Proposition: 1.30: Transitivity of Parallel Lines
(Proposition 30 from Book 1 of Euclid's “Elements”)
(Straightlines) parallel to the same straight line are also parallel to one another.
* Let each of the (straight lines) $AB$ and $CD$ be parallel to $EF$.
* I say that $AB$ is also parallel to $CD$.
Modern Formulation
Straight lines parallel to the same straight line are also parallel to one another, i.e. if \(AB\parallel EF\) and \(EF\parallel CB\) then \(AB\parallel CB\).
Table of Contents
Proofs: 1
Mentioned in:
Proofs: 1 2
Thank you to the contributors under CC BYSA 4.0!
 Github:

 nonGithub:
 @Calahan
 @Casey
 @Fitzpatrick
References
Adapted from CC BYSA 3.0 Sources:
 Callahan, Daniel: "Euclid’s 'Elements' Redux" 2014
Adapted from (Public Domain)
 Casey, John: "The First Six Books of the Elements of Euclid"
Adapted from (subject to copyright, with kind permission)
 Fitzpatrick, Richard: Euclid's "Elements of Geometry"