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 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;
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;
but it is not;
Therefore etc.
Q.E.D