Proposition: Prop. 11.19: Common Section of Planes Perpendicular to other Plane is Perpendicular to that Plane

Euclid's Formulation

If two planes cutting one another are at right angles to some plane then their common section will also be at right angles to the same plane. * For let the two planes $AB$ and $BC$ be at right angles to a reference plane, and let their common section be $BD$. * I say that $BD$ is at "right angles to the reference plane":bookofproofs$2212.


Modern Formulation

(not yet contributed)

Proofs: 1

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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