Proposition: 1.18: Angles and Sides in a Triangle I
(Proposition 18 from Book 1 of Euclid's “Elements”)
In any triangle, the greater side subtends the greater angle.
- For let $ABC$ be a triangle having side $AC$ greater than $AB$.
- I say that angle $ABC$ is also greater than $BCA$.
Modern Formulation
In a given triangle \(\triangle{ABC}\) with the side \(\overline{AC}\) longer than \(\overline{AB}\), the angle \(\angle{ABC}\) opposite to the longer side is greater than the angle \(\angle{BCA}\) opposite to the shorter side.
Table of Contents
Proofs: 1
Mentioned in:
Proofs: 1
Propositions: 2
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References
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"
