PREFACE. A NEW EDITION of the present Work having been called for, I have endeavoured to make this Treatise more deserving of the favourable reception it has met with. Having myself used it for the last five years in teaching Analytic Geometry to beginners, I have gained some experience as to the points where learners are likely to feel difficulties. I have accordingly rewritten a considerable part of the work, introducing in the early chapters copious numerical illustrations, such as I have been in the habit of using with my class. I have also endeavoured to separate, more carefully than in the former editions, between the elementary parts of the work and those intended for more advanced readers. The learner will find all essential parts of the theory of Analytic Geometry included in Chapters I., II., V., VI., X., XI., XII., omitting the articles marked with asterisks. Should he require examples for exercise, in addition to those contained in these chapters, he will find a sufficiently extensive collection of examples in Chapters III., VII., XIII. The remaining chapters treat of the algebraic and geometrical methods which have been introduced into use of late years, but of which no systematic account had been given in any elementary work at the time that the first edition of this Treatise was published. I have made several additions to these chapters in this edition. In the alterations which I have made throughout the book, I have profited by the works on Analytic Geometry which have appeared since the first edition was published, among which I may mention in particular Mr. Gaskin's, and Mr. Walton's "Examples on Analytic Geometry," and Mr. Puckle's "Treatise on Conic Sections." TRINITY COLLEGE, DUBLIN, July, 1855. Co-ordinates of Point cutting that Distance in a given Ratio, Transformation of Co-ordinates, PAGE. Meaning of the Constants in Equation of a Right Line, Equation of a Right Line in terms of its Intercepts on the Axes, in terms of the Perpendicular on it from Origin, and the Angles it makes with Co-ordinates of Intersection of two Right Lines, Condition that three Lines may meet in a Point (see also p. 29), Test that three Equations may represent Right Lines meeting in a Point, Connexion between Ratios in which Sides of a Triangle are cut by any Transversal, Equations of Bisectors of Angles between two given Right Lines, Problems where it is proved that three Lines meet in a Point, Three Bisectors of Sides of Triangle, . Three Bisectors of Angles of do. Perpendiculars from Vertices on Sides, Problems where it is proved that three Points lie on a Right Line, Middle Points of Diagonals of a complete Quadrilateral, Right Line passes through a Fixed Point if Constants in its Equation be con- Algebraic Expression for Anharmonic Ratio of a Pencil, Equations of a pair of Lines equally inclined to a, ß, Expression of Equation of any Right Line in terms of three given ones, Harmonic Properties of a Quadrilateral proved (see also p. 302), If Intersections of corresponding sides of two Triangles lie on a Right Line, lines 67 69 69 |
