A Survey of Geometry

AB,CD ABCD altitude Apollonius bisects C₁ C₂ called Ceva's Theorem chord coaxial collinear points concurrent conjugate corresponding cross ratio cube DEFINITIONS denote Desargues diagonals diameter dissection distinct points Draw ellipse equal Euclid's Elements Euclidean geometry Euclidean tools Figure finite fixed point given circle given line given point given triangle Greek hexagon homographic homographic ranges homothety hyperparallel ideal point infinity inscribed inversion isometry line segment Lobachevskian Lobachevskian plane locus mathematics Menelaus midpoint non-Euclidean geometry orthocenter orthogonal P₁ pair parabola parallel postulate parallelogram passing pencil plane geometry points of intersection polar pole polygon postulate set primitive terms Problem projective geometry proof proper conic propositions Prove radical axis radius rectangle respectively right angles right triangle S₁ Saccheri quadrilateral Section Show sides BC sphere square straight line straightedge T₁ T₂ tangent tetrahedra transformation triangle ABC vertex vertices whence