Proposition: 1.15: Opposite Angles on Intersecting Straight Lines
(Proposition 15 from Book 1 of Euclid's “Elements”)
If two straight lines cut one another then they make the vertically opposite angles equal to one another.
* For let the two straight lines $AB$ and $CD$ cut one another at the point $E$.
* I say that angle $AEC$ is equal to (angle) $DEB$, and (angle) $CEB$ to (angle) $AED$.
If two straight lines \(AB\) and \(CD\) intersect one another at one point \(E\), their opposite angles are equal.
Table of Contents
Proofs: 1 2 3 4 5 6 7 8
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"