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Proposition: Prop. 11.28: Parallelepiped cut by Plane through Diagonals of Opposite Planes is Bisected

(Proposition 28 from Book 11 of Euclid's “Elements”)

If a parallelepipedal solid is cut by a plane (passing) through the diagonals of (a pair of) opposite planes then the solid will be cut in half by the plane.

• For let the parallelepipedal solid $AB$ have been cut by the plane $CDEF$ (passing) through the diagonals of the opposite planes $CF$ and $DE$.
• I say that the solid $AB$ will be cut in half by the plane $CDEF$.

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