Distributive Laws/Arithmetic

Theorem
On all the number systems: the operation of multiplication is distributive over addition.
 * natural numbers $\N$
 * integers $\Z$
 * rational numbers $\Q$
 * real numbers $\R$
 * complex numbers $\C$


 * If there be any number of magnitudes whatever which are, respectively, equimultiples of any magnitudes equal in multitude, then, whatever multiple of one of the magnitudes is of one, that multiple will also be of all.

Proof
This is demonstrated in these pages:


 * Natural Number Multiplication Distributes over Addition
 * Integer Multiplication Distributes over Addition
 * Rational Multiplication Distributes over Addition
 * Real Multiplication Distributes over Addition
 * Complex Multiplication Distributes over Addition