Editing Sphere (section)

==History==
The geometry of the sphere was studied by the Greeks. ''[[Euclid's Elements]]'' defines the sphere in book XI, discusses various properties of the sphere in book XII, and shows how to inscribe the five regular polyhedra within a sphere in book XIII. Euclid does not include the area and volume of a sphere, only a theorem that the volume of a sphere varies as the third power of its diameter, probably due to [[Eudoxus of Cnidus]]. The volume and area formulas were first determined in [[Archimedes]]'s ''[[On the Sphere and Cylinder]]'' by the [[method of exhaustion]]. [[Zenodorus (mathematician)|Zenodorus]] was the first to state that, for a given surface area, the sphere is the solid of maximum volume.<ref name="EB">{{Cite EB1911|wstitle=Sphere |volume=25 |pages=647–648 }}</ref>

Archimedes wrote about the problem of dividing a sphere into segments whose volumes are in a given ratio, but did not solve it. A solution by means of the parabola and hyperbola was given by [[Dionysodorus]].<ref>{{Cite web |last=Fried |first=Michael N. |date=2019-02-25 |title=conic sections |url=https://oxfordre.com/view/10.1093/acrefore/9780199381135.001.0001/acrefore-9780199381135-e-8161 |access-date=2022-11-04 |website=Oxford Research Encyclopedia of Classics |language=en |doi=10.1093/acrefore/9780199381135.013.8161|isbn=978-0-19-938113-5 |quote=More significantly, Vitruvius (On Architecture, Vitr. 9.8) associated conical sundials with Dionysodorus (early 2nd century bce), and Dionysodorus, according to Eutocius of Ascalon (c. 480–540 ce), used conic sections to complete a solution for Archimedes’ problem of cutting a sphere by a plane so that the ratio of the resulting volumes would be the same as a given ratio.}}</ref> A similar problem{{snd}}to construct a segment equal in volume to a given segment, and in surface to another segment{{snd}}was solved later by [[al-Quhi]].<ref name="EB" />