Does Euclid's Book I Proposition 24 prove something that Proposition 18 and 19 don't prove?

Question

The question title says it all.

Book I, Proposition 24 states

If two triangles have two sides equal to two sides respectively, but have one of the angles contained by the equal straight lines greater than the other, then they also have the base greater than the base.

Book I, Proposition 18 states

In any triangle, the angle opposite the greater side is greater.

It seems that Proposition 24 proves exactly the same thing that is proved in Proposition 18.

Does Proposition 24 prove something that Proposition 18 (and possibly Proposition 19) does not ?

It seems that Proposition 24 could be proved in a single step by invoking Proposition 18. What is the reason it could not be done that way ?... an example of why not, would be great.

Answer 1

No, they do not prove the same thing. Think about an isosceles triangle with two short sides and one long. Proposition 18 says that the angle opposite the long side is the largest of the three. Proposition 24 says that if you increase / decrease the long side, the opposite angle also increases / decreases.

Proposition 18 does not say anything about comparing two different triangles. If it were up to only proposition 18, then increasing the long side might as well decrease the largest angle, as long as it stays the largest.

Similarily, proposition 24 says nothing about how the angle opposite the largest side compares to the other angles in the triangle. If it were up to only proposition 24, the largest side needs not be opposite the largest angle. We just know that if we increase the largest side, the opposite angle must increase.