Proposition: Prop. 11.16: Common Sections of Parallel Planes with other Plane are Parallel

Euclid's Formulation

If two parallel planes are cut by some plane then their common sections are parallel. * For let the two parallel planes $AB$ and $CD$ have been cut by the plane $EFGH$. * And let $EF$ and $GH$ be their common sections. * I say that $EF$ is parallel to $GH$.


Modern Formulation

(not yet contributed)

Proofs: 1

Proofs: 1 2

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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