If two commensurable magnitudes are added together then the whole will also be commensurable with each of them. And if the whole is commensurable with one of them then the original magnitudes will also be commensurable (with one another). * For let the two commensurable magnitudes $AB$ and $BC$ be laid down together. * I say that the whole $AC$ is also commensurable with each of $AB$ and $BC$. * And so let $AC$ be commensurable with $AB$. * I say that $AB$ and $BC$ are also commensurable.
(not yet contributed)