Etymology
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halter (n.)

Old English hælfter "rope for leading a horse," from Proto-Germanic *halftra- "that by which something is held" (source also of Old Saxon haliftra "halter," Old High German halftra, Middle Dutch halfter), from suffixed form of PIE *kelp- "to hold, grasp" (see helve). Also "hangman's noose" (mid-15c.). In women's clothing sense, originally "strap attached to the top of a backless bodice and looped around the neck," 1935, later extended to the tops themselves.

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wag (n.1)

"person fond of making jokes," 1550s, perhaps a shortening of waghalter "gallows bird," person destined to swing in a noose or halter, applied humorously to mischievous children, from wag (v.) + halter. Or possibly directly from wag (v.); compare wagger "one who stirs up or agitates" (late 14c.).

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helve (n.)

Old English helfe, hielfe "handle of an axe" or other tool or weapon, from Proto-Germanic *halbma- (source also of Old Saxon helvi, Middle Dutch helf, Old High German halb "handle of an axe," Old High German helmo "tiller"); related to halter and helm (n.1), from PIE *kelp- "to hold, grasp." In Middle English, to holden the axe bi the helve (c. 1200) meant "to take something by the right end."

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hackamore (n.)

halter chiefly used for breaking horses, 1850, American English, of uncertain origin. OED and Klein suggests a corruption of Spanish jaquima (earlier xaquima) "halter, headstall of a horse," which Klein suggests is from Arabic shakimah "bit of a bridle, curb, restraint."

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capstan (n.)

"upright apparatus on a ship, worked by levers, used for raising weights or applying power," late 14c., from Old French cabestant, from Old Provençal cabestan, from capestre "pulley cord," from Latin capistrum "halter," from capere "to hold, take" (from PIE root *kap- "to grasp").

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holder (n.)

c. 1400, "tenant, occupier," agent noun from hold (v.). Meaning "device for holding something" is attested from 1833. Similar formation in Old Frisian haldere, Dutch houder, German Halter. The Old English agent noun, healdend, meant "protector, guardian, ruler, king."

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strangle (v.)

late 13c., from Old French estrangler "choke, suffocate, throttle" (Modern French étrangler), from Latin strangulare "to choke, stifle, check, constrain," from Greek strangalan "to choke, twist," from strangale "a halter, cord, lace," related to strangos "twisted," from PIE root *strenk- "tight, narrow; pull tight, twist" (see string (n.)). Related: Strangled; strangling.

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strap (n.)

1610s, "band of leather," from Scottish and/or nautical variant of strope "loop or strap on a harness" (mid-14c.), probably from Old French estrop "strap," from Latin stroppus "strap, band," perhaps via Etruscan, ultimately from Greek strophos "twisted band; a cord, rope," from strephein "to turn" (from PIE root *streb(h)- "to wind, turn"). Old English stropp, Dutch strop "halter" also are borrowed from Latin, and the Old English word might be the source of the modern one. Slang meaning "credit" is from 1828.

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martingale (n.)

1580s, "strap passing between the forelegs of a horse as part of the harness," from French martingale (16c.), of uncertain origin, perhaps from Old Provençal martegalo, fem. of martegal "inhabitant of Martigue," a commune northwest of Marseilles, making the etymological sense "worn in the manner of the people of Martigue;" or perhaps it is from Spanish almartaga, a word for a sort of halter or rein, from Arabic almartak, in which case it might have been influenced in form by the Provençal word. The nautical sense of  "short, perpendicular spar under the bowsprit-end" is by 1794.

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rein (n.)

c. 1300, reine, "strap of a bridle," attached to it on either side of the head, by which the rider or driver restrains and guides the animal, from Old French rene, resne "reins, bridle strap, laces" (Modern French rêne), probably from Vulgar Latin *retina "a bond, check," a back-formation from Latin retinere "hold back" (see retain). Compare Latin retinaculum "a tether, halter, rein."

The figurative extension of reins to "guidance, means of controlling; control, check, restraint" is by mid-14c. Hence many expressions, originally from horse-management: Hold the reins "wield power" (early 15c.); take the reins "assume the power of guidance or government" (1610s). To give something free rein also is originally of horses; to give (a horse) the reins (1620s) is to allow it free motion.

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