Proposition: Prop. 11.05: Three Intersecting Lines Perpendicular to Another Line are in One Plane

(Proposition 5 from Book 11 of Euclid's “Elements”)

If a straight line is set up at right angles to three straight lines cutting one another, at the common point of section, then the three straight lines are in one plane.

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