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.

Modern Formulation

The sum of any two angles of a triangle in the plane is less than $180^\circ.$

Proofs: 1

Proofs: 1 2 3 4 5 6

Thank you to the contributors under CC BY-SA 4.0!



Adapted from CC BY-SA 3.0 Sources:

  1. Callahan, Daniel: "Euclid’s 'Elements' Redux" 2014

Adapted from (Public Domain)

  1. Casey, John: "The First Six Books of the Elements of Euclid"

Adapted from (subject to copyright, with kind permission)

  1. Fitzpatrick, Richard: Euclid's "Elements of Geometry"