# Greatest Common Measure of Three Commensurable Magnitudes/Porism

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## 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.

(*The Elements*: Book $\text{X}$: Proposition $4$ : Porism)

## Proof

Apparent from the construction.

$\blacksquare$

## Historical Note

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

## Sources

- 1926: Sir Thomas L. Heath:
*Euclid: The Thirteen Books of The Elements: Volume 3*(2nd ed.) ... (previous) ... (next): Book $\text{X}$. Propositions