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Axiom of congruent transformations
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absolute polar analytic assemblage Axiom axis called central conic centres of gravity Chapter circle collinear common perpendiculars concurrent lines cone confocal congruent distances congruent group congruent transformation conjugate imaginary connected space consistent region constant coplanar corresponding cos2 cosine cross ratio curve defined Definition determined dihedral angle domain elliptic space equation euclidean space Gaussian curvature Gaussian curvature zero geometry given line given points half-lines half-plane harmonically separated hence homogeneous coordinates horocycle hyperbolic space hyperboloid identical infinite number infinitesimal intersect invariant involution Let the reader limit linear lines of curvature measure meet necessary and sufficient non-euclidean non-euclidean geometry normal opposite pairs parameter paratactic pencil projective geometry quadric quadrilateral reader show real points restricted region right angle segment sides sphere straight angle sufficient condition suppose tangent plane tetrahedron Theorem triangle values vertex vertices