A TREATISE ON 1239 CONIC SECTIONS: CONTAINING AN ACCOUNT OF SOME OF THE MOST IMPORTANT MODERN BY GEORGE SALMON, D.D., D.C.L., F.R.S., REGIUS PROFESSOR OF DIVINITY IN THE UNIVERSITY OF DUBLIN, 4 Fifth Edition. LONDON: LONGMANS, GREEN, READER, AND DYER. 1869. А HARVARD COLLEGE LIBRARY 1872, Dec. 20. CAMBRIDGE: PRINTED BY WILLIAM METCALFE, GREEN STREET. CONTENTS. [Junior readers will find all essential parts of the theory of Analytical Geometry included in terms of the Perpendicular on it from Origin, and the Angles it makes 25 PAGE Length of Perpendicular from a Point on a Line Equations of Bisectors of Angles between two given Right Lines Condition that three Lines may meet in a Point (see also Area of Triangle formed by three given Lines Equation of Line through the Intersection of two given Lines 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 35 Investigation of rectilinear Loci of Loci leading to Equations of Higher Degree Problems where it is proved that a Moveable Line always passes through a Centre of Mean Position of a series of Points Right Line passes through a Fixed Point if Constants in its Equation be Loci solved by Polar Co-ordinates Meaning of Constant k in Equation a = Bisectors of Angles, Bisectors of Sides, &c. of a Triangle meet in a point Expression of Equation of any Right Line in terms of three given ones Harmonic Properties of a Quadrilateral proved (see also p. 305) middle points of Sides, lie in a Right Line (see also pp. 60, 127) Proof that middle Points of Diagonals of Quadrilateral lie in a Right Line Condition that Equation of second Degree should represent Right Lines (see also pp. 144, 148, 150, 255) Number of conditions that higher Equations may represent Right Lines Conditions that general Equation may represent a Circle Co-ordinates of Centre and Radius Condition that two Circles may be concentric that a Curve should pass through the origin Co-ordinates of Points where a given Line meets a given Circle Distances of two Points from the centre, proportional to the distance of each Expression of Co-ordinates of Point on Circle by auxiliary Angle 96 |