Greatest Common Measure of Commensurable Magnitudes/Porism

From ProofWiki
Jump to navigation Jump to search

Porism to Greatest Common Measure of Commensurable Magnitudes

In the words of Euclid:

From this it is manifest that, if a magnitude measure two magnitudes, it will also measure their greatest common measure.

(The Elements: Book $\text{X}$: Proposition $3$ : Porism)


Proof

Apparent from the construction.

$\blacksquare$


Historical Note

This proof is Proposition $3$ of Book $\text{X}$ of Euclid's The Elements.


Sources