Proposition: 1.20: The Sum of the Lengths of Any Pair of Sides of a Triangle (Triangle Inequality)
(Proposition 20 from Book 1 of Euclid's “Elements”)
In any triangle, (the sum of) two sides taken together in any (possible way) is greater than the remaining (side).
* For let $ABC$ be a triangle.
* I say that in triangle $ABC$ (the sum of) two sides taken together in any (possible way) is greater than the remaining (side).
see triangle inequality.
Table of Contents
Proofs: 1 2 3 4 5 6 7 8
Thank you to the contributors under CC BY-SA 4.0!
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"