Etymology
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insignia (n.)
1640s, from Latin insignia, neuter plural of insigne "badge of honor or office, mark, proof, sign, token," from in- "in" (from PIE root *en "in") + signum "identifying mark, sign" (see sign (n.)). The classically correct singular is insigne.
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ensign (n.)
early 15c., "a token, sign, symbol; badge of office, mark or insignia of authority or rank;" also "battle flag, flag or banner of a ship or troop of soldiers," via Scottish, from Old French enseigne (12c.) "mark, symbol, signal; flag, standard, pennant," from Latin insignia (plural); see insignia, which is a doublet of this word. As the word for the soldier who carries the flag, 1510s. U.S. Navy sense of "commissioned officer of the lowest rank" is from 1862. French navy had rank of enseigne de vaisseau at least since early 18c. Until 1871 one of the lowest grades of commissioned officers in a British army infantry regiment, also a rank in the American Revolutionary army.
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*en 
Proto-Indo-European root meaning "in."

It forms all or part of: and; atoll; dysentery; embargo; embarrass; embryo; empire; employ; en- (1) "in; into;" en- (2) "near, at, in, on, within;" enclave; endo-; enema; engine; enoptomancy; enter; enteric; enteritis; entero-; entice; ento-; entrails; envoy; envy; episode; esoteric; imbroglio; immolate; immure; impede; impend; impetus; important; impostor; impresario; impromptu; in; in- (2) "into, in, on, upon;" inchoate; incite; increase; inculcate; incumbent; industry; indigence; inflict; ingenuous; ingest; inly; inmost; inn; innate; inner; innuendo; inoculate; insignia; instant; intaglio; inter-; interim; interior; intern; internal; intestine; intimate (adj.) "closely acquainted, very familiar;" intra-; intricate; intrinsic; intro-; introduce; introduction; introit; introspect; invert; mesentery.

It is the hypothetical source of/evidence for its existence is provided by: Sanskrit antara- "interior;" Greek en "in," eis "into," endon "within;" Latin in "in, into," intro "inward," intra "inside, within;" Old Irish in, Welsh yn, Old Church Slavonic on-, Old English in "in, into," inne "within, inside."
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S.P.Q.R. 
the insignia of Rome, from Latin Senatus Populusque Romanus "the Senate and People of Rome."
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investiture (n.)
late 14c., "ceremony of clothing in the insignia of office," from Medieval Latin investitura "an investing," from past participle stem of Latin investire "to clothe" (see invest). Related: Investive.
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regalia (n.)

1530s, "rights and powers of a king, royal privilege," from Latin regalia "royal things," noun use of neuter plural of regalis from rex (genitive regis) "king" (from PIE root *reg- "move in a straight line," with derivatives meaning "to direct in a straight line," thus "to lead, rule").

The meaning "decorations or insignia of an order" is recorded from 1670s, probably via the sense of "the emblems or insignia of royalty," e.g. the crown, scepter, etc. (1620s).

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arm (n.2)

"weapon," c. 1300, armes (plural) "weapons of a warrior," from Old French armes (plural), "arms, weapons; war, warfare" (11c.), from Latin arma "weapons" (including armor), literally "tools, implements (of war)," from PIE *ar(ə)mo-, suffixed form of root *ar- "to fit together." The notion seems to be "that which is fitted together."

Meaning "branch of military service" is from 1798, hence "branch of any organization" (by 1952). Meaning "heraldic insignia" (in coat of arms, etc.) is early 14c., from Old French; originally they were borne on shields of fully armed knights or barons. To be up in arms figuratively is from 1704; to bear arms "do military service" is by 1640s.

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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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brass (n.)

"yellow malleable alloy metal, harder than copper," Old English bræs "brass, bronze," originally any alloy of copper, in England usually with tin (this is now called bronze), later and in modern use an alloy of roughly two parts copper to one part zinc. A mystery word, with no known cognates beyond English. Perhaps akin to French brasser "to brew," because it is an alloy. It also has been compared to Old Swedish brasa "fire," but no sure connection can be made. Yet another theory connects it with Latin ferrum "iron," itself of obscure origin.

Words for "brass" in other languages (such as German Messing, Old English mæsling, French laiton, Italian ottone) also tend to be difficult to explain. As brass was unknown in early antiquity (it was well-known to Strabo, 1c., but not mentioned by Homer), the use of the English word in Bible translations, etc., likely means "bronze." The Romans were the first to deliberately make it.

When works of Greek and Roman antiquity in 'brass' began to be critically examined, and their material discriminated, the Italian word for 'brass' (bronzo, bronze) came into use to distinguish this 'ancient brass' from the current alloy. [OED]

Rhetorically or figuratively it was the common type of hardness, durability, or obduracy since late 14c. The meaning "effrontery, impudence, excessive assurance" is from 1620s. Slang sense of "high officials" is first recorded 1899, from their insignia. Meaning "brass musical instruments of a band" is from 1832.

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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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