In any triangle the angle opposite the greater side is greater. I have a small problem with the following :
http://aleph0.clarku.edu/~djoyce/java/elements/bookI/propI18.html
I did understand the proof, but the proposition claims that the angle opposite the greater side is greater and Euclid only proves that it is greater than one other angle. (angle ABC is greater than ACB)
Am I supposed to understand that I must prove for the other case by myself? (I fill in the details ?) OR I didn't understand at all ? Thank you!

I believe you understood the proof. The proof is a general case where $AC$ greater than $AB$. You can place the sides $AC$ and $AB$ anywhere in the picture. For example, switching the letters $A$ and $C$ in the picture, you get the proof of another pair. And notice the proof does not depend on the position of the letters.
