Proposition X.76 — If from a straight line there be subtracted a straight line …

Proof

Negation of X.39. This is the "minor" line (Definition XIII.4).

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Depends on (2)

X.39Proposition X.39If two straight lines incommensurable in square which make the sum of the squares on them rational, but the rectangle…
XIII.4Definition XIII.4A minor straight line is the difference of two straight lines incommensurable in square such that the sum of the…

Required by (dependents) (5)

X.77Proposition X.77If from a straight line there be subtracted a straight line incommensurable in square with the whole which with the…
X.82Proposition X.82Only one straight line can be annexed to a minor.
X.105Proposition X.105A straight line commensurable with a minor is itself a minor.
X.108Proposition X.108If from a rational area a medial area be subtracted, the side of the remaining area arises as one of four irrationals:…
XIII.11Proposition XIII.11If in a circle which has its diameter rational an equilateral pentagon be inscribed, the side of the pentagon is the…

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