A Treatise on Conic Sections: Containing an Account of Some of the Most Important Modern Algebraic and Geometric Methods (Classic Reprint)

Meaning of anE quation resolvable into Factors .. .67 of aH omogeneous Equation of the nth Degree .. ,68 Imaginary Right Lines .. .. ..69 Angle between two Lines given by a single Equation ... 70 Equation of Bisectors of Angles between these Lines .. .71 Condition that Equation of second Degree should represent Right Lines (see also pp. 149, 153, 155, 266 .. ..72 Number of conditions that higher Equations may represent Right Lines .74 Number of terms in Eqxiation of nth Degree .... 74 CHAPTER VL THE CIRCLE. Equation of Circle .... .. 75 Conditions that generalE quation may represent a circle .75 Coordinates of Centre andR adius .. .. .76 Condition that two Circles may be concentric .. .. 77 that aC urve shall pass through the origin .. ..77 Coordinates of Points where a given Line meets a given Circle ., 77 Imaginary Points .. .. .. .77 General definition ofT angents ..... 78 Condition that Circle should touch either A xis .. ,.79 Equation ofT angent to aC ircle at a given Point .. 80, 81 Condition that a Line should touch aC ircle .. ..81 Equation of Polar of a Point with regard to aC ircle or Conic .. 82, 83 Length ofT angent to aC ircle .. .. ..84 Line cut harmonically by aC ircle, Point, and its Polar ... 85 Equation of pair ofT angents from a given Point to aC ircle .. .85 Circle through threeP oints (see also p. 130) .... 86 Condition that four Points should lie on aC ircle, and its Geometrical meaning .86 Polar Equation of aC ircle ...... 87 CHAPTER VII. EXAMPLES ON CIRCLE. Circular Loci .. .. .. .88 Condition that intercept by Circle on a given Line may subtend a right Angle at a given Point ...... 30 If a Point A lie on the polar of B, Blies on the polar of A .. .91 Conjugate and self-con jugate Triangles .... 91 Conjugate Triangles Homologous .. .. .92 If two Chords meet in a Point, Lines joining their extremities transversely meet on its Polar ...
(Typographical errors above are due to OCR software and don't occur in the book.)