The (square) on a rational (straight line), applied to an apotome, produces as breadth a binomial whose terms are commensurable with the terms of the apotome, and in the same ratio. Moreover, the created binomial has the same order as the apotome. * Let $A$ be a rational (straight line), and $BD$ an apotome. * And let the (rectangle contained) by $BD$ and $KH$ be equal to the (square) on $A$, such that the square on the rational (straight line) $A$, applied to the apotome $BD$, produces $KH$ as breadth. * I say that $KH$ is a binomial whose terms are commensurable with the terms of $BD$, and in the same ratio, and, moreover, that $KH$ has the same order as $BD$.
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Proofs: 1
