Divisors obey Distributive Law/Proof 2

Theorem

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

In modern algebraic language:
 * $a = \dfrac 1 n b, c = \dfrac 1 n d \implies a + c = \dfrac 1 n \left({b + d}\right)$

Proof
A direct application of the Distributive Property:
 * $\dfrac 1 n b + \dfrac 1 n d = \dfrac 1 n \left({b + d}\right)$