Definition:Proportion

Definition
Two real variables $x$ and $y$ are proportional one is a constant multiple of the other:
 * $\forall x, y \in \R: x \propto y \iff \exists k \in \R, k \ne 0: x = k y$

Euclid's Definitions


and:

That is, if $a$ is to $b$ as $c$ is to $d$, that is:
 * $a : b = c : d$

where $a : b$ is the ratio of $a$ to $b$, then $a, b, c, d$ are proportional.

The definition is unsatisfactory, as the question arises: "proportional to what?"