Definition:Plane Number/Similar Numbers

Definition

Let $m$ and $n$ be plane numbers.

Let:

$m = p_1 \times p_2$ where $p_1 \le p_2$

$n = q_1 \times q_2$ where $q_1 \le q_2$

Then $m$ and $n$ are similar if and only if:

$p_1 : q_1 = p_2 : q_2$

That is:

$\dfrac {p_1} {q_1} = \dfrac {p_2} {q_2}$

In the words of Euclid:

Similar plane and solid numbers are those which have their sides proportional.

(The Elements: Book $\text{VII}$: Definition $21$)