Since, then, ABCD is about the same diameter with KG,
therefore, as DA is to AB, so is GA to AK. [VI. 24]
But also, because of the similarity of ABCD, EG, as DA is to AB, so is GA to AE;
therefore also, as GA is to AK, so is GA to AE. [V. 11]
Therefore GA has the same ratio to each of the straight lines AK, AE.
Therefore AE is equal to AK [V. 9], the less to the greater: which is impossible.
Therefore ABCD cannot but be about the same diameter with AF;
therefore the parallelogram ABCD is about the same diameter with the parallelogram AF.