A TREATISE ON CONIC 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: 1879. 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 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 k in Equation a = kB 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. 317) Homologous Triangles: Centre and Axis of Homology Condition that two Lines should be mutually Perpendicular Length of Perpendicular on a Line 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 Number of conditions that higher Equations may represent Right Lines 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 General definition of Tangents Condition that Circle should touch either Axis Equation of Tangent to a Circle at a given Point Condition that a Line should touch a Circle Equation of Polar of a Point with regard to a Circle or Conic Line cut harmonically by a Circle, Point, and its Polar Equation of pair of Tangents from a given Point to a Circle . Circle through three Points (see also p. 130) Condition that four Points should lie on a Circle, and its Geometrical meaning Expression of Coordinates of Point on Circle by auxiliary Angle |