Source edition
Archimedes. Archimède, Volume 4. Mugler, Charles, editor. Paris: Les Belles Lettres, 1972.
Source data
Open Greek and Latin · CC BY-SA 4.0
Cloned and adapted by Humanitext, with ongoing edits.
Summary
This work compiles scholarly fragments attributed to ancient Greek mathematicians and astronomers, such as Pappus, Theon, and Heron, focusing on geometry, optics, and astronomy. The first half centers on the theory of polyhedra, where Pappus presents Plato's five regular solids and Archimedes' thirteen semi-regular solids. It details the mathematical rules for calculating the number of faces, edges, and vertices for each, explaining the geometric process of constructing semi-regular solids by truncating the corners of regular ones. Additionally, a fragment from Heron discusses the fourteen-sided polyhedra known to Plato. The second half features Theon's explanation of Ptolemy's theory of atmospheric refraction, analyzing the physical and geometric principles behind why celestial bodies appear larger near the horizon, with reference to Archimedes.