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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 $EGCD$.

Modern Formulation

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Table of Contents

Proofs: 1

Mentioned in:

Proofs: 1 2 3

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References

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", https://proofwiki.org/wiki/Main_Page, 2016