[strung, elastic weapon for shooting arrows] Middle English boue, from Old English boga "archery bow; anything bent or arched, an arch, a rainbow," from Proto-Germanic *bugon (source also of Old Norse bogi, Old Frisian boga, Dutch boog, German Bogen "bow"), from PIE root *bheug- "to bend," with derivatives referring to bent, pliable, or curved objects.
The sense of "a looped knot," especially an ornamental one, is from 1540s. The musician's bow (1570s) formerly was curved like the archer's.
The former popularity of the longbow as a characteristic English weapon is attested in expressions such as bow-legged; to have the bent of (one's) bow "know one's intentions or inclinations" (1560s), to shoot in (another's) bow "practice an art other than one's own;" bow-hand "the left hand," hence "on the wrong side, inaccurately;" have two strings to (one's) bow "have more than one means to accomplish something;" draw the long bow "exaggerate, lie."
[bend the body] Middle English bouen, from Old English bugan "to bend, become bent, have or assume a curved direction; to bow down, bend the body in condescension or reverence, to submit," also "to turn back" (class II strong verb; past tense beag, past participle bogen), from Proto-Germanic *bugon (source also of Dutch buigen, Middle Low German bugen, Old High German biogan, German biegen, Gothic biugan "to bend," Old Norse boginn "bent"), from *beugen, from PIE root *bheug- "to bend." Related: Bowed; bowing. To bow out "withdraw" is from 1942, from the notion of "exit with a bow or bows."
"forward part of a ship," beginning where the sides trend inward, mid-14c., bou, boue, from a source such as Old Norse bogr, Middle Low German boog, Middle Dutch boech "bow of a ship," from Proto-Germanic *bugon-, from PIE root *bheug- "to bend," with derivatives referring to bent, pliable, or curved objects.
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.
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.