Proposition: Prop. 11.14: Planes Perpendicular to same Straight Line are Parallel

(Proposition 14 from Book 11 of Euclid's “Elements”)

Planes to which the same straight line is at right angles will be parallel planes. * For let some straight line $AB$ be at right angles to each of the planes $CD$ and $EF$. * I say that the planes are parallel. fig14e

Modern Formulation

(not yet contributed)

Proofs: 1

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