Proposition: Prop. 11.25: Parallelepiped cut by Plane Parallel to Opposite Planes

(Proposition 25 from Book 11 of Euclid's “Elements”)

If a parallelepipedal solid is cut by a plane which is parallel to the opposite planes (of the parallelepiped) then as the base (is) to the base, so the solid will be to the solid.

For let the parallelepipedal solid $ABCD$ have been cut by the plane $FG$ which is parallel to the opposite planes $RA$ and $DH$.
I say that as the base $AEFV$ (is) to the base $EHCF$, so the solid $ABFU$ (is) to the solid $EGCD$.

fig25e