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"that with which anything is tied," Old English teag, from Proto-Germanic *taugo (cf. Old Norse taug "tie," tygill "string"), from PIE *deuk- "to pull, to lead" (cf. Old English teon "to draw, pull, drag;" see duke (n.)).
Figurative sense is recorded from 1550s. Meaning "equality between competitors" is first found 1670s, from notion of a connecting link (tie-breaker is recorded from 1961). Sense of "necktie, cravat" first recorded 1761. The railway sense of "transverse sleeper" is from 1857, American English.
Old English tigan, tiegan, from the source of tie (n.). Related: Tied; tying. Tie-dye first attested 1904. Tie one on "get drunk" is recorded from 1951. In the noun sense of "connection," tie-in dates from 1934.