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).
Modern Formulation
see triangle inequality.
Table of Contents
Proofs: 1
Mentioned in:
Proofs: 1 2 3 4 5 6 7 8
Propositions: 9
Sections: 10
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References
Adapted from CC BYSA 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"