A medial (area) , incommensurable with the whole, being subtracted from a medial (area) , the two remaining irrational (straight lines) arise (as) the (square root of the area) - either a second apotome of a medial (straight line), or that (straight line) which with a medial (area) makes a medial whole. * For, as in the previous figures, let the medial (area) $BD$, incommensurable with the whole, have been subtracted from the medial (area) $BC$. * I say that the square root of $EC$ is one of two irrational (straight lines) - either a second apotome of a medial (straight line), or that (straight line) which with a medial (area) makes a medial whole.
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Proofs: 1