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.


Modern Formulation

(not yet contributed)

Proofs: 1

Proofs: 1 2

Thank you to the contributors under CC BY-SA 4.0!



Adapted from (subject to copyright, with kind permission)

  1. Fitzpatrick, Richard: Euclid's "Elements of Geometry"

Adapted from CC BY-SA 3.0 Sources:

  1. Prime.mover and others: "Pr∞fWiki",, 2016