Etymology
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cop (n.)

"policeman," 1859, abbreviation (said to be originally thieves' slang) of earlier copper (n.2), which is attested from 1846, agent noun from cop (v.) "to capture or arrest as a prisoner." Cop-shop "police station" is attested from 1941. The children's game of cops and robbers is attested from 1900.

Each child in Heaven's playground knows each other child by name.
They choose up sides as all take part in some exciting game
Like Hide=and=Seek, Red Rover, Cops and Robbers, Pris'ner's Base.
Our Lord is glad to referee their every game and race.

[John Bernard Kelly, "Heaven is a Circus," 1900]

English has many nouns cop, some archaic or obsolete, many connected more or less obscurely to Old English cop "top, summit," which is related to the source of cup (n.).

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fair (adv.)
Old English fægere "beautifully," from fæger "beautiful" (see fair (adj.)). From c. 1300 as "honorably;" mid-14c. as "correctly; direct;" from 1510s as "clearly." Fair and square is from c. 1600. Fair-to-middling is from 1829, of livestock markets.
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cop (v.)

"to seize, to catch, capture or arrest as a prisoner," 1704, northern British dialect, of uncertain origin; perhaps ultimately from French caper "seize, to take," from Latin capere "to take" (from PIE root *kap- "to grasp"); or from Dutch kapen "to take," from Old Frisian capia "to buy," which is related to Old English ceapian (see cheap). Related: Copped; copping.

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fair (adj.)

Old English fæger "pleasing to the sight (of persons and body features, also of objects, places, etc.); beautiful, handsome, attractive," of weather, "bright, clear, pleasant; not rainy," also in late Old English "morally good," from Proto-Germanic *fagraz (source also of Old Saxon fagar, Old Norse fagr, Swedish fager, Old High German fagar "beautiful," Gothic fagrs "fit"), perhaps from PIE *pek- (1) "to make pretty" (source also of Lithuanian puošiu "I decorate").

The meaning in reference to weather preserves the oldest sense "suitable, agreeable" (opposed to foul (adj.)). Of the main modern senses of the word, that of "light of complexion or color of hair and eyes, not dusky or sallow" (of persons) is from c. 1200, faire, contrasted to browne and reflecting tastes in beauty. From early 13c. as "according with propriety; according with justice," hence "equitable, impartial, just, free from bias" (mid-14c.).

Of wind, "not excessive; favorable for a ship's passage," from late 14c. Of handwriting from 1690s. From c. 1300 as "promising good fortune, auspicious." Also from c. 1300 as "above average, considerable, sizable." From 1860 as "comparatively good."

The sporting senses (fair ball, fair catch, etc.) began to appear in 1856. Fair play is from 1590s but not originally in sports (earlier it meant "pleasant amusement," c. 1300, and foul play was "sinful amusement"). Fair-haired in the figurative sense of "darling, favorite" is from 1909. First record of fair-weather friends is from 1736 (in a letter from Pope published that year, written in 1730). The fair sex "women" is from 1660s, from the "beautiful" sense (fair as a noun meaning "a woman" is from early 15c.). Fair game "legitimate target" is from 1776, from hunting.

Others, who have not gone to such a height of audacious wickedness, have yet considered common prostitutes as fair game, which they might pursue without restraint. ["Advice from a Father to a Son, Just Entered into the Army and about to Go Abroad into Action," London, 1776]
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fair (n.)
"a stated market in a town or city; a regular meeting to buy, sell, or trade," early 14c., from Anglo-French feyre (late 13c.), from Old French feire, faire "fair, market; feast day," from Vulgar Latin *feria "holiday, market fair," from Latin feriae "religious festivals, holidays," related to festus "solemn, festive, joyous" (see feast (n.)).
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copout (n.)

"a cowardly escape, an evasion," 1942; see cop out.

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copper (n.2)

"policeman," 1846; probably an agent noun from the verb cop "to seize, to catch, capture or arrest as a prisoner" (see cop (v.)).

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dummkopf (n.)

"stupid person," 1809 (dom cop, in Washington Irving), from German dummkopf, literally "dumb head;" see dumb (adj.) + cup (n.).

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