In this book the author has presented the elements of Coordinate Geometry in a manner suitable for beginners and junior students. Cartesian and Polar Coordinates only are used, and the book forms Part I of the complete work. Part II deals with Trilinear Coordinates, Projection, Reciprocation, etc.
The Straight Line and Circle have been treated more fully than the other portions of the subject, since it is generally in the elementary conceptions that beginners find great difficulties.
The book is divided into 17 chapters. There are a large number of Examples, over 1100 in all, and they are, in general, of an elementary character. The examples are especially numerous in the earlier parts of the book.
CONTENTS 1. Introduction 2. Coordinates, Lengths of Straight Lines and Areas of Triangles Polar coordinates 3. Locus, Equation to a Locus 4. The Straight Line, Rectangular Coordinates Straight line through two points Angle between two given straight lines Conditions that they may be parallel and perpendicular Length of a perpendicular Bisectors of angles 5. The Straight Line (Continued) Polar Equations and Oblique Coordinates Equations involving an arbitrary constant Examples of loci 6. On Equations Representing Two or More Straight Lines Angle between two lines given by one equation General equation of the second degree 7. Transformation of Coordinates Invariants 8. The Circle Equation to a tangent Pole and polar Equation to a circle in polar coordinates Equation referred to oblique axes Equations in terms of one variable 9. Systems of Circles Orthogonal circles Radical axis Coaxal circles 10. The Parabola Equation to a tangent Some properties of the parabola Pole and polar Diameters Equations in terms of one variable 11. The Parabola (Continued) Loci connected with the parabola Three normals passing through a given point Parabola referred to two tangents as axes 12. The Ellipse Auxiliary circle and eccentric angle Equation to a tangent Some properties of the ellipse Pole and polar Conjugate diameters Four normals through any point Examples of loci 13. The Hyperbola Asymptotes Equation referred to the asymptotes as axes One variable. Examples 14. Polar Equation of a Conic Section, Its Focus being the Pole Polar equation to a tangent, polar, and normal 15. General Equation of the Second Degree, Tracing of Curves Particular cases of conic sections Transformation of equation to centre as origin Equation to asymptotes Tracing a parabola Tracing a central conic Eccentricity and foci of general conic 16. The General Conic Tangent Conjugate diameters Conics through the intersections of two conics The equation S = ï¬uv General equation to the pair of tangents drawn from any point The director circle The foci The axes Lengths of straight lines drawn in given directions to meet the conic. Conics passing through four points Conics touching four lines The conic LM = R2 17. Miscellaneous Propositions On the four normals from any point to a central conic Confocal conics Circles of curvature and contact of the third order Envelopes Answers
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