Source edition
Archimedes. Archimède, Volume 3. Mugler, Charles, editor. Paris: Les Belles Lettres, 1971.
Source data
Open Greek and Latin · CC BY-SA 4.0
Cloned and adapted by Humanitext, with ongoing edits.
Summary
This book is a classical work of plane geometry comprising fifteen propositions and their proofs concerning circles, chords, tangents, and specific complex plane figures. Each chapter presents a geometric configuration, asserts a theorem, and provides a rigorous proof. The opening chapters deal with basic equality relations involving tangent circles, chords, and perpendiculars. In the middle section, the text focuses on the "arbelos" (shoemaker's knife), a figure formed by three semicircles, proving its area properties and the equality of its inscribed circles. The latter part explores the properties of orthogonal chords within a circle, relationships between tangents and secants, and the area of another unique figure, the "salinon" (salt-cellar). The final chapter concludes with the properties of a regular pentagon inscribed in a semicircle, deriving a corollary related to the golden ratio (extreme and mean ratio). The work showcases the exquisite logical progression of ancient geometry, resolving complex relations of areas and ratios through ingenious proofs.