A (straight line) "commensurable (in length) > A (straight line) commensurable (in length) with an apotome of a medial (straight line) is an apotome of a medial (straight line), and (is) the same in order^{1}. * Let $AB$ be an apotome of a medial (straight line), and let $CD$ be commensurable in length with $AB$. * I say that $CD$ is also an apotome of a medial (straight line), and (is) the same in order as $AB$.
(not yet contributed)
Proofs: 1
Proofs: 1
Euclid's expression "(not) being the same in order" means that the resulting irrational number is "(not) of the same kind" as that irrational number, with which it is commensurable. ↩