# Greatest Common Measure of Three Commensurable Magnitudes/Porism

## Porism to Greatest Common Measure of Three Commensurable Magnitudes

In the words of Euclid:

From this it is manifest that, if a magnitude measure three magnitudes, it will also measure their greatest common measure.
Similarly too, with more magnitudes, the greatest common measure can be found, and the porism can be extended.

## Proof

Apparent from the construction.

$\blacksquare$

## Historical Note

This proof is Proposition $4$ of Book $\text{X}$ of Euclid's The Elements.