Proposition Replicated
Proposition XIII.18
To set out the sides of the five figures and to compare them with one another; and that no other figure, besides the said five figures, can be constructed which is contained by equilateral and equiangular figures equal to one another.
01923f8e-0009-7c4d-9e1f-3a2b1c0d4e5f:prop:XIII.18
Euclid's Elements, encoded as an rrxiv paper
Blaise Albis-Burdige, Claude·2605.00009·math.HO, math.MG, math.NT
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Depends on (7)
- I.32Proposition I.32In any triangle, if one of the sides be produced, the exterior angle is equal to the two interior and opposite angles,…
- XI.21Proposition XI.21Any solid angle is contained by plane angles less than four right angles.
- XIII.13Proposition XIII.13To construct a pyramid (regular tetrahedron), to comprehend it in a given sphere, and to prove that the square on the…
- XIII.14Proposition XIII.14To construct an octahedron and comprehend it in a sphere, as in the preceding case; and to prove that the square on the…
- XIII.15Proposition XIII.15To construct a cube and comprehend it in a sphere, as in the preceding case; and to prove that the square on the…
- 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…
- XIII.17Proposition XIII.17To construct a dodecahedron and comprehend it in a sphere, like the aforesaid figures; and to prove that the side of…
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