Franz Rothe
eBook, ePUB

Old and New Topics in Geometry: Volume I (eBook, ePUB)

Projective, Neutral and Basic Euclidean Geometry

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The present first volume begins with Hilbert's axioms from the \emph{Foundations of Geometry}.After some discussion of logic and axioms in general, incidence geometries, especially the finite ones, and affine and projective geometry in two and three dimensions are treated. As in Hilbert's system, there follow sections about the axioms of order, and congruence in neutral geometry, the axioms of measurement and of completeness, and deviating from Hilbert, about circles.The insight of independence of the parallel axiom leaves many open roads to pursue,but the desire to develop a natural as well a...

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