Synopses & Reviews
Elegant exposition of the postulation geometry of planes, including coordination of affine and projective planes. Historical background, set theory, propositional calculus, affine planes with Desargues and Pappus properties, construction of metrical planes, much more. Rigorous, lucid treatment of important area in modern mathematics. Corrected republication of the 3rd (1961) edition. Includes 56 figures.
Synopsis
"On the required reading list for all thoughtful students who wish to see mathematics from the 'higher standpoint'." American Mathematical Monthly
Elegant and original, this exposition discusses the foundations and development of both Euclidean and non-Euclidean geometry, particularly the postulational geometry of planes. Emphasis is placed upon the coordination of affine and projective planes as well as the basic unity of algebra and geometry.
Geared toward undergraduate and graduate students, the treatment begins with a brief but engaging sketch of the historical background of Euclidean geometry and an elementary summary of set theory and propositional calculus. Subsequent chapters explore coordinates in an affine plane, including those with Desargues and Pappus properties, and coordinatizing projective planes. The final two chapters containdetailed developments of simple sets of postulates for the Euclidean and non-Euclidean planes."
Synopsis
Elegant exposition of the postulation geometry of planes, including coordination of affine and projective planes. Historical background, set theory, propositional calculus, affine planes with Desargues and Pappus properties, much more. Includes 56 figures.