Etymology
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tie (n.)

Old English teag, "cord, band, thong, fetter," literally "that with which anything is tied," from Proto-Germanic *taugo (source also of Old Norse taug "tie," tygill "string"), from PIE root *deuk- "to lead" (source also of Old English teon "to draw, pull, drag").

Figurative sense is recorded from 1550s. Sense of "cravat, necktie" (usually a simple one knotted in front) first recorded 1761. The railway sense of "cross-beam between and beneath rails to keep them in place" is from 1857, American English. Meaning "equality between competitors" is first found 1670s, from notion of a connecting link. Tie-breaker is recorded from 1938. The figurative old school tie (1938) in its literal sense was a necktie of a characteristic pattern worn by former students of a particular English school.

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tie (v.)
Old English tigan, tiegan "to tie, bind, join, connect," from the source of tie (n.). Meaning "to finish equal to a competitor" is from 1888. Related: Tied; tying. To tie the knot in the figurative sense "form a union" is from 1707. Tie one on "get drunk" is recorded from 1944.
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tie-in (n.)
"connection," 1934, from verbal phrase (attested by 1793), from tie (v.) + in (adv.).
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tie-dye (v.)
1904, from tie (v.) + dye (v.) in reference to the method. Related: Tie-dyed.
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bow tie (n.)
by 1887, from bow (n.) in the sense "ribbon or other fabric tied in a bow-knot" (by 1874) + tie (n.).
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cross-tie (n.)

"transverse connecting piece of lumber," later especially "a railway tie, timber placed under opposite rails for support and to prevent spreading," from cross- + tie (n.).

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hog-tie (v.)
also hogtie, "bind hands and feet by crossing and tying them," 1887, from hog (n.) + tie (v.). Related: Hog-tied.
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black-tie (n.)
as an article of male attire, 1848, from black (adj.) + tie (n.). As an adjective, indicating the style of formal attire that features it, or situations where such is the proper dress, by 1933.
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untie (v.)
Old English untigan "loosen, unchain," from un- (2) "opposite of" + tie (v.). Related: Untied; untying.
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necktie (n.)

"narrow band of silk, satin, etc., worn around the neck and tied in front," 1838, from neck (n.) + tie (n.). American English slang necktie party "a lynching" is recorded from 1871.

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