Etymology
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sauce (n.)
mid-14c., from Old French sauce, sausse, from Latin salsa "things salted, salt food," noun use of fem. singular or neuter plural of adjective salsus "salted," from past participle of Old Latin sallere "to salt," from sal (genitive salis) "salt" (from PIE root *sal- "salt").

Meaning "something which adds piquancy to words or actions" is recorded from c. 1500; sense of "impertinence" first recorded 1835 (see saucy, and compare sass). Slang meaning "liquor" first attested 1940.
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sauce (v.)
mid-15c., "to season," from sauce (n.). From 1862 as "to speak impertinently." Related: Sauced; saucing.
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apple-sauce (n.)
also applesauce, by 1739, American English, from apple + sauce (n.). Slang meaning "nonsense" is attested from 1921 and was noted as a vogue word early 1920s. Mencken credits it to cartoonist T.A. ("Tad") Dorgan. DAS suggests the word was thus used because applesauce was cheap fare served in boardinghouses.
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saucebox (n.)
"one addicted to making saucy remarks," 1580s, from sauce (n.) + box (n.1).
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saucepan (n.)
1680s, from sauce (n.) + pan (n.). Originally a pan for cooking sauces.
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sass (n.)
"impudence," 1835, back-formation from sassy. The verb is first recorded 1856, from the noun. Related: Sassed; sassing. Sass (n.) as a variant of sauce is attested from 1775.
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salsa (n.)
kind of sauce, 1846; kind of dance music, 1975, from Spanish, literally "sauce," from Vulgar Latin *salsa "condiment" (see sauce (n.)). In American Spanish especially used of a kind of relish with chopped-up ingredients; the music so called from its blend of Latin jazz and rock styles.
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saucy (adj.)
c. 1500, "resembling sauce," later "impertinent, flippantly bold, cheeky" (1520s), from sauce (n.) + -y (2). The connecting notion is the figurative sense of "piquancy in words or actions." Compare sauce malapert "impertinence" (1520s), and slang phrase to have eaten sauce "be abusive" (1520s). Also compare salty in same senses.
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saucer (n.)
mid-14c., from Anglo-Latin saucerium and Old French saussier (Modern French saucière) "sauce dish," from Late Latin salsarium, neuter of salsarius "of or for salted things," from Latin salsus (see sauce (n.)). Originally a small dish or pan in which sauce is set on a table. Meaning "small, round, shallow vessel for supporting a cup and retaining any liquid which might be spilled" is attested from c. 1702.
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*sal- 
Proto-Indo-European root meaning "salt."

It forms all or part of: hali-; halide; halieutic; halite; halo-; halogen; sal; salad; salami; salary; saline; salmagundi; salsa; salsify; salt; salt-cellar; saltpeter; sauce; sausage; silt; souse.

It is the hypothetical source of/evidence for its existence is provided by: Greek hals "salt, sea;" Latin sal, Old Church Slavonic soli, Old Irish salann, Welsh halen, Old English sealt, German Salz "salt."
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