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Corollary: Cor. 10.004: Greatest Common Measure of Three Commensurable Magnitudes

(related to Proposition: Prop. 10.004: Greatest Common Measure of Three Commensurable Magnitudes)

(Corollary to Proposition 4 from Book 10 of Euclid's “Elements”)

So (it is) clear, from this, that if a magnitude measures three magnitudes then it will also measure their greatest common measure. So, similarly, the greatest common measure of more (magnitudes) can also be taken, and the (above) corollary will go forward. (Which is) the very thing it was required to show.

Modern Formulation

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References

Adapted from (subject to copyright, with kind permission)

1. Fitzpatrick, Richard: Euclid's "Elements of Geometry"