◀ ▲ ▶Branches / Geometry / Euclidean-geometry / Elements-euclid / Book-11-elementary-stereometry / Proposition: Prop. 11.07: Line joining Points on Parallel Lines is in Same Plane

Proposition: Prop. 11.07: Line joining Points on Parallel Lines is in Same Plane

Euclid's Formulation

If there are two parallel straight lines, and random points are taken on each of them, then the straight line joining the two points is in the same plane as the parallel (straight lines). * Let $AB$ and $CD$ be two parallel straight lines, and let the random points $E$ and $F$ have been taken on each of them (respectively). * I say that the straight line joining points $E$ and $F$ is in the same (reference) plane as the parallel (straight lines).

Modern Formulation

(not yet contributed)

Table of Contents

Proofs: 1

Mentioned in:

Proofs: 1 2

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

Github:

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