If the remainder of two unequal magnitudes (which are) [laid out] never measures the (magnitude) before it, (when) the lesser (magnitude is) continually subtracted in turn from the greater, then the (original) magnitudes will be incommensurable. * For, $AB$ and $CD$ being two unequal magnitudes, and $AB$ (being) the lesser, let the remainder never measure the (magnitude) before it, (when) the lesser (magnitude is) continually subtracted in turn from the greater. * I say that the magnitudes $AB$ and $CD$ are incommensurable.
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Proofs: 1
Proofs: 1