Titlebook: Euclidean Geometry and its Subgeometries; Edward John Specht,Harold Trainer Jones,Donald H. Book 2015 Springer International Publishing S

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exercises; solutions to many of these, including all that are needed for this development, are available online at the homepage for the book at www.springer.com. Supplementary material is available online cover978-3-319-79533-1978-3-319-23775-6

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https://doi.org/10.1007/978-3-642-69250-5trices and determinants are given; there is also discussion of the roles of axioms, theorems, and definitions in a mathematical theory. The main development of the book begins here with the statement of eight incidence axioms and proof of a few theorems including one from Desargues.

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Book 2015ailed proofs. The axioms for incidence, betweenness, and plane separation are close to those of Hilbert. This is the only axiomatic treatment of Euclidean geometry that uses axioms not involving metric notions and that explores congruence and isometries by means of reflection mappings. The authors p

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Devotion to St. Anne in Texts and Imagesexistence of a line (not necessarily unique) through a given point parallel to a given line. Ordering of angles is defined, leading to the notions of acute angle, obtuse angle, and maximal angle of a triangle.

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Dilations of a Euclidean Plane (DLN),in an intricate process; these, in turn, are used to define dilations, which are shown to be belineations. A method is provided for point-wise construction of a dilation having a given action. A classical proposition attributed to Pappus of Alexandria is proved.

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Edward John Specht,Harold Trainer Jones,Donald H. Provides a complete and rigorous axiomatic treatment of Euclidean geometry..Proofs for many theorems are worked out in detail..Takes a modern approach by replacing congruence axioms with a transformat