Proposition VI.28 — To a given straight line to apply a parallelogram equal to a…

Proof

Construct the application by VI.25 to match the given figure, then verify the bound via VI.27. The construction effectively solves a quadratic equation in geometric form.

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Depends on (2)

VI.25Proposition VI.25To construct one and the same figure similar to a given rectilineal figure and equal to another given rectilineal…
VI.27Proposition VI.27Of all parallelograms applied to the same straight line and deficient by parallelogrammic figures similar and similarly…

Required by (dependents) (3)

VI.29Proposition VI.29To a given straight line to apply a parallelogram equal to a given rectilineal figure and exceeding by a…
X.17Proposition X.17If there be two unequal straight lines, and to the greater there be applied a parallelogram equal to the fourth part of…
X.18Proposition X.18If there be two unequal straight lines, and to the greater there be applied a parallelogram equal to the fourth part of…

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