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 $EGCD$.
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Table of Contents
Proofs: 1 2 3
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Adapted from (subject to copyright, with kind permission)
- Fitzpatrick, Richard: Euclid's "Elements of Geometry"
Adapted from CC BY-SA 3.0 Sources:
- Prime.mover and others: "Pr∞fWiki", https://proofwiki.org/wiki/Main_Page, 2016