Proposition XIII.11 — If in a circle which has its diameter rational an equilatera…

Proof

By XIII.10 the pentagon side is

h^{2} + d^{2}

with

h

rational and

d

an apotome (XIII.6); the resulting form falls in Book X's minor class (Definition XIII.4 / X.76).

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

Full neighborhood

Depends on (4)

X.76Proposition X.76If from a straight line there be subtracted a straight line incommensurable in square with the whole, which with the…
XIII.6Proposition XIII.6If a rational straight line be cut in extreme and mean ratio, each of the segments is the irrational straight line…
XIII.10Proposition XIII.10If an equilateral pentagon be inscribed in a circle, the square on the side of the pentagon is equal to the squares on…
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) (1)

XIII.16Proposition XIII.16To construct an icosahedron and comprehend it in a sphere, as in the case of the aforesaid figures; and to prove that…

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.