If from a parallelogram there be taken away a parallelogram similar and similarly situated to the whole and having a common angle with it, it is about the same diameter with the whole.
Proof
Reductio: if the inner parallelogram is not about the diagonal, then
VI.24 forces a similar parallelogram on the actual diagonal that
differs from the given one; matching corresponding sides via the
similarity contradicts the assumed common-angle configuration.