italian gabbia "basket for fowls, coop;" see cave (n.)). From c. 1300 in English as "a cage for prisoners, jail, prison, a cell."
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*keue- 
*keuə-, Proto-Indo-European root meaning "to swell," also "vault, hole."

It forms all or part of: accumulate; accumulation; cave; cavern; cavity; coeliac; church; codeine; coelacanth; coeliac; coelomate; concave; cumulate; cumulative; cumulus; enceinte; excavate; kirk; kymatology; Kyrie eleison.

It is the hypothetical source of/evidence for its existence is provided by: Sanskrit svayati "swells up, is strong;" Greek kyein "to swell," koilos "hollow, hollowed out, spacious, deep;" Latin cumulus "a heap, pile, mass, surplus;" Lithuanian šaunas "firm, solid, fit, capable;" Middle Irish cua "hollow;" Armenian soyl "cavity."
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cabinet (n.)

1540s, "secret storehouse, treasure chamber; case for valuables," from French cabinet "small room" (16c.), diminutive of Old French cabane "cabin" (see cabin); perhaps influenced by (or rather, from) Italian gabbinetto, diminutive of gabbia, from Latin cavea "stall, stoop, cage, den for animals" (see cave (n.)).

Meaning "case for safe-keeping" (of papers, liquor, etc.) is from 1540s, gradually shading to mean a piece of furniture that does this. Sense of "private room where advisers meet" (c. 1600) led to modern political meaning "an executive council" (1640s); perhaps originally short for cabinet council (1620s); compare board (n.1) in its evolution from place where some group meets to the word for the group that meets there. From 1670s also "building or part of a building set aside for the conservation and study of natural specimens, art, antiquities, etc."

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jail (n.)
c. 1300 (c. 1200 in surnames) "a jail, prison; a birdcage." The form in j- is from Middle English jaile, from Old French jaiole "a cage; a prison," from Medieval Latin gabiola "a cage," from Late Latin caveola, diminutive of Latin cavea "a cage, enclosure, stall, coop; a hollow place, a cavity" (see cave (n.)).

The form in g- was the more usual in Middle English manuscripts (gaile, also gaiole), from Old French gaiole "a cage; a prison," a variant spelling that seems to have been frequent in Old North French, which would have been the system familiar to Norman scribes. Now pronounced "jail" however it is spelled. Persistence of gaol (preferred in Britain) is "chiefly due to statutory and official tradition" [OED], and, probably, the fact that it is known the Americans spell it the other way.

In U.S. usually a place of confinement for petty offenders. The Medieval Latin word also is the source of Spanish gayola, Italian gabbiula.
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spelunk (n.)
"a cave, cavern, a vault," c. 1300, from Old French spelonque (13c.) or directly from Latin spelunca "a cave, cavern, grotto," from Greek spelynx (accusative spelynga, genitive spelyngos) "a cave, cavern," from spelos "a cave." An adjective, speluncar "of a cave" is recorded from 1855.
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