Etymology
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duct (n.)

1640s, "course, direction," from Latin ductus "a leading, a conduit pipe," noun use of past participle of ducere "to lead" (from PIE root *deuk- "to lead"). Anatomical sense "vessel of an animal body by which blood, lymph, etc., are conveyed" is from 1660s. Meaning "conduit, channel" is 1713; that of "air tube in a structure" is from 1884.

Duct tape originally was duck tape (1894), long, non-adhesive strips of plain cotton duck cloth used in various mechanical processes; from duck (n.2). The name was transferred to a plastic-coated adhesive tape used by U.S. soldiers in World War II (perhaps in part because it was waterproof). It continued in civilian use after the war, and the name shifted to duct tape by 1958, perhaps because it was frequently used on air ducts, which also accounts for its standard silver-gray color. 

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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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ureter (n.)
1570s, from medical Latin ureter, from Greek oureter "urinary duct of the kidneys," from ourein "to urinate," from ouron (see urine). Related: Ureteral.
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vas (n.)
in anatomy, "a tube, duct, or conduit for conveying blood, lymph, semen, etc.," plural vasa, Latin, literally "vessel." Vas deferens (plural vasa defferentia) is from 1570s.
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vessel (n.)
c. 1300, "container," from Old French vessel "container, receptacle, barrel; ship" (12c., Modern French vaisseau) from Late Latin vascellum "small vase or urn," also "a ship," alteration of Latin vasculum, diminutive of vas "vessel." Sense of "ship, boat" is found in English from early 14c. "The association between hollow utensils and boats appears in all languages" [Weekley]. Meaning "canal or duct of the body" (especially for carrying blood) is attested from late 14c.
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viaduct (n.)

1816, from Latin via "road" (see via) + -duct as in aqueduct. French viaduc is a 19c. English loan-word.

An extensive bridge consisting, strictly of a series of arches of masonry, erected for the purpose of conducting a road or a railway a valley or a district of low level, or over existing channels of communication, where an embankment would be impracticable or inexpedient; more widely, any elevated roadway which artificial constructions of timber, iron, bricks, or stonework are established. [Century Dictionary]

But the word apparently was coined by English landscape gardener Humphry Repton (1752-1818) for an architectural feature, "a form of bridge adapted to the purposes of passing over, which may unite strength with grace, or use with beauty ...."

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ductile (adj.)

mid-14c., "hammered, beaten out or shaped with a hammer," from Old French ductile or directly from Latin ductilis "that may be led or drawn," from past participle of ducere "to lead" (from PIE root *deuk- "to lead"). From 1560s as "flexible, pliable;" 1620s as "capable of being drawn out in wires or threads." Of persons, "capable of being led or drawn," 1620s. Related: Ductility.

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pipe (n.1)

Old English pipe "simple tubular musical wind instrument," also "tube for conveying water," from Vulgar Latin *pipa "a pipe, tube-shaped musical instrument" (source also of Italian pipa, French pipe, Old Frisian pipe, German Pfeife, Danish pibe, Swedish pipa, Dutch pijp), a back-formation from Latin pipare "to chirp or peep," of imitative origin.

All the tubular senses ultimately derive from the meaning "small reed, whistle." From late 14c. as "a tube or duct of the body." From mid-15c. as "one of the tubes from which the tones of an organ are produced." Meaning "narrow tubular device for smoking" is recorded by 1590s. As "the sound of the voice," 1570s.

Pipe-bomb, "home-made bomb contained in a metal pipe," is attested from 1960. Pipe-cleaner, "piece of wire coated with tufted material," is recorded from 1863. Pipe-clay "white clay suitable for making smoking pipes" is attested by 1777.

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main (n.)

Old English mægen (Mercian megen) "power, bodily strength; force, violent effort; strength of mind or will; efficacy; supernatural power," from Proto-Germanic *maginam "power" (source also of Old High German megin "strength, power, ability"), suffixed form of PIE root *magh- "to be able, have power."

Original sense of "power" is preserved in phrase might and main. Also used in Middle English for "royal power or authority" (c. 1400), "military strength" (c. 1300), "application of force" (c. 1300). Meaning "chief or main part" (c. 1600) now is archaic or obsolete. Meaning "principal duct, pipe, or channel in a utility system" is first recorded 1727 in main drain.

Used since 1540s for "continuous stretch of land or water;" in nautical jargon used loosely for "the ocean," but in Spanish Main the word is short for mainland and refers to the coast between Panama and Orinoco (as contrasted to the islands of the West Indies).

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