Proposition: Prop. 11.18: Plane through Straight Line Perpendicular to other Plane is Perpendicular to that Plane

(Proposition 18 from Book 11 of Euclid's “Elements”)

If a straight line is at right angles to some plane then all of the planes (passing) through it will also be at right angles to the same plane. * For let some straight line $AB$ be at right angles to a reference plane. * I say that all of the planes (passing) through $AB$ are also at "right angles to the reference plane":bookofproofs$2212.


Modern Formulation

(not yet contributed)

Proofs: 1

Proofs: 1

Thank you to the contributors under CC BY-SA 4.0!



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