◀ ▲ ▶Branches / Geometry / Elements-euclid / Book-11-elementary-stereometry / Proposition: Prop. 11.15: Planes through Parallel Pairs of Meeting Lines are Parallel

Proposition: Prop. 11.15: Planes through Parallel Pairs of Meeting Lines are Parallel

(Proposition 15 from Book 11 of Euclid's “Elements”)

If two straight lines joined to one another are parallel (respectively) to two straight lines joined to one another, which are not in the same plane, then the planes through them are parallel (to one another).

• For let the two straight lines joined to one another, $AB$ and $BC$, be parallel to the two straight lines joined to one another, $DE$ and $EF$ (respectively), not being in the same plane.
• I say that the planes through $AB$, $BC$ and $DE$, $EF$ will not meet one another (when) produced.

Modern Formulation

(not yet contributed)

Table of Contents

Proofs: 1

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