Etymology
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foul (adj.)

Old English ful "rotten, unclean, vile, corrupt, offensive to the senses," from Proto-Germanic *fulaz (source also of Old Saxon and Old Frisian ful, Middle Dutch voul, Dutch vuil, Old High German fül, German faul, Gothic füls), from PIE *pu- (2) "to rot, decay," perhaps from the sound made in reaction to smelling something bad (see pus).

Old English ful occasionally meant "ugly" (as contrasted with fæger (adj.), modern fair (adj.)), and this sense became frequent in Middle English. The cognate in Swedish is the usual word for "ugly." Of weather from mid-14c. In the sporting sense of "irregular, unfair, contrary to established rule or practice" it is first attested 1797, though foul play is recorded from mid-15c. Baseball sense of "out of play" attested by 1860.

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foul (v.)

Old English fulian "to become foul, rot, decay," from ful (see foul (adj.)). Transitive meaning "make foul, pollute" is from c. 1200. Meaning "become entangled" (chiefly nautical) is from 1832, probably from foul (adj.) in the sense "obstructed by anything fixed or attached" (late 15c.). "A term generally used in contrast to clear, and implies entangled, embarrassed or contrary to: e.g. to foul the helm, to find steerage impracticable owing to the rudder becoming entangled with rope or other gear" [Sir Geoffrey Callender, "Sea Passages," 1943]. Related: Fouled; fouling. Hence also foul anchor (1769), one with the slack of the cable twisted round the stock or a fluke; noted by 1832 as naval insignia.

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shot (n.)

Middle English shot "a missile, arrow, dart" (senses now archaic or obsolete); "a swift movement, a gushing out," from Old English scot, sceot "a shot, a shooting, an act of shooting; that which is discharged in shooting, what is shot forth; darting, rapid motion."

This is from Proto-Germanic *skutan (source also of Old Norse skutr, Old Frisian skete, Middle Dutch scote, German Schuß "a shot"), from PIE root *skeud- "to shoot, chase, throw." The Old English noun is related to sceotan "to shoot." The meaning "discharge of a bow, missile," also is from related Old English gesceot.

The noun was extended to other projectiles (balls, bullets) by mid-15c. Especially "lead in small pellets, a small ball or pellet," a number of which are combined in one charge, which is attested by 1770 (shortened from earlier small shot, 1727).

The general sense of "an attempt to hit with a projectile" is by 1650s. Extended to sports (hockey, basketball, etc.) by 1772, originally in curling. It is attested by early 15c. as "range or distance of a missile in flight," hence "range" in general (c. 1600), as in earshot

Another original meaning, "payment" (perhaps literally "money thrown down") is preserved in scot-free; also see scot (n.). The notion of "throwing down" might have led to the meaning "a drink," first attested 1670s; the more precise meaning "small drink of straight liquor" is by 1928.

The sense of "hypodermic injection" is attested from 1904; the figurative phrase shot in the arm "stimulant" is by 1922. The broad meaning "a try, an attempt" is by 1756; the sense of "remark meant to wound" is by 1841. The meaning "an expert in shooting with a firearm" is from 1780; the sense of "a rocket flight" is by 1934. The camera-view sense is by 1958.

To call the shots "control events, make decisions" is American English, 1922, perhaps from sport shooting. Shot in the dark "uninformed guess, random attempt" is by 1885. Big shot "important person" is from 1861. 

By the rude bridge that arched the flood,
   Their flag to April’s breeze unfurled,
Here once the embattled farmers stood
   And fired the shot heard round the world.
[Emerson, from "Concord Hymn"]  
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shot (adj.)

early 15c., of fish (implied in shotfish), "having discharged its spawn," past-participle adjective from shoot (v.). The meaning "wounded or killed by a bullet or other projectile" is from 1837.

The modern slang figurative sense of "ruined, used up, worn out" is attested by 1933, American English; the slang phrase shot to hell "in a state of collapse" is attested by 1926 (Hemingway).

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one-shot (adj.)

1907, "achieved in a single attempt" (original reference is to golf), from one + shot (n.). Meaning "happening or of use only once" is from 1937.

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foul-mouthed (adj.)

also foulmouthed, 1590s, apparently first in Shakespeare ["Henry IV," 1596]. Earlier were foul-tongued (1540s); foul-spoken (1580s).

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long shot (n.)

also long-shot, in the figurative sense of "something unlikely," 1867, from long (adj.) + shot (n.). The notion is of a shot at a target from a great distance, thus difficult to make. The phrase by a long shot "by a considerable amount," frequently negative, is attested by 1830, American English colloquial. The cinematic sense of the noun phrase is from 1922. As an adjective by 1975.

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big shot (n.)

"important person," 1929, American English, from Prohibition-era gangster slang; earlier in the same sense was great shot (1861). Ultimately a reference to large type of gunshot; see shot (n.).

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mug-shot (n.)

also mugshot, "photograph taken by police of a person after an arrest for identification purposes," 1950; see mug (n.2) "a person's face" + shot (n.) in the photographic sense.

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cannon-shot (n.)

"distance a cannon will throw a ball," 1570s, from cannon (n.) + shot (n.).

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