Proposition X.33 — To find two straight lines incommensurable in square which m…

Proof

Apply X.30: a difference-of-squares construction with an incommensurable discriminant produces such a pair.

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Depends on (1)

X.30Proposition X.30To find two rational straight lines commensurable in square only such that the square on the greater is greater than…

Required by (dependents) (2)

X.34Proposition X.34To find two straight lines incommensurable in square which make the sum of the squares on them medial but the rectangle…
X.39Proposition X.39If two straight lines incommensurable in square which make the sum of the squares on them rational, but the rectangle…

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