Source edition
Euclid. Euclidis Opera Omnia, Volume 8. Menge, Heinrich, editor. Leipzig: Teubner, 1916.
Source data
Open Greek and Latin · CC BY-SA 4.0
Cloned and adapted by Humanitext, with ongoing edits.
Summary
This work is a collection of fragments that reconstructs several lost geometrical treatises by the ancient Greek mathematician Euclid, based on quotations from ancient commentators and surviving manuscript fragments. The text begins with an introduction to "On Divisions," which deals with dividing figures, and "Pseudaria" (Book of Fallacies), an educational work designed to help beginners detect geometrical errors. It then transitions to the core of the collection, detailing the "Porisms"—a concept positioned between theorems and problems—accompanied by numerous auxiliary proofs preserved by Pappus. These proofs demonstrate advanced propositions concerning collinearity, the composition of ratios, and the geometrical properties of circles and lines. In the latter section, the focus shifts to "Surface Loci," which extends two-dimensional relations into three-dimensional space, providing constructions and proofs of loci that trace conic sections such as parabolas and ellipses. The work concludes with propositions from "Conics," drawing on testimonies from Archimedes and Apollonius, thereby laying bare the sophisticated analytical and synthetic methods of ancient geometry.