The French term "quatrième" (ka-tree-EHM) is from the word "quatre," meaning "four." There are eight basic body positions in classical ballet and "quatrième" refers to the fourth position. Dancers traditionally learn the eight body positions when they begin training in ballet, and even professional dancers continue to conduct drills in the eight positions to achieve greater precision and flow.
The term "derrière" (dih-ree-AIR) means "back" and indicates that the moving leg extends backward. In contrast, when the working leg extends frontward or the dancer propels himself forward, the proper directional term is "devant," meaning "in front of" the body.
The term "quatrième derrière" suggests movement in a particular direction, so it is prefaced by the French term "à la," meaning "in the direction of." An extension of the leg that is "à la quatrième derrière" is therefore in the direction of the fourth position and backward.
The term "à la quatrième derrière" is a general term that allows for many variations. From fourth position, a dancer can extend the back leg in a simple tendu or brush along the floor. Alternatively, she may bring the foot to the knee and slowly extend it upward behind her in develope or she can brush it into the air swiftly in battement. The term also makes no reference to the position of the arms; indeed, there are numerous variations in the way the dancer positions her arms when moving "à la quatrième derrière."