Oh! Thank you! The Quadrille connection is interesting!
"The quadrille (in French quadrille de contredanses) was now a lively dance with four couples, arranged in the shape of a square, with each couple facing the center of that square. One pair was called the head couple, the other pairs the side couples. A dance figure was often performed first by the head couple, and then repeated by the side couples. In the original French version only two couples were used, but two more couples were eventually added to form the sides of a square. The couples in each corner of the square took turns, in performing the dance, where one couple danced, and the other couples rested. Terms used in the quadrille are mostly the same as those in ballet. Dance figures have names such as jeté, chassé, croisé, plié, arabesque, and so on."
That is interesting. I had not known quadrille was its own type of dance.
In terms of the Larousee definition though, also remember that in French the lowest rank in the corps de ballet is still/now called quadrille. (Ranks at POB: quadrille, coryphée, sujet, premier danseur, étoile)