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Proposition: Prop. 11.01: Straight Line cannot be in Two Planes

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

Some part of a straight line cannot be in a reference plane, and some part in a more elevated (plane).

fig01e

Modern Formulation

(not yet contributed)

Table of Contents

Proofs: 1

Mentioned in:

Proofs: 1 2 3 4

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

Github:
bookofproofs
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

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) ↩