Definition 5
A surface is that which has length and breadth only.
This statement suggests that a surface has two dimensions, but says very little, if anything, since neither length nor breadth have been defined yet, nor will they be. From the next definition, it is clear that a surface does not have to be a plane. Other examples of surfaces that appear in the Elements are surfaces of cones, cylinders, and spheres.
Book I Introduction -
Definition 4 -
Definition 6.
© 1996
D.E.Joyce
Clark University