Fundamental Concepts of Geometry |
Contents
FOUNDATIONS OF GEOMETRY | 1 |
SYNTHETIC PROJECTIVE GEOMETRY | 25 |
COORDINATE SYSTEMS | 69 |
Copyright | |
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Common terms and phrases
absolute involution affine geometry affine transformation algebraic analytic projective geometry called century collinear complete quadrangle concepts conic considered construction coordinate system coplanar cross ratio defined definitions determined diagonal directed angle elements elliptic geometry equations equiareal transformation equivalent Euclid's euclidean geometry euclidean transformations exists fifth postulate harmonic sets homeomorphic homogeneous coordinates homothetic transformation hyperbolic geometry hyperbolic line ideal line ideal point identity transformation integer intersect invariant points involution isomorphic line segment mathematical matrix noneuclidean geometries nonhomogeneous coordinates obtained ordinary points orthogonal line reflections parallel pencil of lines pencil of points perpendicular perspective plane dual point reflection points and lines polarity Postulates P-1 projective transformation proof properties Prove quadrangular set quadrilateral rational real numbers real projective plane Repeat Exercise right angles rotation set of points set of postulates sides similarity transformations statement surface synthetic projective geometry Theorem three distinct points three-space tion topological trans triples undefined vertices