Proposition VI.26 — If from a parallelogram there be taken away a parallelogram …

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.

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Depends on (2)

VI.24Proposition VI.24In any parallelogram the parallelograms about the diameter are similar both to the whole and to one another.
V.9Proposition V.9Magnitudes which have the same ratio to the same are equal to one another; and magnitudes to which the same has the…

Required by (dependents) (1)

VI.27Proposition VI.27Of all parallelograms applied to the same straight line and deficient by parallelogrammic figures similar and similarly…

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