On the Sphere and Cylinder

On the Sphere and Cylinder (Greek: Περὶ σφαίρας καὶ κυλίνδρου) is a treatise that was published by Archimedes in two volumes c. 225 BCE.

[1] It most notably details how to find the surface area of a sphere and the volume of the contained ball and the analogous values for a cylinder, and was the first to do so.

This result would eventually lead to the Lambert cylindrical equal-area projection, a way of mapping the world that accurately represents areas.

Archimedes used an inscribed half-polygon in a semicircle, then rotated both to create a conglomerate of frustums in a sphere, of which he then determined the volume.

[6] A palimpsest stolen from the Greek Orthodox Church in the early 20th century, which reappeared at auction in 1998, contained many of Archimedes works, including The Method of Mechanical Theorems, in which he describes a method to determine volumes which involves balances, centers of mass and infinitesimal slices.

A page from "On the Sphere and Cylinder" in Latin
The ratio of the volume of a sphere to the volume of its circumscribed cylinder is 2:3, as was determined by Archimedes