Euclid's 13th Proposition goes as :
Proposition 13. If a straight-line stood on a(nother) straight-line makes angles, it will certainly either make two rightangles, or (angles whose sum is) equal to two rightangles.
I am annoyed because I find some text book treats this Proposition as an AXIOM.
It confused me a lot. I need an expert comment.
Axioms are pedagogy: a means of exposition. The same theory can be presented in many different forms. Axiomness isn't an intrinsic quality of a statement, so some presentations may have different axioms than others.
(axioms also have technical value, but I believe that's unrelated to this question: e.g. you can show that something is a model of a theory by showing it satisfies a choice of axioms for the theory)