"paralysis of both arms and legs," 1895, a medical hybrid coined from Latin-based quadri- "four" + -plegia, as in paraplegia, which is ultimately from Greek plege "stroke," from root of plēssein "to strike" (from PIE root *plak- (2) "to strike"). A correct, all-Greek formation would be *tetraplegia.

"going in four directions," 1820, from Latin quadrivius "of the crossroads," literally "going four ways," from quadrivium "crossroads" (see quadrivium).

"arithmetic, music, geometry, astronomy" (the four branches of mathematics, according to the Pythagoreans), by 1751, from Latin quadrivium, which meant "place where four roads meet, crossroads," from quadri- "four" (from PIE root *kwetwer- "four") + via "way, road, channel, course" (see via). Compare liberal arts, and also see trivium.

The adjective quadrivial is attested from mid-15c. in English with the sense of "belonging to the quadrivium," late 15c. with the sense of "having four roads, having four ways meeting in a point."

by 1781, an alteration (by influence of words in quadr-) of quarteroon (1707), "offspring of a white and a mulatto," from Spanish cuarteron (used chiefly of the offspring of a European and a mestizo), literally "one who has a fourth" (Negro blood), from cuarto "fourth," from Latin quartus "the fourth, fourth part," which is related to quattuor "four" (from PIE root *kwetwer- "four").

So called because he or she has one quarter African blood. There also was some use in 19c. of quintroon (from Spanish quinteron) "one who is fifth in descent from a Negro; one who has one-sixteenth Negro blood." OED lists quarter-caste as an Australian and New Zealand term for a person whose ancestry is one-quarter Aboriginal or Maori and 3/4 white (1948).

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-.

"a four-footed animal," especially "a four-footed mammal," 1640s, from French quadrupède (16c.), from Latin quadrupes (genitive quadrupedis) "four-footed, on all fours," also, as a noun, "a four-footed animal," from quadri- "four" (from PIE root *kwetwer- "four") + pes "foot" (from PIE root *ped- "foot").

The adjective is attested from 1741, "four-footed, having four limbs fitted for sustaining the body and locomotion, habitually going on all fours." Related: Quadrupedal (1610s). In zoology, quadrumane (from Latin manus "hand") was "a four-handed animal," in reference to monkeys, apes, lemurs, etc.; attested by 1786.

"to make fourfold, double twice," 1660s, from Latin quadruplicatus, past participle of quadruplicare "make fourfold," from quadri- "four" (from PIE root *kwetwer- "four") + plicare "to fold" (see ply (v.1)).  The sense of "make or provide in four identical versions" is by 1879. Related: Quadruplicated; quadruplicating.

"consisting of four parts, fourfold, four times told," 1550s, from French quadruple (13c.), from Latin quadruplus "fourfold," from quadri- "four" (from PIE root *kwetwer- "four") + -plus "-fold" (see -plus). Earlier in English as a noun, "a fourfold amount," early 15c., from Latin quadruplum.

late 14c., "to make four times as much or as many," from French quadrupler, from Late Latin quadruplare "make fourfold, multiply by four," from Latin quadruplus (adj.) "quadruple, fourfold," from quadri- "four" (from PIE root *kwetwer- "four") + -plus "-fold" (see -plus). Intransitive sense of "become four times as much" is by 1776.

"fourfold, four times repeated," 1650s, from Latin quadruplicatus, past participle of quadruplicare "make fourfold," from quadri- "four" (from PIE root *kwetwer- "four") + plicare "to fold" (from PIE root *plek- "to plait").