# Euclidean Algorithm/Euclid's Proof/Porism

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## 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.*

(*The Elements*: Book $\text{VII}$: Proposition $2$ : Porism)

## 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*.

## Sources

- 1926: Sir Thomas L. Heath:
*Euclid: The Thirteen Books of The Elements: Volume 2*(2nd ed.) ... (previous) ... (next): Book $\text{VII}$. Propositions