Journey into Geometries

added Alice angle of parallelism angular answered asked Alice axioms become belonging centre Chapter circle circles orthogonal common congruent construction contains continued critical defect Denote diameter distance draw elliptic family equal Euclid Euclidean geometry exactly Figure follows given glasses going hence Hostess hyperbolic family hyperbolic plane ideal Infinity inside intersect inverse joining least length Lewis Carroll lies light looked mean measure meet move Note orthogonal pair pass perpendicular perspectivity plane Poincaré Poincaré line possible postulate Problem projective prove question radical axis radius reflection remains respectively right angles segments Show sides similar square straight line suddenly Suppose sure tangent theorem things thought touching transformation triangle turned unique voice Whatif