Proposition: 1.17: The Sum of Two Angles of a Triangle
(Proposition 17 from Book 1 of Euclid's “Elements”)
For any triangle, (the sum of) two angles taken together in any (possible way) is less than two right angles.
* Let $ABC$ be a triangle.
* I say that (the sum of) two angles of triangle $ABC$ taken together in any (possible way) is less than two right angles.
The sum of any two angles of a triangle in the plane is less than $180^\circ.$
Table of Contents
Proofs: 1 2 3 4 5 6
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"