WW Ben ano 15.1993 PREFACE TO THE FIRST EDITION. In the following work I have investigated the more elementary properties of the Ellipse, Parabola, and Hyperbola, defined with reference to a focus and directrix, before considering the General Equation of the Second Degree. I believe that this arrangement is the best for beginners. The examples in the body of each chapter are for the most part very easy applications of the book-work, and have been carefully selected and arranged to illustrate the principles of the subject. The examples at the end of each chapter are more difficult, and include very many of those which have been set in the recent University and College examinations, and in the examinations for Open Scholarships, in Cambridge. The answers to the examples, together with occasional hints and solutions, are given in an appendix. I have also, in the body of the work, given complete solutions of some illustrative examples, which I hope will be found especially useful. S. C. S. b Although I have endeavoured to present the elementary parts of the subject in as simple a manner as possible for the benefit of beginners, I have tried to make the work in some degree complete; and have therefore included a chapter on Trilinear Co-ordinates, and short accounts of the methods of Reciprocation and Conical Projection. For fuller information on these latter subjects the student should consult the works of Dr Salmon, [The Arti Dr Ferrers, and Dr C. Taylor, to all of whom it will be seen that I am largely indebted. I am indebted to several of my friends for their kindness in looking over the proof sheets, for help in the verification of the examples, and for valuable suggestions ; and it is hoped that few mistakes have escaped detection. CHAPTE CHAPTE Exar CHAPTE CHAP THE second edition has been carefully revised, and some additions have been made, particularly in the last Chapter SIDNEY SUSSEX COLLEGE, July, 1883. ? ele ler a mak CONTENTS. after they have read Chapter IX.] Every curve whose equation is of the second degree is a conic Co-ordinates of the centre of a conic The Discriminant Position and magnitude of the axes of a central conic . 179 181 182 183 Axis and latus recium of a parabola Equation of the asymptotes of a conic. Condition for a rectangular hyperbola . CHAPTER X. MISCELLANEOUS PROPOSITIONS. Equation of the tangent at any point of a conic Condition that a given straight line may touch a conic Equation of the polar of any point with respect to a conic Conjugate points and conjugate lines A chord of a conic is cut harmonically by a point and its Condition that two given lines may be parallel to conjugate Equi-conjugate diameters of a conic Common conjugate diameters of two conics Pairs of common chords of a circle and a conic are equally inclined to the axes of the conic Meaning of S-AS'=0, S-luv=0 and S - Nu-=0 Equation of a pair of tangents Equation of the director-circle Equation of a conic referred to tangent and normal CHAPTER XI. SYSTEMS OF CONICS. Conics through four points. [See also 295] Two parabolas through four points Centre-locus of conics through four points. [See also 296] Diagonal-points of a quadrangle are angular points of a |