Multiples of Divisors obey Distributive Law/Proof 2

Theorem

 * If a (natural) number be parts of a (natural) number, and another be the same parts of another, the sum will also be the same parts of the sum that the one is of the one.

In modern algebraic language:
 * $a = \dfrac m n b, c = \dfrac m n d \implies a + c = \dfrac m n \left({b + d}\right)$

Proof
A direct application of the Distributive Property:
 * $\dfrac m n b + \dfrac m n d = \dfrac m n \left({b + d}\right)$