Proposition: Prop. 12.13: Volumes of Parts of Cylinder cut by Plane Parallel to Opposite Planes are as Parts of Axis

Euclid's Formulation

If a cylinder is cut by a plane which is parallel to the opposite planes (of the cylinder) then as the cylinder (is) to the cylinder, so the axis will be to the axis.

For let the cylinder $AD$ have been cut by the plane $GH$ which is parallel to the opposite planes (of the cylinder), $AB$ and $CD$.
And let the plane $GH$ have met the axis at point $K$.
I say that as cylinder $BG$ is to cylinder $GD$, so $EK$ (is) to $KF$.