Then, in a similar manner to the preceding, we can prove that BA, AF are rational straight lines commensurable in square only.
And since, as DC is to CE, so is the square on BA to the square on AF,
therefore, convertendo, as CD is to DE, so is the square on AB to the square on BF. [V. 19, Por., III. 31, I. 47]
But CD has not to DE the ratio which a square number has to a square number;
therefore neither has the square on AB to the square on BF the ratio which a square number has to a square number;
therefore AB is incommensurable in length with BF. [X. 9]
And the square on AB is greater than the square on AF by the square on FB incommensurable with AB.
Complete text
Book I