Proposition: 1.19: Angles and Sides in a Triangle II
(Proposition 19 from Book 1 of Euclid's “Elements”  this a the conversion to the proposition 1.18)
In any triangle, the greater angle is subtended by the greater side.
* Let $ABC$ be a triangle having the angle $ABC$ greater than $BCA$.
* I say that side $AC$ is also greater than side $AB$.
Modern Formulation
In a given triangle \(\triangle{ABC}\) with the angle \(\angle{ABC}\) greater than the angle \(\angle{BCA}\), the side \(\overline{AC}\) opposite to the greater angle is longer than \(\overline{AB}\), opposite to the smaller angle.
Table of Contents
Proofs: 1
Mentioned in:
Proofs: 1 2 3 4 5
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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"