SURFACE

A mathematical surface or superficies is defined by Euclid to be that which has only length and breadth. This definition excludes a line, which has length only; and a solid, which has length, breadth, and thickne . As a line is generated by the motion of a point, so a surface is generated by the motion of a line. If the generating line be a straight line, and move subject to the condition of having always two consecutive positions in the same plane, the surface generated is developable, and can be stretched out on a plane, as the surface of a cone, a cylinder, . But if the generating straight line is constrained to move so that no two of its consecutive positions are in the same plane, the surface cannot be developed on a plane. Such a surface is called by the French geometers surface gauche. [s. 1209]