◀ ▲ ▶Branches / Geometry / Elements-euclid / Book-11-elementary-stereometry / Proposition: Prop. 11.04: Line Perpendicular to Two Intersecting Lines is Perpendicular to their Plane

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).

• For let some straight line $EF$ have (been) set up at right angles to two straight lines, $AB$ and $CD$, cutting one another at point $E$, at $E$.
• I say that $EF$ is also at right angles to the plane (passing) through $AB$ and $CD$.

Modern Formulation

(not yet contributed)

Table of Contents

Proofs: 1

Mentioned in:

Proofs: 1 2 3 4 5 6

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

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non-Github:

@Fitzpatrick

References

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", https://proofwiki.org/wiki/Main_Page, 2016