Excursions in Geometry

altitude Apollonius axioms bisected C₁ called center of inversion circle of inversion collinear cone congruent conic constant convex cross-ratio curve Dandelin sphere diagram diameter distance draw ellipse equal equation Euclidean figure fixed circle fixed point given circles H. S. M. Coxeter hence hexagon hexlet Howard Eves hyperbola infinite number inscribed interior angles intersect invariant inverse points inversive geometry inverted model isosceles line at infinity locus lying mathematics mean nine-point circle orthogonal pair Pappus parabola parallel Pascal's Theorem passes pentagon perpendicular bisector plane polygons position postulate preserved problem projective geometry proof prove radical axis radii radius rectangle right angle right triangle ruler and compass S₁ semicircle similar six spheres Soddy's Hexlet solution solved square ẞ circle Steiner chain straight line Theorem 14 three circles three lines transformation trisection vertex vertices