Proposition VI.27 — Of all parallelograms applied to the same straight line and …

Proof

Comparison of areas via VI.20 and VI.24: the application to the half exhausts the bound, while any other application produces a smaller parallelogram by a square-on-the-deviation.

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Depends on (3)

VI.20Proposition VI.20Similar polygons are divided into similar triangles, equal in multitude and in the same ratio as the wholes; and the…
VI.24Proposition VI.24In any parallelogram the parallelograms about the diameter are similar both to the whole and to one another.
VI.26Proposition VI.26If from a parallelogram there be taken away a parallelogram similar and similarly situated to the whole and having a…

Required by (dependents) (1)

VI.28Proposition VI.28To a given straight line to apply a parallelogram equal to a given rectilineal figure and deficient by a…

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