Etymology
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taut (adj.)

mid-13c., tohte "stretched or pulled tight," possibly from tog-, past participle stem of Old English teon "to pull, drag," from Proto-Germanic *theuhanan, from PIE root *deuk- "to lead," which would connect it to tow (v.) and tie. Related: Tautness.

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*deuk- 
Proto-Indo-European root meaning "to lead."

It forms all or part of: abduce; abducent; abduct; abduction; adduce; aqueduct; circumduction; conduce; conducive; conduct; conductor; conduit; deduce; deduction; dock (n.1) "ship's berth;" doge; douche; ducal; ducat; Duce; duchess; duchy; duct; ductile; duke (n.); educate; education; induce; induction; introduce; introduction; misconduct; produce; production; reduce; reduction; seduce; seduction; subduce; subduction; taut; team (n.); teem (v.1) "abound, swarm, be prolific;" tie (n.); tow (v.); traduce; transducer; tug; zugzwang.

It is the hypothetical source of/evidence for its existence is provided by: Latin dux (genitive ducis) "leader, commander," in Late Latin "governor of a province," ducere "to lead;" Old English togian "to pull, drag," teonteon "to pull, drag;" German Zaum "bridle," ziehen "to draw, pull, drag;" Middle Welsh dygaf "I draw."
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ligament (n.)

band of tough tissue binding bones, late 14c., from Latin ligamentum "a band, bandage, tie, ligature," from ligare "to bind, tie," from PIE root *leig- "to tie, bind." Related: Ligamental; ligamentous; ligamentary.

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legato (adv.)

in music, "smoothly, without intervals," 1811, from Italian legato, literally "bound," past participle of legare, from Latin ligare "tie" (from PIE root *leig- "to tie, bind"). Related: Legatissimo.

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lien (n.)

"right to hold property of another until debt is paid," 1530s, from French lien "a band or tie" (12c.), from Latin ligamen "bond," from ligare "to bind, tie" (from PIE root *leig- "to tie, bind"). The word was in Middle English in the literal sense "a bond, fetter," also figuratively, "moral restraint."

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alloy (v.)

c. 1400, "mix (a metal) with a baser metal," from Old French aloiier, aliier "assemble, join," from Latin alligare "bind to, tie to," from ad "to" (see ad-) + ligare "to bind, bind one thing to another, tie" (from PIE root *leig- "to tie, bind"). In figurative use often implying debasement or reduction. The meaning "mix any two metals" without reference to values is from 1822. Related: Alloyed; alloying.

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ally (v.)

late 13c., allien, "join in marriage" (transitive), from Old French alier "combine, unite," from a differentiated stem of aliier (from Latin alligare "bind to, tie to," from ad "to" (see ad-) + ligare "to bind, bind one thing to another, tie" (from PIE root *leig- "to tie, bind"). The meaning "form an alliance, join, associate" is late 14c. Related: allied; allying.

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lariat (n.)
rope or cord used for tying or catching horses, 1832, American English, from Spanish la reata "the rope," from reatar "to tie against," from re- "back" (see re-) + atar "to tie," from Latin aptare "to join," from aptus "fitted" (see apt). Compare lasso.
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denouement (n.)

"the solution of a mystery, the winding up of a plot, the outcome of a course of conduct," 1752, from French dénouement "an untying" (of plot), from dénouer "untie" (Old French desnouer) from des- "un-, out" (see dis-) + nouer "to tie, knot," from Latin nodus "a knot," from PIE root *ned- "to bind, tie."

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liable (adj.)

mid-15c., "bound or obliged by law," from Old French lier, liier "to bind, tie up, fasten, tether; bind by obligation" (12c.), from Latin ligare "to bind, to tie" (from PIE root *leig- "to tie, bind"). With -able.

Perhaps it is from an Anglo-French *liable, or from an unattested word in Old French or Medieval Latin. The general sense of "exposed to" (something undesirable) is attested by 1590s. The unetymological use for "likely" is attested by 1850.

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