Etymology
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cage (v.)
"to confine in a cage, to shut up or confine," 1570s, from cage (n.). Related: Caged; caging.
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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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bird-cage (n.)
also birdcage, "portable enclosure for birds," late 15c., from bird (n.1) + cage (n.).
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cajole (v.)

"deceive or delude by flattery," 1640s, from French cajoler "to cajole, wheedle, coax," a word of uncertain origin; perhaps a blend of cageoler "to chatter like a jay" (16c., from gajole, southern diminutive of geai "jay;" see jay (n.)), and Old French gaioler "to cage, entice into a cage" (see jail (n.)). Related: Cajoled; cajoling.

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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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mew (n.2)

"cage for birds; place where hawks are put to molt," late 14c., from Old French mue "cage for hawks," especially when molting, from muer "to molt," from Latin mutare "to change" (from PIE root *mei- (1) "to change"). In extended use, "a place of retirement or confinement" (early 15c.). Also as a verb, "to shut up, confine" (mid-15c.).

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bower (n.)
Old English bur "room, hut, dwelling, chamber," from Proto-Germanic *bowan (source also of Old Norse bur "chamber," Swedish bur "cage," Old Danish both "dwelling, stall," Old Saxon bur "a house; a cage," Old High German bur "dwelling, chamber," buan "to dwell," German Vogelbauer "cage" for a bird), from PIE root *bheue- "to be, exist, grow."

Modern spelling developed after mid-14c. Sense of "leafy arbor" (place closed in, shaded, or sheltered by trees) is first attested 1520s. Hence, too, Australia's bower-bird (1847), so called for the ornamented play-houses it builds.
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dock (n.2)

"where accused stands in court," 1580s, probably originally rogue's slang, from Flemish dok "pen or cage for animals," which is of unknown origin.

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jail-bird (n.)
also jailbird, 1610s, based on an image of a caged bird; from jail (n.), which in its Middle English, French, and Latin ancestry also meant "cage" + bird (n.1).
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decoy (n.)

1610s, "a swindler;" 1650s, "anything intended to lead (someone) into a snare;" 1660s, "a lure employed in enticing game into a snare or within range of a weapon;" perhaps from Dutch kooi "cage," used of a pond surrounded by nets, into which wildfowl were lured for capture, from West Germanic *kaiwa, from Latin cavea "cage" (from cavus "a hollow" (from PIE root *keue- "to swell," also "vault, hole").

The first element is possibly the Dutch definite article de, mistaken in English as part of the word. If this is right, the later sense in English is the etymological one. But decoy, of unknown origin, was the name of a card game popular c. 1550-1650, and this may have influenced the form of the word.

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