When a right triangle with one side of those about the right angle remains fixed is carried round and restored again to the same position from which it began to be moved, the figure so comprehended is a cone. And, if the straight line which remains fixed equals the remaining side about the right angle which is carried round, the cone will be right-angled; if less, obtuse-angled; and if greater, acute-angled.

The axis of the cone is the straight line which remains fixed and about which the triangle is turned.

And the base is the circle described by the straight line which is carried round.

The right triangle ABC with right angle at A is rotated about the side AC to produce a cone. The axis of the cone is AC, and its base is the circle with center at A and radius AB.
The three different kinds of cone are not used by Euclid in the |