"a blank, low-cast type used by typographers to fill in larger spaces at the end of or between printed lines," 1680s, from French quadrat "a quadrat," literally "a square," from Latin quadratrus, past participle of quadrare "to make square," related to quadrus "a square," quattuor "four" (from PIE root *kwetwer- "four"). Earlier in English it meant a type of surveying instrument with a square plate (c. 1400).

1820 as a shortening of quadrangle (n.) in the building-court sense (in this case "quadrangle of a college," Oxford student slang); also in old slang the quadrangle of a jail or prison, where prisoners take their exercise. By 1880 as short for the printer's quadrat (n.). By 1896 as "a quadricycle, a bicycle for four riders" (quadricycle is attested by 1879, quadruplet in this sense by 1893). As "one of four young at a single birth" by 1951 (in reference to armadillos), short for quadruplet; 1970 as a shortening of quadraphonic (adj.). Related: Quads.

"a square-shaped muscle," 1727, from Latin quadratus "square, squared," past participle of quadrare "to square, make square; put in order," related to quadrus "a square," quattuor "four" (from PIE root *kwetwer- "four"). Especially the Quadratus femoris, the muscle situated at the back of the hip-joint.

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, make square; put in order," related to quadrus "a square," quattuor "four" (from PIE root *kwetwer- "four"). In mathematics by 1660s; the algebraic quadratic equations (1680s) are so called because they involve the square and no higher power of x.