Etymology
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firkin (n.)

"small cask," late 14c., apparently from Middle Dutch *vierdekijn, diminutive of vierde, literally "fourth, fourth part" (from vier "four," from PIE root *kwetwer- "four"); so called because it usually is the fourth part of a barrel.

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quartan (adj.)

"having to do with the fourth," especially of attacks of an intermittent fever, etc., "occurring every fourth day" (by inclusive reckoning; now we would say every third day), early 14c., (feuer) quartain, from Old French (fievre) quartaine or cartaine and directly from Latin (febris) quartana, "quartan (fever)," fem. of quartanus "of or belonging to the fourth; of or occurring on the fourth day," from quartus "the fourth, fourth part" (related to quattuor "four," from PIE root *kwetwer- "four").

Also as a noun, "an ague or fever which recurs on the fourth (third) day," late 14c. Under inclusive reckoning, both days of consecutive occurrence are counted (if you have it on Wednesday and again on Saturday, the ancients would count that as "every four days"). 

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quartet (n.)

also quartette, 1773, "musical composition for four solo instruments or voices," from French quartette, from Italian quartetto, diminutive of quarto "fourth," from Latin quartus "the fourth, fourth part" (related to quattuor "four," from PIE root *kwetwer- "four"). Meaning "set of four singers or musical players who perform quartets" is from 1814.

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quarto (n.)

"book from paper folded twice to make four pages to the sheet, size of book in which the leaf is one-fourth of a certain size of paper," late 15c., in the phrase in quarto, from Medieval Latin in quarto "in the fourth (part of a sheet of paper)," from quarto, ablative singular of Latin quartus "the fourth, fourth part" (related to quattuor "four," from PIE root *kwetwer- "four").

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quadroon (n.)

by 1781, an alteration (by influence of words in quadr-) of quarteroon (1707), "offspring of a white and a mulatto," from Spanish cuarteron (used chiefly of the offspring of a European and a mestizo), literally "one who has a fourth" (Negro blood), from cuarto "fourth," from Latin quartus "the fourth, fourth part," which is related to quattuor "four" (from PIE root *kwetwer- "four").

So called because he or she has one quarter African blood. There also was some use in 19c. of quintroon (from Spanish quinteron) "one who is fifth in descent from a Negro; one who has one-sixteenth Negro blood." OED lists quarter-caste as an Australian and New Zealand term for a person whose ancestry is one-quarter Aboriginal or Maori and 3/4 white (1948).

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hemidemisemiquaver (n.)

"sixty-fourth note" in music, 1846, from hemi- + demi- + semi- + quaver (n.).

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quartile (adj.)

mid-15c., "90 degrees apart" (of the relative position of two heavenly bodies in astronomical measurements), from Old French quartil, from Medieval Latin quartilus "of a quartile," from Latin quartus "the fourth, fourth part" (related to quattuor "four," from PIE root *kwetwer- "four").

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carat (n.)

also karat, late 15c., "a measure of the fineness of gold," from Old French carat "measure of the fineness of gold" (14c.), from Italian carato or Medieval Latin carratus, both from Arabic qirat "fruit of the carob tree," also "weight of 4 grains," from Greek keration "carob seed," also the name of a small weight of measure, literally "little horn" diminutive of keras "horn of an animal" (from PIE root *ker- (1) "horn; head").

Carob beans were a standard in the ancient world for weighing small quantities. The Greek measure was the equivalent of the Roman siliqua, which was one-twenty-fourth of a golden solidus of Constantine; hence karat took on a sense of "a proportion of one twenty-fourth, a twenty-fourth part," especially in expressing the fineness of gold when used as jewelry, and thus it became a measure of gold purity (1550s): 18-carat gold is eighteen parts gold, six parts alloy; 14-carat gold is 10/24ths alloy, etc.

As a measure of weight for diamonds or other precious stones, carat is attested from 1570s in English. In U.S., karat is used for "proportion of fine gold in an alloy" and carat for "measure of weight of a precious stone."

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staggard (n.)

"stag in its fourth year," thus not quite full-grown, c. 1400, from stag + -ard.

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home front (n.)

also homefront, 1918, from home (n.) + front (n.) in the military sense. A term from World War I; popularized (if not coined) by the agencies running the U.S. propaganda effort.

The battle front in Europe is not the only American front. There is a home front, and our people at home should be as patriotic as our men in uniform in foreign lands. [promotion for the Fourth Liberty Loan appearing in U.S. magazines, fall 1918]
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