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Part One Analytic Geometry
Distance Between Two Points
Dividing a Line Segment in a Given Ratio
166 other sections not shown
arbitrary point asymptotic axiom system axis Cartesian coordinates Cartesian model centre chords circle coefficients coincides congruent conic section conjugate constructed convex coordinate axes coordinate system corresponding curve dihedral angles distance Dupin indicatrix edges ellipse equal Euclidean geometry Euler characteristic face angles Form the equation formulas fundamental form Gaussian curvature given point given straight line half-line half-plane Hence homogeneous coordinates hyperbola length line segment linear Lobachevsky locus of points motion normal curvature obtain origin of coordinates osculating plane parabola paraboloid parametric equations perpendicular point x0 points Ax points of intersection polar polygon polyhedron projective transformation Proof prove scalar second fundamental form Show sides solution sphere straight line ax straight line passing straight lines parallel surface tangent plane theorem three points tion translation triangle ABC vector vertex vertices x-axis xy-plane z-axis zero