Definition:Right Circular Cone/Base

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Let $\triangle AOB$ be a right-angled triangle such that $\angle AOB$ is the right angle.

Let $K$ be the right circular cone formed by the rotation of $\triangle AOB$ around $OB$.

Let $BC$ be the circle described by $B$.

The base of $K$ is the plane surface enclosed by the circle $BC$.

In the words of Euclid:

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

(The Elements: Book $\text{XI}$: Definition $20$)