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Proposition: 11.02: Two Intersecting Straight Lines are in One Plane

(Proposition 2 from Book 11 of Euclid's “Elements”)1

If two straight lines cut one another then they are in one plane, and every triangle (formed using segments of both lines) is in one plane. * For let the two straight lines $AB$ and $CD$ have cut one another at point $E$. * I say that $AB$ and $CD$ are in one plane, and that every triangle (formed using segments of both lines) is in one plane.

fig02e

Modern Formulation

(not yet contributed)

Table of Contents

Proofs: 1

Mentioned in:

Proofs: 1 2 3

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

Github:
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non-Github:
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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

Footnotes

  1. The proofs of the first three propositions in this book are not at all rigorous. Hence, these three propositions should properly be regarded as additional axioms (translator's note) ↩