Britannica
Sources used in this answer
What three-dimensional figures are studied in Books XI through XIII of Euclidâs Elements?
Created from Britannica articles
using AI.
AI can make mistakes, so verify using Britannica articles.
Euclid
Euclid, coloured woodcut, 1584. His Elements, a treatise on geometry and mathematics, is one of the most influential books ever written.
In Books XI through XIII of the Elements, Euclid explores three-dimensional figures, a field referred to in Greek as stereometria.1
- Book XI focuses on the intersections of planes and lines, as well as the properties of parallelepipeds, which are solids defined by parallel parallelograms as opposite faces.21
- Book XII utilizes the method of exhaustion to examine the volumes of various solid figures, including the sphere, the pyramid, and the relationship between the volumes of spheres and their diameters.21
- Book XIII serves as the culmination of the work by describing the construction of the five regular Platonic solids (the pyramid or tetrahedron, cube, octahedron, dodecahedron, and icosahedron) within a given sphere.213