"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").

"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).

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

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

1773, "lively square dance for four couples," consisting regularly of five complete parts, 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" (from PIE root *kwetwer- "four"). The craze for the dance hit England in 1816, and it underwent a vigorous revival late 19c. among the middle classes.

Earlier it was the name of a popular card game for four hands, and in this sense it is from French quadrille (1725), from Spanish cuartillo, from cuarto "fourth," from Latin quartus. OED notes it as fashionable ("and was in turn superseded by whist") from 1726, the year of Swift's (or Congreve's) satirical ballad on the craze: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.

"figure formed of four straight lines," 1640s, with -al (1) + Latin quadrilaterus, from quadri- "four" (from PIE root *kwetwer- "four") + latus (genitive lateris) "the side, flank of humans or animals, lateral surface," a word of uncertain origin. As an adjective, "four-sided, composed of four lines," from 1650s. Related: Quadrilaterally.

"consisting of four letters;" also, of Semitic roots, "consisting of four consonants," 1771, from quadri- "four" + literal.

1670s, from French quadrillion (16c.) from quadri- "four" (from PIE root *kwetwer- "four") + (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).

Thomas Hope, first of the family to possess the Deepdene, was the author of "Anastasius," a book of the same class as Beckford's "Vathek." In each case a millionaire (we shall soon have billionaires, trillionaires, quadrillionaires) fettered, imprisoned, by abject opulence, strove to reveal himself to the world through a romance. [Mortimer Collins, "A Walk Through Surrey," Temple Bar, August 1866]

early 15c., "divided into four parts," also "written in four identical versions" (of contracts, indentures, etc.), from Latin quadripartitus "divided into four parts, fourfold," from quadri- "four" (from PIE root *kwetwer- "four") + partitus, past participle of partiri "to divide" (from pars "a part, piece, a share," from PIE root *pere- (2) "to grant, allot"). Related: Quadripartition.

also quadraplegic, "person paralyzed in both arms and legs," 1897, from quadriplegia + -ic. A correct, all-Greek formation would be *tessaraplegic. The noun is first attested 1912, from the adjective.