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quadrangular (adj.)[quadrangular 词源字典]: early 15c., from Medieval Latin quadrangularis "having four corners," from Late Latin quadrangulus (see quadrangle).[quadrangular etymology, quadrangular origin, 英语词源]
quadrant (n.): late 14c., "a quarter of a day, six hours," from Middle French quadrant, from Latin quadrantem (nominative quadrans) "fourth part," also the name of a coin worth a quarter of an as, noun use of present participle of quadrare "to make square; put in order, arrange, complete; run parallel, be exact," figuratively "to fit, suit, be proper," related to quadrus "a square," quattuor "four" (see four). The surveying instrument is first so called c. 1400, because it forms a quarter circle. Related: Quadrantal.
quadraphonic (adj.): 1969, irregular formation from quadri- "four" + phonic, from Greek phone "sound, voice," from PIE root *bha- (2) "to speak, tell, say" (see fame (n.)). The goal was to reproduce front-to-back sound distribution in addition to side-to-side stereo. The later term for the same idea, surround sound, is preferable to this.
quadrat (n.): "a blank, low-cast type used by typographers to fill in larger spaces in printed lines," 1680s, from French quadrat "a quadrat," literally "a square," from Latin quadratrus, past participle of quadrare "to square, make square" (see quadrant). Earlier in English it meant a type of surveying instrument (c. 1400).
quadratic (adj.): 1650s, "square," with -ic + obsolete quadrate "a square; a group of four things" (late 14c.), from Latin quadratum, noun use of neuter adjective quadratus "square, squared," past participle of quadrare "to square, set in order, complete" (see quadrant). Quadratic equations (1660s) so called because they involve the square of x.
quadratus (n.): "square-shaped muscle," 1727, from Latin quadratus "square, squared" (see quadratic).
quadrennial (adj.): 1650s, "lasting four years;" as "happening once every four years," 1701; from quadri- + ending from biennial, etc. Correct formation would be quadriennial (compare Latin quadriennium "period of four years"). As a noun from 1640s. Related: Quadrennially.
quadri-: before vowels quad- (before -p- often quadru-, from an older form in Latin), word-forming element meaning "four, four times, having four, consisting of four," from Latin quadri-, related to quattor "four" (see four).
quadricentennial (n.): also quadri-centennial, 1859, from quadri- + centennial.
quadricep (n.): large extensor muscle of the leg, 1840, from quadri- on model of bicep. Related: Quadriceps. So called because divided into four parts.
quadriceps (n.): 1840, see quadricep.
quadrifid (adj.): "divided in four parts," 1660s, from quadri- + -fid.
quadrilateral (n.): "four-sided," 1640s, with -al (1) + Latin quadrilaterus, from quadri- "four" (see quadri-) + latus (genitive lateris) "side" (see oblate (n.)). As an adjective from 1650s. Related: Quadrilaterally.
quadriliteral (adj.): "consisting of four letters," 1771, from quadri- + literal.
quadrille (n.): 1773, "lively square dance for four couples," from French quadrille (17c.), originally one of four groups of horsemen in a tournament (a sense attested in English from 1738), from Spanish cuadrilla, diminutive of cuadro "four-sided battle square," from Latin quadrum "a square," related to quattuor "four" (see four). The craze for the dance hit England in 1816, and it underwent a vigorous revival late 19c. among the middle classes.

Earlier the name of a popular card game for four hands, and in this sense from French quadrille (1725), from Spanish cuartillo, from cuarto "fourth," from Latin quartus. OED notes it as fashionable from 1726 ("and was in turn superseded by whist"), the year of Swift's (or Congreve's) satirical ballad on the craze:
The commoner, and knight, the peer,
Men of all ranks and fame,
Leave to their wives the only care,
To propagate their name;
And well that duty they fulfil
When the good husband's at Quadrille &c.
quadrillion (n.): 1670s, from French quadrillion (16c.) from quadri- "four" (see quadri-) + (m)illion. Compare billion. In Great Britain, the fourth power of a million (1 followed by 24 zeroes); in the U.S., the fifth power of a thousand (1 followed by 15 zeroes).
quadripartite (adj.): early 15c., from Latin quadripartitus, from quadri- "four" (see quadri-) + partitus, past participle of partiri "to divide" (see part (v.)).
quadriplegia (n.): 1895, a medical hybrid coined from Latin-based quadri- "four" + -plegia, as in paraplegia, ultimately from Greek plege "stroke," from root of plessein "to strike" (see plague (n.)). A correct, all-Greek formation would be *tetraplegia.
quadriplegic (adj.): also quadraplegic, 1897, from quadriplegia + -ic. A correct, all-Greek formation would be *tessaraplegic. The noun is first attested 1912, from the adjective.
quadrivium (n.): "arithmetic, music, geometry, astronomy," 1804 (see liberal arts), from Latin quadrivium, which meant "place where four roads meet, crossroads," from quadri- "four" (see quadri-) + via "way, road, channel, course" (see via). The adjective quadrivial is attested from late 15c. in English with the sense "having four roads."