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 $KF$.
Modern Formulation
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Table of Contents
Proofs: 1
Mentioned in:
Proofs: 1 2
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References
Adapted from (subject to copyright, with kind permission)
 Fitzpatrick, Richard: Euclid's "Elements of Geometry"
Adapted from CC BYSA 3.0 Sources:
 Prime.mover and others: "Pr∞fWiki", https://proofwiki.org/wiki/Main_Page, 2016