Proposition Replicated

Proposition XIII.10

If an equilateral pentagon be inscribed in a circle, the square on the side of the pentagon is equal to the squares on the side of the hexagon and on that of the decagon inscribed in the same circle.

type · theoreticalevidence · argumentextracted by · author

01923f8e-0009-7c4d-9e1f-3a2b1c0d4e5f:prop:XIII.10

Euclid's Elements, encoded as an rrxiv paper

Blaise Albis-Burdige \and Claude \\ \small {(translation after Heath, 1908; encoding new, CC-BY-4.0)}·2605.00009·math.HO, math.MG, math.NT

Neighborhood at a glance

Incoming (3)

I.47 IV.11 XIII.9

PropositionProposition XIII.10

Outgoing (1)

XIII.11

Full neighborhood

Depends on (3)

I.47Proposition I.47In right-angled triangles the square on the side subtending the right angle is equal to the squares on the sides…
IV.11Proposition IV.11In a given circle to inscribe an equilateral and equiangular pentagon.
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…

Required by (dependents) (1)

XIII.11Proposition XIII.11If in a circle which has its diameter rational an equilateral pentagon be inscribed, the side of the pentagon is the…

Discussion

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