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Proposition·Untested·2605.00009

Proposition X.18

If there be two unequal straight lines, and to the greater there be applied a parallelogram equal to the fourth part of the square on the less and deficient by a square figure, and if it divide it into parts incommensurable in length, then the square on the greater will be greater than the square on the less by the square on a straight line incommensurable in length with the greater.

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Proof

Same construction as X.17 with the opposite hypothesis; incommensurability of the parts forces incommensurability of the discriminant.

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Full neighborhood

Depends on (3)

Required by (dependents) (1)

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