1773, "lively square dance for four couples," from Fr. quadrille,
originally one of four groups of horsemen in a tournament (a sense attested in Eng. from 1738), from Sp. cuadrilla,
dim. of cuadro
"four-sided battle square," from L. 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 a popular card game for four hands (1726).
"Quadrille began to take the place of ombre as the fashionable card game about 1726, and was in turn superseded by whist." [OED]