Proposition: Prop. 11.04: Line Perpendicular to Two Intersecting Lines is Perpendicular to their Plane

Euclid's Formulation

If a straight line is set up at right angles to two straight lines cutting one another, at the common point of section, then it will also be at right angles to the plane (passing) through them (both).


Modern Formulation

(not yet contributed)

Proofs: 1

Proofs: 1 2 3 4 5 6

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