Etymology
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broth (n.)

"liquid in which flesh is boiled," Old English broþ, from Proto-Germanic *bruthan (source also of Old High German *brod, Old Norse broð), from verb root *bhreue- "to heat, boil, bubble;" also "liquid in which something has been boiled" (from PIE root *bhreu- "to boil, bubble, effervesce, burn"). Picked up from Germanic by the Romanic and Celtic languages (Italian brodo, Spanish brodio, Old French breu, Irish broth, Gaelic brot).

The Irishism broth of a boy, which is in Byron, was "thought to originate from the Irish Broth, passion — Brotha passionate, spirited ..." [Farmer], and if so is not immediately related, but rather, with Scottish braith, from Middle English bratthe "violence, impetuosity; anger, rage" (c. 1200), which is from Old Norse braðr "sudden, hasty," from brað "haste."

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brose (n.)

Scottish dish of boiling milk, liquid in which meat has been broiled, seasoning, etc., poured over oatmeal or barley meal, 1650s, Scottish, earlier browes, from Old French broez, nominative of broet (13c.) "stew, soup made from meat broth," diminutive of breu, from Medieval Latin brodium, from Old High German brod "broth" (see broth). Athol brose (1801) was "honey and whisky mixed together in equal parts," taken as a cure for hoarseness or sore throat.

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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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juice (n.)

c. 1300, jus, juis, jouis, "liquid obtained by boiling herbs," from Old French jus "juice, sap, liquid" (13c.), from Latin ius "broth, sauce, juice, soup," from PIE root *yeue- "to blend, mix food" (cognates: Sanskrit yus- "broth," Greek zymē "a leaven," Old Church Slavonic jucha "broth, soup," Lithuanian jūšė "fish soup"). Meaning "the watery part of fruits or vegetables" is from early 14c. Meaning "liquor" is from 1828; that of "electricity" is first recorded 1896.

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soup (n.)

"liquid food," 1650s, from French soupe "soup, broth" (13c.), from Late Latin suppa "bread soaked in broth," from a Germanic source (compare Middle Dutch sop "sop, broth"), from Proto-Germanic *sup-, from PIE *sub-, from root *seue- (2) "to take liquid" (see sup (v.2)).

Primordial soup is from a concept first expressed 1929 by J.B.S. Haldane. Soup to nuts "everything" is from 1910. Soup-kitchen, "public establishment supported by voluntary contributions, for preparing and serving soup to the poor at no cost" is attested from 1839. In Ireland, souper meant "Protestant clergyman seeking to make proselytes by dispensing soup in charity" (1854).

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puree (n.)

kind of broth or soup made from vegetables, etc., boiled to a pulp and passed through a sieve, 1707, from French purée, a word of disputed and uncertain origin. Compare porridge.

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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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potage (n.)

"thick soup," 1560s, from French potage "soup, broth" (see pottage, which is an earlier English borrowing of the same French word and originally also was spelled with one -t-). Related: Potager.

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bouillon (n.)

broth or soup from boiled beef or other meat, 1650s, from French bouillon (11c.), noun use of past participle of bouillir "to boil," from Old French bolir (see boil (v.)).

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dish-water (n.)

also dishwater, "water in which dishes have been washed," late 15c., from dish (n.) + water (n.1). Used figuratively of weak broth, coffee, etc. from 1719. Earlier in Middle English was dischwaschyngs (c. 1300).

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