Proposition X.71 — If a rational and a medial area be added together, four irra…

Proof

The square of any of the four classes (X.36, X.37, X.39, X.40) is the sum of a rational and a medial; conversely, every such sum arises in exactly one of these forms.

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

Full neighborhood

Depends on (4)

X.36Proposition X.36If two rational straight lines commensurable in square only be added together, the whole is irrational; and let it be…
X.37Proposition X.37If two medial straight lines commensurable in square only and containing a rational rectangle be added together, the…
X.39Proposition X.39If two straight lines incommensurable in square which make the sum of the squares on them rational, but the rectangle…
X.40Proposition X.40If two straight lines incommensurable in square which make the sum of the squares on them medial, but the rectangle…

Required by (dependents) (2)

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.