A Treatise on the Analytic Geometry of Three Dimensions

angles axes axis becomes called centre circle co-ordinates coefficients common condition cone confocal conic conjugate consecutive consider constant contain corresponding cosß cosy cubic curvature curve denote determine developable diameters difference differential direction distance double point drawn edges eliminating envelope equal equation evidently expressed fixed focus follows four geodesic give given given line Hence hyperboloid infinity intersection last article length line joining line of curvature locus manner meets normal obtain origin parallel pass perpendicular plane curve point of contact pole principal projections properties proved quadric quantity radii radius of curvature ratio reciprocal regard relation represents respect result right angles right line roots seen sheet sides sphere squares substituting surface tangent plane theorem touch transformed triangle umbilic values vanish vertex written