CONIC ON SECTIONS: CONTAINING AN ACCOUNT OF SOME OF THE MOST IMPORTANT MODERN BY GEORGE SALMON, D.D., D.C.L., LL.D.. F.R.S., = REGIUS PROFESSOR OF DIVINITY IN THE UNIVERSITY OF DUBLIN. SIXTH EDITION. London: LONGMANS, GREEN, AND CO. 1879. 025 N 07 M.C.T. CONTENTS. [Junior readers will find all essential parts of the theory of Analytical Geometry included 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 168970 Length of Perpendicular from a Point on a Line Condition that three Lines may meet in a Point (see also p. 34) Equation of Line through the Intersection of two given Lines Test that three Equations may represent Right Lines meeting in a Point by Lines through the Vertices which meet in a Point Polar Equation of a Right Line EXAMPLES ON THE RIGHT LINE. 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 Coordinates Meaning of Constant & in Equation a = kß 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 Proof that middle Points of Diagonals of Quadrilateral lie in a Right Line Conditions that general Equation may represent a circle Coordinates of Centre and Radius Condition that two Circles may be concentric that a Curve shall pass through the origin Coordinates of Points where a given Line meets a given Circle Line cut harmonically by a Circle, Point, and its Polar Equation of pair of Tangents from a given Point to a Circle . Expression of Coordinates of Point on Circle by auxiliary Angle 96 |