(related to Proposition: Prop. 10.004: Greatest Common Measure of Three Commensurable Magnitudes)
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.
(not yet contributed)