Proposition: 1.30: Transitivity of Parallel Lines
(Proposition 30 from Book 1 of Euclid's “Elements”)
(Straight-lines) parallel to the same straight line are also parallel to one another.
![fig30e](https://github.com/bookofproofs/bookofproofs.github.io/blob/main/_sources/_assets/images/euclid/Book01/fig30e.png?raw=true)
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 BY-SA 4.0!
![](https://github.com/bookofproofs/bookofproofs.github.io/blob/main/_sources/_assets/images/calendar-black.png?raw=true)
- Github:
-
![bookofproofs](https://github.com/bookofproofs.png?size=32)
- non-Github:
- @Calahan
- @Casey
- @Fitzpatrick
References
Adapted from CC BY-SA 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"