Proposition Replicated

Proposition XIII.8

If in an equilateral and equiangular pentagon straight lines subtend two adjacent angles, they cut one another in extreme and mean ratio, and the greater segments are equal to the side of the pentagon.

type · theoreticalevidence · argumentextracted by · author

01923f8e-0009-7c4d-9e1f-3a2b1c0d4e5f:prop:XIII.8

Euclid's Elements, encoded as an rrxiv paper

Blaise Albis-Burdige, Claude·2605.00009·math.HO, math.MG, math.NT

Neighborhood at a glance

Incoming (3)

IV.10 IV.11 VI.4

PropositionProposition XIII.8

Outgoing (1)

XIII.9

Full neighborhood

Depends on (3)

IV.10Proposition IV.10To construct an isosceles triangle having each of the angles at the base double of the remaining one.
IV.11Proposition IV.11In a given circle to inscribe an equilateral and equiangular pentagon.
VI.4Proposition VI.4In equiangular triangles the sides about the equal angles are proportional, and those are corresponding sides which…

Required by (dependents) (1)

XIII.9Proposition XIII.9If the side of the hexagon and that of the decagon inscribed in the same circle be added together, the whole straight…

Discussion

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