Proposition X.39 — If two straight lines incommensurable in square which make t…

Proof

Sum of an X.33 pair has square = rational + medial: irrational.

Knowledge graph · drag to pan, scroll to zoom, click a node to navigate

Full neighborhood

Depends on (2)

X.33Proposition X.33To find two straight lines incommensurable in square which make the sum of the squares on them rational but the…
X.36Proposition X.36If two rational straight lines commensurable in square only be added together, the whole is irrational; and let it be…

Required by (dependents) (6)

X.40Proposition X.40If two straight lines incommensurable in square which make the sum of the squares on them medial, but the rectangle…
X.45Proposition X.45A major straight line is divided at one and the same point only.
X.57Proposition X.57If an area be contained by a rational straight line and the fourth binomial, the side of the area is the irrational…
X.68Proposition X.68A straight line commensurable with a major straight line is itself major.
X.71Proposition X.71If a rational and a medial area be added together, four irrational straight lines arise, namely either a binomial, a…
X.76Proposition X.76If from a straight line there be subtracted a straight line incommensurable in square with the whole, which with the…

Discussion

No replications, contradictions, or comments registered yet for this claim.

Replicate or annotate this claim

Replicate to register a fresh attempt; contradict, extend, or comment otherwise. Authors can post a claim-retraction with the reason taxonomy from RRP-0020.