## A Treatise on Conic SectionsThe classic book on the subject, covering the whole ground and full of touches of genius. |

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### Contents

CHAPTER | 1 |

Polar Coordinates | 10 |

Meaning of the Constants in Equation of a Right Line | 17 |

Equation of Line joining two given Points | 23 |

Length of Perpendicular from a Point on a Line | 28 |

Test that three Equations may represent Right Lines meeting in a Point | 34 |

Loci solved by Polar Coordinates | 51 |

Algebraic Expression for Anharmonic Ratio of a Pencil | 57 |

Polar Equation of Parabola | 207 |

Radii Vectores through Foci have equal difference of Reciprocals | 212 |

Similar Conic Sections | 222 |

CHAPTER XIV | 232 |

Equation of Conic passing through five given Points | 233 |

Form of Equation referred to a selfconjugate Triangle see also p 253 | 239 |

Pascals Theorem see also pp 280 301 316 319 379 | 246 |

Selfconjugate Triangle common to two Conies see also pp 348 361 | 256 |

Intersections of Perpendiculars of Bisectors of Sides and of Perpendiculars | 63 |

Meaning of an Equation resolvable into Factors | 67 |

Number of conditions that higher Equations may represent Eight Lines | 74 |

Equation of Tangent to a Circle at a given Point 80 | 80 |

Circle through three Points see also p 130 | 86 |

Conjugate Triangles Homologous | 92 |

Equation of radical Axis of two Circle3 | 99 |

Centres of Similitude | 105 |

To describe a Circle touching three given Circles see also pp 115 135 291 | 113 |

Locus of Point such that Area of Triangle formed by feet of Perpendiculars | 119 |

Equation of inscribed Circle derived from that of circumscribing | 125 |

Condition that four Circles may have a common orthogonal Circle | 131 |

Transformation to Parallel Axes of Equation of second Degree | 137 |

Discussion of Quadratic which determines Points where Line meets a Conic 183 | 139 |

Diameters of Parabola meet Curve at infinity | 145 |

Analytic condition that four Points should form a Harmonic System 305 | 146 |

Case where one of the Lines meets the Curve at infinity | 151 |

Functions of the Coefficients which are unaltered by transformation | 157 |

Figure of Hyperbola | 163 |

Locus of intersection of Normals at extremities of a Focal Chord see also p 335 211 | 166 |

Length of central Perpendicular on Tangent | 169 |

To draw a Normal through a given Point see also p 335 | 174 |

Rectangle under Focal Perpendiculars on Tangent is constant | 180 |

Origin of names Parabola Hyperbola and Ellipse see also p 328 | 186 |

Lines joining two fixed to variable Point make constant Intercept on Asymptote | 192 |

Parabola the limit of the Ellipse when one Focus passes to infinity | 200 |

Discriminant of Tangential Equation | 262 |

Equation of pair of Tangents through a given Point see also p 149 | 269 |

To inscribe in a Conic a Triangle whose sides pass through fixed Points see | 273 |

Principle of Duality | 276 |

Locus of Focus given four Tangents see also p 277 | 277 |

Polar of one Circle with regard to another | 283 |

Carnots Theorem respecting Triangle cut by Conic see also p 319 | 290 |

Centre the Pole of the line at infinity | 296 |

Generalizations of MacLaurins Method of generating Conies see also p 300 251 | 300 |

Criterion whether two Systems of Points be Homographic see also p 383 | 304 |

Condition that Line should be cut Harmonically by two Conies | 306 |

System of Conies touching four Lines when cut a Transversal in Involution | 313 |

Projective proof of Camots Theorem see also p 289 | 319 |

Sections of a Cone | 326 |

Orthogonal Projection | 332 |

Criterion whether Conies intersect in two real and two imaginary Points or not | 337 |

Tangential equation of four Points common to two Conies | 343 |

Envelope of Base of Triangle inscribed in one Conic two of whose sides touch | 349 |

Equation of reciprocal of two Conies having double contact | 356 |

To form the equation of the sides of selfconjugate Triangle common to | 362 |

Three Conies derived from a single Cubic method of forming its Equation | 368 |

Line which cuts off from a Curve constant Arc or which is of a constant length | 374 |

Theorems on complete Figure formed by six Points on a Conic 879 | 383 |

On systems of Conies satisfying four Conditions 38S | 391 |

### Common terms and phrases

anharmonic ratio asymptotes axes bisected bisector centre chord of contact circumscribing coefficients coincide common tangents condition confocal conic section conies conjugate diameters corresponding denote determine directrix double contact drawn ellipse envelope equal express find the coordinates find the equation find the locus fixed line fixed point focal foci focus four points geometrically given line given point harmonic Hence hyperbola imaginary points infinite distance inscribed intercept joining the points last Article length line at infinity line joining line meets meet the curve middle points ordinate origin pair of tangents parabola parallel Pascal's theorem pencil perpendicular point of contact point x'y points at infinity points of intersection polar equation pole quadratic quadrilateral quantity radical axis radius vector reciprocal rectangle represents right angles right line second degree sides square substituting subtended tangential equation theorem transform trilinear coordinates values vanish vertex vertices