Etymology
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wink (v.)
Old English wincian "to blink, wink, close one's eyes quickly," from Proto-Germanic *wink- (source also of Dutch winken, Old High German winkan "move sideways, stagger; nod," German winken "to wave, wink"), a gradational variant of the root of Old High German wankon "to stagger, totter," Old Norse vakka "to stray, hover," from PIE root *weng- "to bend, curve." The meaning "close an eye as a hint or signal" is first recorded c. 1100; that of "close one's eyes (to fault or irregularity)" first attested late 15c. Related: Winked; winking.
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wink (n.)
"a quick shutting and opening of the eyes," c. 1300, from wink (v.); meaning "very brief moment of time" is attested from 1580s.
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winch (n.)
late 13c., from Old English wince "winch, pulley," from Proto-Germanic *winkja-, from PIE *weng- "to bend, curve" (see wink (v.)). Perhaps so called in reference to the bent handle.
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hoodwink (v.)
1560s, "to blindfold, blind by covering the eyes," from hood (n.1) + wink (n.); figurative sense of "blind the mind, mislead, deceive by disguise" is c. 1600. Related: Hoodwinked; hoodwinking.
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gauche (adj.)
"awkward, tactless," 1751 (Chesterfield), from French gauche "left" (15c., replacing senestre in that sense), originally "awkward, awry," from gauchir "turn aside, swerve," from Proto-Germanic *wankjan (source also of Old High German wankon, Old Norse vakka "to stagger, totter"), from PIE *weng- "to bend, curve" (see wink (v.)).
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wince (v.)
c. 1300, wincen; mid-13c. winchen, "to recoil suddenly," from Anglo-French *wenchir, Old North French *wenchier (Old French guenchir) "to turn aside, avoid," from Frankish *wenkjan, from Proto-Germanic *wankjan (source also of Old High German wankon "to stagger, totter," Old Norse vakka "to stray, hover;" see wink (v.)). Originally of horses. Modern form is attested from late 13c. Related: Winced; wincing.
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periwinkle (n.2)

kind of sea snail, 1520s, apparently an alteration of Old English pinewincle (probably by influence of Middle English parvink; see periwinkle (n.1)); from Old English pine-, which probably is from Latin pina "mussel," from Greek pine. The second element is wincel "corner; spiral shell," from Proto-Germanic *winkil-, from PIE root *weng- "to bend, curve" (see wink (v.)). But no Middle English forms have been found.

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lapwing (n.)
Middle English lappewinke (late 14c.), lapwyngis (early 15c.), folk etymology alteration of Old English hleapewince "lapwing," probably literally "leaper-winker," from hleapan "to leap" (see leap (v.)) + wince "totter, waver, move rapidly," related to wincian "to wink" (see wink (v.)).

Said to be so called from "the manner of its flight" [OED] "in reference to its irregular flapping manner of flight" [Barnhart], but the lapwing also flaps on the ground pretending to have a broken wing to lure egg-hunters away from its nest, which seems a more logical explanation. Its Greek name was polyplagktos "luring on deceitfully."
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wench (n.)

late 13c., wenche "girl, young woman," especially if unmarried, also "female infant," shortened from wenchel "child," also in Middle English "girl, maiden," from Old English wencel, probably related to wancol "unsteady, fickle, weak," from Proto-Germanic *wankila- (source also of Old Norse vakr "child, weak person," Old High German wanchal "fickle"), from PIE *weng- "to bend, curve" (see wink (v.)).

The wenche is nat dead, but slepith. [Wyclif, Matthew ix.24, c. 1380]

In Middle English occasionally with disparaging suggestion, and secondary sense of "concubine, strumpet" is attested by mid-14c. Also "serving-maid, bondwoman, young woman of a humble class" (late 14c.), a sense retained in the 19c. U.S. South in reference to slave women of any age. In Shakespeare's day a female flax-worker could be a flax-wench, flax-wife, or flax-woman.

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connivent (adj.)

1640s, "willfully blind or tolerant," from Latin conniventem (nominative connivens), present participle of connivere "to wink," hence, "to wink at (a crime), be secretly privy" (see connive). In natural history, "having a gradually inward direction, gradually convergent," 1757.

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