Etymology
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cape (n.1)
"sleeveless cloak, circular covering for the shoulders," a Spanish style, late 16c., from French cape, from Spanish capa, from Late Latin cappa "hooded cloak" (see cap (n.), which is a doublet). Late Old English had capa, cæppe "cloak with a hood," directly from Late Latin.
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cape (n.2)

"promontory, piece of land jutting into a sea or lake," late 14c., from Old French cap "cape; head," from Latin caput "headland, head" (from PIE root *kaput- "head"). The Cape of Good Hope at the southern tip of Africa has been the Cape since 1660s. Old sailors called low cloud banks that could be mistaken for landforms on the horizon Cape fly-away (1769).

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capote (n.)
"large cloak with a hood," 1812, from French capote, fem. of capot (17c.), diminutive of cape (see cape (n.1)).
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carapace (n.)
"upper shell of a turtle or tortoise; shell of an insect, crustacean, etc.," 1836, from French carapace "tortoise shell" (18c.), from Spanish carapacho or Portuguese carapaça, which is of uncertain origin, perhaps somehow from Latin capa (see cape (n.1)). Related: Carapacial.
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Cape Cod 
peninsula of New England, named 1602 by English navigator Bartholomew Gosnold for the abundance of fish his men caught there (see cod). In reference to houses reminiscent of New England architecture, from 1916.
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coping (n.)

c. 1600 as an architectural term, "the top or cover of a wall, usually sloped to shed water," a specialized use of cope (n.), the cape-like vestment worn by priests, which is a a variant of cape (n.1). Cope (v.) "to provide (someone) with a cope or cloak" is attested from late 14c., and in the architectural sense of "to form a cope, bend as an arch or vault" it is recorded from 1660s. Coping saw, used for cutting curved patterns, is attested by 1887.

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*kaput- 
Proto-Indo-European root meaning "head."

It forms all or part of: achieve; behead; biceps; cabbage; cabochon; caddie; cadet; cap; cap-a-pie; cape (n.1) "garment;" cape (n.2) "promontory;" capital (adj.); capital (n.3) "head of a column or pillar;" capitate; capitation; capitulate; capitulation; capitulum; capo (n.1) "leader of a Mafia family;" capo (n.2) "pitch-altering device for a stringed instrument;" caprice; capsize; captain; cattle; caudillo; chapter; chef; chief; chieftain; corporal (n.); decapitate; decapitation; forehead; head; hetman; kaput; kerchief; mischief; occipital; precipice; precipitate; precipitation; recapitulate; recapitulation; sinciput; triceps.

It is the hypothetical source of/evidence for its existence is provided by: Sanskrit kaput-; Latin caput "head;" Old English heafod, German Haupt, Gothic haubiþ "head."
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cap (n.)

late Old English cæppe "hood, head-covering, cape," a general Germanic borrowing (compare Old Frisian and Middle Dutch kappe, Old High German chappa) from Late Latin cappa "a cape, hooded cloak" (source of Spanish capa, Old North French cape, French chape), a word of uncertain origin. Possibly a shortened from capitulare "headdress," from Latin caput "head" (from PIE root *kaput- "head").

The Late Latin word apparently originally meant "a woman's head-covering," but the sense was transferred to "hood of a cloak," then to "cloak" itself, though the various senses co-existed. Old English took in two forms of the Late Latin word, one meaning "head-covering," the other "ecclesiastical dress" (see cape (n.1)). In most Romance languages, a diminutive of Late Latin cappa has become the usual word for "head-covering" (such as French chapeau).

Meaning "soft, small, close-fitted head covering" in English is from early 13c., originally for women; extended to men late 14c. Extended to cap-like coverings on the ends of anything (such as hubcap) from mid-15c. Meaning "contraceptive device" is first recorded 1916.

Meaning "cap-shaped piece of copper lined with gunpowder and used to ignite a firearm" is by 1825, hence cap-gun (1855); extended to paper version used in toy pistols, 1872 (cap-pistol is from 1879).

Figurative thinking cap is from 1839 (considering cap is 1650s). Cap and bells (1781) was the insignia of a fool; cap and gown (1732) of a scholar. To set one's cap at or for (1773) means "use measures to gain the regard or affection of," usually in reference to a woman seeking a man's courtship.

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Trafalgar 
cape in southwestern Spain, from Arabic taraf-al-garb "end of the west," or taraf-agarr "end of the column" (in reference to the pillars of Hercules). The British naval victory over the French there was fought Oct. 21, 1805; hence London's Trafalgar Square, named in commemoration of it.
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Bushman (n.)
one of an aboriginal tribe near the Cape of Good Hope, 1785, from South African Dutch boschjesman, literally "man of the bush," from boschje, from Dutch bosje, diminutive of bosch, bos (see bush (n.)).
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