Proposition XVIII. Theorem.
|(96)||In any triangle (B A C) if one side (A C) be greater than another (A B), the angle opposite to the greater side is greater than the angle opposite to the less.|
From the greater side A C cut off the part A D equal to the less (III), and conterminous with it, and join B D.
The triangle B A D being isosceles (V), the angles A B D and A D B are equal; but A D B is greater than the internal angle A C B (XVI): therefore A B D is greater than A C B, and therefore A B C is greater than A C B: but A B C is opposite the greater side A C, and A C B is opposite the less A B.
Book I: Euclid, Book I (ed. Dionysius Lardner, 11th Edition, 1855)
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