Definition:Prism/Base/Euclidean Variant

Definition

Although the base of a prism is generally understood to be one of the opposite faces which defines the prism, Euclid was inconsistent in his usage in The Elements.

In his Proposition $39$ of Book $\text{XI} $: Prisms of equal Height with Parallelogram and Triangle as Base, he defines the base of one prism as being one of the opposite parallel faces, but of the other he defines the base as being an arbitrary one of the parallelograms.

Using this definition, the parallelogram $PQTS$ in the above diagram is the base of the prism $PQRSTU$.

In the words of Euclid:

If there be two prisms of equal height, and one have a parallelogram as base and the other a triangle, and if the parallelogram be double the triangle, the prisms will be equal.

(The Elements: Book $\text{XI}$: Proposition $39$)