Euclid's Elements: Book I: Proposition 19
Proposition 19: In any triangle the greater angle is subtended by the greater side.
Let ABC be a triangle having the angle ABC greater than the angle BCA;
I say that the side AC is also greater than the side AB.
For, if not, AC is either equal to AB or less.
Now AC is not equal to AB; for then the angle ABC would also have been equal to the angle ACB; I. 5 but it is not; therefore AC is not equal to AB.
Neither is AC less than AB, for then the angle ABC would also have been less than the angle ACB; I. 18 but it is not; therefore AC is not less than AB.
And it was proved that it is not equal either. Therefore AC is greater than AB.
Therefore etc.
Q.E.D. | 
