Etymology
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hinge (n.)

late 14c., "movable joint of a gate or door," not found in Old English, cognate with Middle Dutch henghe "hook, handle," Middle Low German henge "hinge," from Proto-Germanic *hanhan (transitive), *hangen (intransitive), from PIE *konk- "to hang" (see hang (v.)). The notion is the thing from which a door hangs. Figurative sense of "that on which events, etc., turn" is from c.1600. Stamp-collecting sense is from 1883.

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hinge (v.)
c. 1600, "to bend," from hinge (n.). Meaning "turn on, depend" (figuratively) is from 1719. Related: Hinged; hinging.
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unhinge (v.)
recorded earlier in the mental sense of "to disorder" the mind, etc. (1612) than in the literal one of "to take (a door, etc.) off its hinges" (1616); from un- (2) "opposite of" + hinge (n.). Hinge as a verb meaning "to attach by a hinge" is recorded only from 1758. Related: Unhinged; unhinging.
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kern (n.)
1680s, "part of a metal type projecting beyond the body," as the head of an -f- or the tail of a -j-. According to Century Dictionary this is identical with kern "a grain" (see kernel), but OED says it is from French carne "projecting angle, quill of a pen" (12c.), Old North French form of Old French charne "hinge, pivot," from Latin cardinem "hinge." Related: Kerned "having the top or bottom projecting beyond the body;" kerning.
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vertebra (n.)
"bone of the spine," early 15c., from Latin vertebra "joint or articulation of the body, joint of the spine" (plural vertebræ), perhaps from vertere "to turn" (from PIE root *wer- (2) "to turn, bend") + instrumental suffix -bra. The notion would be the spine as the "hinge" of the body.
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valise (n.)

1610s, "suitcase, soldier's kit bag," from French valise (16c.), from Italian valigia, a word of uncertain origin. Attested in Medieval Latin forms valisia (early 15c.), valixia (late 13c.). "The name is generally given to a leather case of moderate size, opening wide on a hinge or like a portfolio ...." [Century Dictionary]

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hasp (n.)
Old English hæpse "fastening, clip," with later Old English metathesis of -p- and -s-. Related to Old Norse hespa "hasp, fastening," Middle Dutch, German haspe "clamp, hinge, hook," but all are of uncertain origin. The meaning "a quantity of yarn" is from c. 1400 but perhaps not the same word.
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pivot (n.)

"pin on which a wheel or other object turns," 1610s, from French pivot, from Old French pivot "hinge pin, pivot" (12c.), also "penis," a word of uncertain origin. Pevetsheres, evidently some kind of shears, is mentioned in a will registered in York in 1398. Figurative sense of "turning point, that on which some matter hinges or depends" is recorded from 1813.

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cardinal (adj.)
Origin and meaning of cardinal

"chief, pivotal," early 14c., from Latin cardinalis "principal, chief, essential," a figurative use, literally "pertaining to a hinge," from cardo (genitive cardinis) "that on which something turns or depends; pole of the sky," originally "door hinge," which is of unknown origin. Related: Cardinally.

The cardinal numbers (1590s) are "one, two, three," etc. as opposed to ordinal numbers "first, second, third," etc.; they are so called because they are the principal numbers and the ordinals depend on them.

The cardinal points (1540s) are north, south, east, west. The cardinal sins (c. 1600) are too well known to require rehearsal. The cardinal virtues (c. 1300) were divided into natural (justice, prudence, temperance, fortitude) and theological (faith, hope, charity). The natural ones were the original classical ones, which were amended by Christians. But typically in Middle English only the first four were counted as the cardinal virtues:

Of þe uour uirtues cardinales spekeþ moche þe yealde philosofes. ["Ayenbite of Inwyt," c. 1340]

By analogy of this, and cardinal winds (late 14c.), cardinal signs (four zodiacal signs marking the equinoxes and the solstices, late 14c.), etc., the adjective in Middle English acquired an association with the number four.

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twist (n.)
mid-14c., "flat part of a hinge" (now obsolete), probably from Old English -twist "divided object; fork; rope" (as in mæsttwist "mast rope, stay;" candeltwist "wick"), from Proto-Germanic *twis-, from PIE root *dwo- "two." Original senses suggest "dividing in two" (source also of cognate Old Norse tvistra "to divide, separate," Gothic twis- "in two, asunder," Dutch twist, German zwist "quarrel, discord," though these senses have no equivalent in English), but later ones are of "combining two into one," hence the original sense of the word may be "rope made of two strands."

Meaning "thread or cord composed of two or more fibers" is recorded from 1550s. Meaning "act or action of turning on an axis" is attested from 1570s. Sense of "beverage consisting of two or more liquors" is first attested c. 1700. Meaning "thick cord of tobacco" is from 1791. Meaning "curled piece of lemon, etc., used to flavor a drink" is recorded from 1958. Sense of "unexpected plot development" is from 1941.

The popular rock 'n' roll dance craze is from 1961, so called from the motion involved, but twist was used to describe popular dances in 1894 and again in the 1920s. To get one's knickers in a twist "be unduly agitated" is British slang first attested 1971.
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