Associative Law of Multiplication/Euclid's Statement

Theorem
That is, if:
 * $n a, n b$ are equimultiples of $a, b$

and if:
 * $m \cdot n a, m \cdot nb$ are equimultiples of $n a, n b$

then:
 * $m \cdot n a$ is the same multiple of $a$ that $m \cdot n b$ is of $b$

This can also be expressed as:
 * $m \cdot n a = m n \cdot a$