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

Longmans, Brown, Green, Longman, and Roberts, 1863 - 362 páginas

THE POINT	1

Properties of Circles cutting two Circles at right Angles or at constant	7

Polar Coordinates	10

Meaning of the Constants in Equation of a Right Line	17

Equation of Line joining two given Points	23

Equations of Bisectors of Angles between two given Right Lines	30

Polar Equation of a Right Line	37

Circular Loci	37

Focal properties of Conics	196

Locus of intersection of Tangents which cut at a given Angle see	200

SIMILAR CONIC SECTIONS	208

All Conics having same Foci have four imaginary common Tangents	209

CHAPTER XIV	218

All Circles have imaginary common Points at infinity see also p 312	224

Anharmonic Ratio of four Points the same as that of their Polars	226

282	243

a Fixed point	49

Meaning of Constant in Equation a	55

Length of Perpendicular on a Line	62

To inscribe in a Conic a Triangle whose sides pass through fixed Points	64

CHAPTER V	68

Locus of the latter Point when Point on Curve varies	75

Condition for Equilateral Hyperbola and for Parabola in Trilinear	77

Common Tangent to two Circles	104

Conditions that general Equation should represent a Circle	115

CHAPTER X	126

Conjugate Diameters	136

Condition that a given Line should touch a Conic see also pp 253 326	143

Transformation of general Equation to the centre	144

Sum of Squares of Reciprocals of Semidiameters at right Angles is constant	150

Subnormal Constant	153

Equations of Tangents and Polars	156

To construct a pair of Conjugate Diameters inclined at a given Angle	162

185	168

Property of Focus and Directrix	169

193	175

Origin of names Parabola Hyperbola and Ellipse see also p 315	176

213	188

CHAPTER XIII	194

Locus of Vertex of a Triangle whose sides pass through fixed Points	244

Formation of Trilinear Equation of a Conic from Tangential and vice versa	248

Condition that Equation of second Degree should represent Right Lines	252

Equation of pair of Tangents through a given Point see also p 139	254

Lines from two fixed Points to a variable Point how cut any Parallel	259

Degree of Polar Reciprocal in general	265

p 271	271

Reciprocals of equal Circles have same Parameter	272

CHAPTER XVI	280

Parallels to Asymptotes through any Point on Curve how cut any Diameter	283

Circles circumscribing the Triangles formed by four lines meet in a Point	285

CHAPTER XVII	300

Locus of Pole of a Line with regard to a system of Confocal Conics	308

Analytic basis of Method of Projection	313

Area of any Polygon 32	319

Meaning of the Invariants when one Conic is a pair of Lines	325

Their eight Points of Contact lie on a Conic	331

General Tangential Equation of two Circular Points at infinity	337

Four Conics having double contact with S and passing through three	343

Direction of Tangents of Conics	349

Difference of Arc and Tangent constant from any Point on Confocal	355

Theorems on complete Figure formed by six Points on a Conic	362

Condition that three Lines may meet in a Point see also p 31 32	31

Título	A Treatise on Conic Sections: Containing an Account of Some of the Most Important Modern Algebraic and Geometric Methods
Autor	George Salmon
Edición	4
Editor	Longmans, Brown, Green, Longman, and Roberts, 1863
Procedencia del original	Universidad de Roma "La Sapienza"
Digitalizado	11 Jun. 2013
Largo	362 páginas

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