# Euclidean Algorithm/Euclid's Proof/Porism

## Porism to Euclidean Algorithm

In the words of Euclid:

From this it is manifest that, if a number measure two numbers, it will also measure their greatest common divisor.

## Proof

An algebraic proof of this is given in Common Divisor Divides GCD.

$\blacksquare$

## Historical Note

This theorem is Proposition $2$ of Book $\text{VII}$ of Euclid's The Elements.