Etymology
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imbroglio (n.)

1750, "a jumble;" 1818 as "complicated misunderstanding, intricate entanglement" (of persons, nations, etc.), from Italian imbroglio, from imbrogliare "confuse, tangle," from assimilated form of in- "into, in, on, upon" (from PIE root *en "in") + brogliare "embroil," probably from French brouiller "confuse" (see broil (v.2); also compare embroil).

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broil (v.2)
early 15c., "to quarrel, brawl," also "mix up, present in disorder," from Anglo-French broiller "mix up, confuse," Old French brooillier "to mix, mingle," figuratively "to have sexual intercourse" (13c., Modern French brouiller), perhaps from breu, bro "stock, broth, brew," from Frankish or another Germanic source (compare Old High German brod "broth"), from PIE root *bhreu- "to boil, bubble, effervesce, burn." Compare Italian brogliare "to stir, disorder" (see imbroglio).
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*bhreu- 
also *bhreuə-, *bhreəu-, Proto-Indo-European root meaning "to boil, bubble, effervesce, burn," with derivatives referring to cooking and brewing.

It forms all or part of: barm; barmy; bourn (n.1) "small stream;" braise; bratwurst; brawn; brawny; braze (v.1) "to expose to the action of fire;" brazier; Brazil; bread; breed; brew; broth; broil (v.2) "to quarrel, brawl;" brood; effervesce; effervescence; effervescent; embroil; ferment; fervent; fervid; fervor; imbroglio.

It is the hypothetical source of/evidence for its existence is provided by: Sanskrit bhurnih "violent, passionate;" Greek phrear "well, spring, cistern;" Latin fervere "to boil, foam," Thracian Greek brytos "fermented liquor made from barley;" Russian bruja "current;" Old Irish bruth "heat;" Old English breowan "to brew," beorma "yeast;" Old High German brato "roast meat."
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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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