Etymology
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farthing (n.)

Old English feorðing (Old Northumbrian feorðung) "quarter of a penny; a fourth part," a diminutive derivative of feorða "fourth" (from feower "four;" from PIE root *kwetwer- "four") + -ing "fractional part." Cognate with Old Frisian fiardeng, Middle Low German verdink, Old Norse fjorðungr, Old Danish fjerdung "a fourth part of anything."

In late Old English also a division of land, probably originally a quarter of a hide. The modern English coin first was minted under Edward I and abolished 1961. The word was used in biblical translations for Latin quadrans "quarter of a denarius."

I shall geat a fart of a dead man as soone As a farthyng of him. [Heywood, "Proverbs," 1562]
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pennyfarthing (adj.)

also penny farthing, penny-farthing, "ineffective," 1887, from penny + farthing, the two together making but a small sum. The noun, in reference to the kind of bicycle with a small wheel in back and a big one in front (so called from the notion of different size coins) is attested by 1920.

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-ling 
diminutive word-forming element, early 14c., from Old English -ling a nominal suffix (not originally diminutive), from Proto-Germanic *-linga-; attested in historical Germanic languages as a simple suffix, but probably representing a fusion of two suffixes: 1. that represented by English -el (1), as in thimble, handle; and 2. -ing, suffix indicating "person or thing of a specific kind or origin;" in masculine nouns also "son of" (as in farthing, atheling, Old English horing "adulterer, fornicator"), from PIE *-(i)ko- (see -ic).

Both these suffixes had occasional diminutive force, but this was only slightly evident in Old English -ling and its equivalents in Germanic languages except Norse, where it commonly was used as a diminutive suffix, especially in words designating the young of animals (such as gæslingr "gosling"). Thus it is possible that the diminutive use that developed in Middle English is from Old Norse.
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shilling (n.)

English monetary unit, Middle English shilling, from Old English scilling, scylling, a coin of account consisting of a varying number of pence (on the continent and in England after the Conquest, commonly 12 pennies to a shilling, 20 shillings to a pound), from Proto-Germanic *skillingoz- (source also of Old Saxon, Danish, Swedish, Old Frisian, Old High German skilling, Old Norse skillingr, Dutch schelling, German Schilling, Gothic skilliggs).

Some etymologists trace this to the root *skell- "to resound, to ring," and others to the root *(s)kel- (1) "to cut" (perhaps via sense of "shield" from resemblance to one or as a device on coins (see shield (n.)) or from the cut or clipped segments of precious metal used as money).

The ending may represent the diminutive suffix -ling, or Germanic -ing "fractional part" (compare farthing). Old Church Slavonic skulezi, Polish szeląg, Spanish escalin, French schelling, Italian scellino are loan-words from Germanic. The modern English silver shilling dates to Henry VII.

Reckoning by the shilling is still not uncommon in some parts of the United States, especially in rural New England. [Century Dictionary, 1891]
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*kwetwer- 
Proto-Indo-European root meaning "four."

It forms all or part of: cadre; cahier; carillon; carrefour; catty-cornered; diatessaron; escadrille; farthing; firkin; fortnight; forty; four; fourteen; fourth; quadrant; quadraphonic; quadratic; quadri-; quadrilateral; quadriliteral; quadrille; quadriplegia; quadrivium; quadroon; quadru-; quadruped; quadruple; quadruplicate; quarantine; quarrel (n.2) "square-headed bolt for a crossbow;" quarry (n.2) "open place where rocks are excavated;" quart; quarter; quarterback; quartermaster; quarters; quartet; quarto; quaternary; quatrain; quattrocento; quire (n.1) "set of four folded pages for a book;" squad; square; tessellated; tetra-; tetracycline; tetrad; tetragrammaton; tetrameter; tetrarch; trapezium.

It is the hypothetical source of/evidence for its existence is provided by: Sanskrit catvarah, Avestan čathwaro, Persian čatvar, Greek tessares, Latin quattuor, Oscan petora, Old Church Slavonic četyre, Lithuanian keturi, Old Irish cethir, Welsh pedwar.
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quarter (n.1)

c. 1300, "one-fourth of anything; one of four equal parts or divisions into which anything is or may be divided;" often in reference to the four parts into which a slaughtered animal is cut, from Old French quartier, cartier (12c.), from Latin quartarius "fourth part," from quartus "the fourth, fourth part" (related to quattuor "four," from PIE root *kwetwer- "four"). One of the earliest dated references in English is to "parts of the body as dismembered during execution" (c. 1300).

Used of the phases of the moon from early 15c. The phrase quarter of an hour is attested from mid-15c. In Middle English quarter also meant "one of the four divisions of a 12-hour night" (late 14c.), and the quarter of the night meant "nine o'clock p.m." (early 14c.). As a period of time in a football game, from 1911. 

From late 14c. as "one of the four quadrants of the heavens;" hence, from the notion of the winds, "a side, a direction" (c. 1400). In heraldry from mid-14c. as "one of the four divisions of a shield or coat of arms."

Meaning "region, locality, area, place" is from c. 1400. Meaning "distinct portion of a town" (identified by the class or race of people who live there) is first attested 1520s. For military sense, see quarters.

The coin (one fourth of a dollar, originally silver) is peculiar to U.S. and dates to 1783. But quarter could mean "a farthing" (one quarter of a penny) in Middle English (late 14c.), and compare quadrant "a farthing" (c. 1600), and classical Latin quadrans, the name of a coin worth a quarter of an as (the basic unit of Roman currency).

Quarter horse, bred strong for racing on quarter-mile tracks, is recorded by 1834. The word's connection with "four" loosened in Middle English and by 15c. expressions such as six-quartered for "six-sided" are found.  

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farthingale (n.)

contrivance for extending the skirts of women's dresses, formerly also vardingale, etc., 1550s, from French verdugale, from Spanish verdugado "hooped, hooped skirt," from verdugo "rod, stick, young shoot of a tree," from verde "green," from Latin viridis (see verdure). Originally made with cane hoops or rods. The form perhaps influenced by martingale.

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care (v.)

Old English carian, cearian "be anxious or solicitous; grieve; feel concern or interest," from Proto-Germanic *karo- "lament," hence "grief, care" (source also of Old Saxon karon "to lament, to care, to sorrow, complain," Old High German charon "complain, lament," Gothic karon "be anxious"), said to be from PIE root *gar- "cry out, call, scream" (source also of Irish gairm "shout, cry, call;" see garrulous).

If so, the prehistoric sense development is from "cry" to "lamentation" to "grief." A different sense evolution is represented in related Dutch karig "scanty, frugal," German karg "stingy, scanty." It is not considered to be related to Latin cura. Positive senses, such as "have an inclination" (1550s); "have fondness for" (1520s) seem to have developed later as mirrors to the earlier negative ones.

To not care as a negative dismissal is attested from mid-13c. Phrase couldn't care less is from 1946; could care less in the same sense (with an understood negative) is from 1955. Care also has figured since 1580s in many "similies of indifference" in the form don't care a _____, with the blank filled by fig, pin, button, cent, straw, rush, point, farthing, snap, etc., etc. Related: Cared; caring.

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Q 

16th letter of the classical Roman alphabet, occurring in English only before a -u- that is followed by another vowel (with a few exceptions; see below), whether the -u- is sounded or not (pique). The letter is from the Phoenician equivalent of Hebrew koph, qoph, which was used for the deeper and more guttural of the two "k" sounds in Semitic. The letter existed in early Greek (where there was no such distinction), and called koppa, but it was little used and not alphabetized; it mainly served as a sign of number (90).

The connection with -u- began in Latin. Anglo-Saxon scribes at first adopted the habit, but later used spellings with cw- or cu-. The qu- pattern returned to English with the Normans and French after the Conquest and had displaced cw- by c. 1300.

In some spelling variants of late Middle English, quh- also took work from wh-, especially in Scottish and northern dialects, for example Gavin Douglas, Provost of St. Giles, in his vernacular "Aeneid" of 1513:

Lyk as the rois in June with hir sueit smell
The marygulde or dasy doith excell.
Quhy suld I than, with dull forhede and vane,
With ruide engine and barrand emptive brane,
With bad harsk speche and lewit barbour tong,
Presume to write quhar thi sueit bell is rong,
Or contirfait sa precious wourdis deir?

Scholars use -q- alone to transliterate Semitic koph or the equivalent in Turkish or Iranian (as in Quran, Qatar, Iraq). In Christian theology, Q has been used since 1901 to signify the hypothetical source of passages shared by Matthew and Luke but not in Mark; in this sense probably it is an abbreviation of German Quelle "source" (from Old High German quella, from the same Proto-Germanic source as Old English cwiella, cwylla"spring; well"). In Middle English accounts, it is an abbreviation of quadrans "farthing" (mid-15c.). In Roman personal names it is an abbreviation of Quintus.

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gazette (n.)

"newspaper," c. 1600, from French gazette (16c.), from Italian gazzetta, Venetian dialectal gazeta "newspaper," also the name of a small copper coin, literally "little magpie," from gazza; applied to the monthly newspaper (gazeta de la novità) published in Venice by the government, either from its price or its association with the bird (typical of false chatter), or both. First used in English 1665 for the paper issued at Oxford, whither the court had fled from the plague.

The coin may have been so called for its marking; Gamillscheg writes the word is from French gai (see jay). The general story of the origin of the word is broadly accepted, but there are many variations in the details:

We are indebted to the Italians for the idea of newspapers. The title of their gazettas was, perhaps, derived from gazzera, a magpie or chatterer; or, more probably, from a farthing coin, peculiar to the city of Venice, called gazetta, which was the common price of the newspapers. Another etymologist is for deriving it from the Latin gaza, which would colloquially lengthen into gazetta, and signify a little treasury of news. The Spanish derive it from the Latin gaza, and likewise their gazatero, and our gazetteer, for a writer of the gazette and, what is peculiar to themselves, gazetista, for a lover of the gazette. [Isaac Disraeli, "Curiosities of Literature," 1835]
Gazzetta It., Sp. gazeta, Fr. E. gazette; prop. the name of a Venetian coin (from gaza), so in Old English. Others derive gazette from gazza a magpie, which, it is alleged, was the emblem figured on the paper; but it does not appear on any of the oldest Venetian specimens preserved at Florence. The first newspapers appeared at Venice about the middle of the 16th century during the war with Soliman II, in the form of a written sheet, for the privilege of reading which a gazzetta (= a crazia) was paid. Hence the name was transferred to the news-sheet. [T.C. Donkin, "Etymological Dictionary of the Romance Languages" (based on Diez), 1864]
GAZETTE. A paper of public intelligence and news of divers countries, first printed at Venice, about the year 1620, and so called (some say) because una gazetta, a small piece of Venetian coin, was given to buy or read it. Others derive the name from gazza, Italian for magpie, i.e. chatterer.—Trusler. A gazette was printed in France in 1631; and one in Germany in 1715. [Haydn's "Dictionary of Dates," 1857]
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