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?"

Also known as
The term direct proportion can frequently be seen for this concept, in order to specifically distinguish it from inverse proportion.

The term direct variation can also be seen.

The term proportion is more usually known nowadays by the less elegant and more cumbersome word proportionality.