For, if possible, let BD be so annexed;
therefore AD, DB are also straight lines incommensurable in square which fulfil the given conditions. [X. 77]
Since then, as in the preceding cases, the excess of the squares on AD, DB over the squares on AC, CB is also the excess of twice the rectangle AD, DB over twice the rectangle AC, CB, while twice the rectangle AD, DB exceeds twice the rectangle AC, CB by a rational area,
for both are rational, therefore the squares on AD, DB also exceed the squares on AC, CB by a rational area: which is impossible,
for both are medial. [X. 26]