Coordinate Geometry

A thorough, complete, and unified introduction, this volume affords exceptional insights into coordinate geometry. Invariants of conic sections and quadric surfaces receive full treatments. Algebraic equations on the first degree in two and three unknowns are carefully reviewed. Throughout the book, results are formulated precisely, with clearly stated theorems. More than 500 helpful exercises. 1939 edition Table Of Contents: IntroductionixChapter 1Points and Lines in the PlaneSection 1The Equation of the First Degree in x and y3Section 2Cartesian Coordinates in the Plane8Section 3Distance between Two Points - Direction Numbers and Direction Cosines - Angle between Directed Line Segments11Section 4Internal and External Division of a Line Segment17Section 5An Equation of a Line - Parametric Equations of a Line20Section 6Direction Numbers and Direction Cosines of a Line - Angle between Two Lines27Section 7The Slope of a Line33Section 8Directed Distance from a Line to a Point35Section 9Two Equations of the First Degree in x and y - Determinants of the Second Order39Section 10The Set of Lines through a Point47Section 11Oblique Axes53Section 12The Circle54Section 13Resume - Line Coordinates62Chapter 2Lines and Planes in Space - DeterminantsSection 14Rectangular Coordinates in Space71Section 15Distance between Two Points - Direction Numbers and Direction Cosines of a Line Segment - Angle between Two Line Segments76Section 16Equations of a Line - Direction Numbers and Direction Cosines of a Line - Angle of Two Lines82Section 17An Equation of a Plane88Section 18The Directed Distance from a Plane to a Point - The Distance from a Line to a Point95Section 19Two Equations of the First Degree in Three Unknowns - A Line as the Intersection of Two Planes98Section 20Two Homogeneous Equations of the First Degree in Three Unknowns104Section 21Determinants of the Third Order - Three Equations of the First Degree in Three Unknowns106Section 22Three Homogeneous Equations of the First