"to cut in quarters, divide into four equal parts," mid-14c., from quarter (n.1). From late 14c. specifically as the word for a form of criminal punishment (Old English had slitcwealm "death by rending"). Related: Quartered; quartering. Middle English also had a verb quartle "to divide into four parts" (late 14c.).
The meaning "furnish with lodgings, shelter, etc. as a temporary means of living" is recorded from 1590s (see quarters), often specifically "to put up soldiers" under orders from authority.
"indulgence or mercy shown to a vanquished foe; exemption from being immediately killed upon being defeated in battle or armed contest," 1610s, presumably from quarter (n.1) or its French equivalent quartier in this meaning, but OED writes that "the precise origin of this sense is obscure ...." It suggests quarter in a now-obsolete sense of "relations with, or conduct towards, another" (attested from 1640s), or possibly quarter in the sense of "place of stay or residence" (compare quarters), on the notion of sending the vanquished to an assigned place until his fate is decided. German quartier, Swedish quarter, Danish kvarteer, etc. probably are from French.
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.
1620s, "the part of the spar-deck of a man-of-war between the poop and the main-mast," originally "a smaller deck above the half-deck," covering about a quarter of the vessel [OED], from quarter (n.1).
"It is used as a promenade by the officers only" [Century Dictionary], hence the colloquial nautical noun quarter-decker (by 1867) "an officer who is more looked upon as a stickler for small points of etiquette than as a thorough seaman."
mid-15c., "day that begins a quarter of the year," designated as days when rents were paid and contracts and leases began or expired, from quarter (n.1). They were, in England, Lady day (March 25), Midsummer day (June 24), Michaelmas day (Sept. 29), and Christmas day (Dec. 25); in Scotland, keeping closer to the pre-Christian Celtic calendar, they were Candlemas (Feb. 2), Whitsunday (May 15), Lammas (Aug. 1), and Martinmas (Nov. 11). Quarter in the sense "period of three months; one of the four divisions of a year" is recorded from late 14c. Related: Quarter days.
"military dwelling place," 1590s, from quarter (n.1) in sense of "portion of a town." As "part of an American plantation where the slaves live," from 1724. The military sense seems to be also the source of quartermaster and it might be behind the phrase give quarter "spare from immediate death" (1610s, often in the negative), on the notion of "provide a prisoner with shelter;" see quarter (n.2).
early 15c., quarterli, "four times a year, once a quarter," from quarter (n.1) + -ly (2). As an adjective from mid-15c., "occupying alternate quarters" (of a coat of arms), with -ly (1). As a noun, "a quarterly publication," from 1830, from the adjective. Earlier the adverb was used in a now-obsolete sense of "into quarters" (c. 1400).
As a verb, "to play quarterback," by 1945. The figurative sense (the quarterback when on the field typically directed the team's plays) is from 1952. Monday morning quarterback is by 1932 as a noun, "second-guesser of other people's decisions, one who criticizes or passes judgment afterward on how something was done;" by 1972 as a verb; originally pro football player slang for sportswriters (U.S. professional football games typically were played on Sundays).
late 14c., sessioun, "periodical sitting of a court," from Old French session "act or state of sitting; assembly," from Latin sessionem (nominative sessio) "act of sitting; a seat; loitering; a session," noun of action from past-participle stem of sedere "to sit" (from PIE root *sed- (1) "to sit").
By 1550s in the general sense of "the time or term during which a legislature, etc. meets daily for business." The still more general sense of "period set aside for some activity" is recorded by 1920, in bull session, which probably is extended from quarter sessions courts (see quarter (n.1)).
The musical sense of "recording occasion in a studio" is from 1927. The literal classical sense has been rare in English except in theology, of Christ's enthronement at the right hand of the Father (early 15c.). Related: Sessional.
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.