Proposition XVIII. Theorem.
[Euclid, ed. Lardner, 1855, on Google Books]
| (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, Elements, Book I (ed. Dionysius Lardner, 11th Edition, 1855)
Next: Proposition 19
Previous: Proposition 17
This proposition in other editions:
This proposition might also be proved by producing the lesser side A B, and taking A E equal to the greater side. In this case the angle A E C is equal to A C E (V), and therefore greater than A C B. But A B C is greater than A E C (XVI), and therefore A B C is greater than A C B