Subtraction of Divisors obeys Distributive Law/Proof 2

Theorem

 * If a (natural) number be that part of a (natural) number, which a (natural) number subtracted is of a (natural) number subtracted, the remainder will also be the same part of the remainder that that the whole is of the whole.

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: