Etymology
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Words related to quadri-

quadru- 

word-forming element meaning "four, having four, consisting of four," a variant of quadri- which was used in Latin especially before -p-, from an older form of the element which perhaps was influenced later by tri-.

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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.
quadraphonic (adj.)

1969, irregular hybrid formation from Latin-derived quadri- "four" + phonic, from Greek phonē "sound, voice" (from PIE root *bha- (2) "to speak, tell, say"). 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. Quadrasonic (1970) was at least not a hybrid. Related: Quadraphonics; quadraphony.

quadrennial (adj.)

1650s, "lasting four years, comprising four years;" as "happening once in four years," 1701; from quadri- + ending from biennial, etc. Correct formation would be quadriennial (compare Latin quadriennium "period of four years," which also is sometimes used in English). As a noun from 1640s. Quadrennium as "a period of four years" is by 1735. Related: Quadrennially.

quadricentennial 

"pertaining to or consisting of a period of 400 years," as a noun, "commemoration or celebration of an event which occurred 400 years ago," also quadri-centennial, 1859, from quadri- + centennial. Alternative quater-centennial (1868, meaning "four times a year") is from Latin quater "four times" (compare quaternary).

quadricep (n.)

large extensor muscle of the thigh, 1840, Modern Latin, from quadri- on model of bicep (q.v.). Related: Quadriceps. So called because divided into four parts.

quadricipital (adj.)

"having four heads or points of origin," by 1853, in reference to muscles, from Modern Latin; see quadri- "four" + Latin caput (genitive capitis) "head" (from PIE root *kaput- "head").

quadricorn (adj.)

"having four horns," 1875; also, as a noun, "a four-horned animal or insect" (1848); see quadri- "four" + Latin cornus "horn" (from PIE root *ker- (1) "horn; head"). Alternative quadrucorn is older (c. 1600).

quadrifid (adj.)

"having four lobes; deeply cut, but not entirely divided, into four parts," 1660s, from quadri- "four" + -fid.

quadrifoliate (adj.)

in botany, "four-leafed," by 1845; see quadri- "four" + foliate (adj.).