Then, in manner similar to the foregoing, we can prove that D, L, E and G, M, N, H are continuously proportional in the ratio of A to B,
and further E, O, F and H, P, Q, K are continuously proportional in the ratio of B to C.
Now, as A is to B, so is B to C;
therefore D, L, E are also in the same ratio with E, O, F, and further G, M, N, H in the same ratio with H, P, Q, K.
And the multitude of D, L, E is equal to the multitude of E, O, F, and that of G, M, N, H to that of H, P, Q, K;
therefore, ex acquali, as D is to E, so is E to F,
and, as G is to H, so is H to K. [VII. 14]
Q. E. D.
Complete text
Book I