For, if possible, let BD be so annexed;
therefore AD, DB are also straight lines incommensurable in square which fulfil the aforesaid conditions. [X. 76]
Now, since 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 the squares on AD, DB exceed the squares on AC, CB by a rational area,
for both are rational, therefore twice the rectangle AD, DB also exceeds twice the rectangle AC, CB by a rational area: which is impossible,
for both are medial. [X. 26]