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This book offers a unique opportunity to understand the essence of one of the great thinkers of western civilization. A guided reading of Euclid's Elements leads to a critical discussion and rigorous modern treatment of Euclid's geometry and its more recent descendants, with complete proofs. Topics include the introduction of coordinates, the theory of area, history of the parallel postulate, the various non-Euclidean geometries, and the regular and semi-regular polyhedra.
Geometry as studied in this way is usually called synthetic Euclidean geometry and is the subject of Chapter 1 of Geometry: Euclid and Beyond. Interest in the synthetic geometry of triangles and circles flourished during the late 19th century and early 20th century.