Proving the length of a circle's arc is proportional to the size of the angle How can I prove that:

The length of the arc is proportional to the size of the angle.

Every book use this fact in explaining radians and the fundamental arc length equation $s = r\theta$. However no book proofs this fact.
Is this fact some axiom, some natural law like $\pi$ and the triangle side proportions?
Can I proof the above? Or is it something that you should just accept?

It is a linear relationship. $ s = R \theta$.  $R$ is the ratio of these two quantities. There is $nothing$ to prove here. It is a $definition$ in flat Euclidean geometry.Definitions are not meant for proving.
In non-euclidean elliptic geometry the arc is less than $ \theta R$ and in the hyperbolic geometry it is more than $ \theta R$, where arcs $s$  are measured on doubly curved surfaces and $\theta$ between principal polar coordinate geodesic lines.
