Monday (n.)youdaoicibaDictYouDict[Monday 词源字典]
second day of the week, Old English mondæg, monandæg "Monday," literally "day of the moon," from mona (genitive monan; see moon (n.)) + dæg (see day). Common Germanic (Old Norse manandagr, Old Frisian monendei, Dutch maandag, German Montag) loan-translation of Late Latin Lunæ dies, source of the day name in Romance languages (French lundi, Italian lunedi, Spanish lunes), itself a loan-translation of Greek selenes hemera. The name for this day in Slavic tongues generally means "day after Sunday."

Phrase Monday morning quarterback is attested from 1932, Monday being the first day back at work after the weekend, when school and college football games were played. Black Monday (mid-14c.) is the Monday after Easter day, though how it got its reputation for bad luck is a mystery. Saint Monday (1753) was "used with reference to the practice among workmen of being idle Monday, as a consequence of drunkenness on the Sunday" before [OED]. Clergymen, meanwhile, when indisposed complained of feeling Mondayish (1804) in reference to effects of Sunday's labors.[Monday etymology, Monday origin, 英语词源]
quarter (n.)youdaoicibaDictYouDict
c. 1300, "one-fourth of anything; one of four parts or divisions of a thing;" 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 "fourth" (see quart). 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 use of 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.).

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." The word's connection with "four" loosened in Middle English and by 15c. expressions such as six-quartered for "six-sided" are found. Meaning "region, locality, area, place" is from c. 1400. Meaning "portion of a town" (identified by the class or race of people who live there) is first attested 1520s. For military sense, see quarters. As a period of time in a football game, from 1911. Quarter horse, bred strong for racing on quarter-mile tracks, first recorded 1834.

The coin (one fourth of a dollar) is peculiar to U.S., first recorded 1783. But quarter could mean "a farthing" in Middle English (late 14c.), and compare British 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 days (mid-15c.), designated as days when rents were paid and contracts and leases began or expired, 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 pagan 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.
quarterback (n.)youdaoicibaDictYouDict
in U.S. football, 1876, from quarter (n.) + back (n.); so called from his position on the field at the start of play, between the halfback and the center. As a verb from 1945. Figurative sense from 1952. Monday morning quarterback is 1932 (n.), 1972 (v.); originally pro football player slang for sportswriters (U.S. professional football games typically are played on Sundays).