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

Longman, Brown, Green, and Longmans, 1855 - Počet stran: 324

CHAPTER I	1

Distance between two Points	10

in any Position	18

Condition that three Lines may meet in a Point see also p 29	29

Problems where it is proved that three Lines meet in a Point	30

9	36

Investigation of Loci	39

11	46

CHAPTER XII	175

Intercept on Axis by two Lines equal to projection of distance between their Poles	181

CHAPTER XIII	188

20	190

Locus of intersection of Tangents which cut at a given Angle see also p 234	194

SIMILAR CONIC SECTIONS	201

Equation of Asymptotes to a Conic	202

Anharmonic Property of Conics proved see also p 225	203

Condition that four Points of a Conic should lie on a Circle	208

Diagonals of inscribed and circumscribed Quadrilateral pass through the same Point	218

Proof of Pascals Theorem	221

Condition that either Axis should be an Asymptote	224

Locus of centre of a Conic through four Points	233

All Conics having same Foci have four imaginary common Tangents	244

Equation of Circle inscribed in a Triangle	245

Lines joining corresponding Vertices of Conjugate Triangles meet in a Point	246

Condition that Equation of second Degree should represent Right Lines see also	250

CHAPTER XV	253

Polar of one Circle with regard to another	259

Evolutes of Conics	260

Locus of a Point whence Tangents to two Conics form a Harmonic Pencil	273

To inscribe a Polygon in a Conic whose sides pass through fixed Points	280

MacLaurins Method of generating Conics see also pp 281 283	281

231	310

Method of deducing Properties of Plane Curves from those of Spherical	315

Determination of a Conic five Conditions being given	321

Equation of Conic having double contact with two given Conics	324

Název	A Treatise on Conic Sections: Containing an Account of Some of the Most Important Modern Algebraic and Geometric Methods
Autor	George Salmon
Vydání	3
Vydavatel	Longman, Brown, Green, and Longmans, 1855
Délka	Počet stran: 324

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Expression of Equation of any Right Line in terms of three given ones	53

Meaning of an Equation resolvable into Factors	62

THE CIRCLE	70

13	80

Condition that four Points should lie on a Circle and its Geometrical meaning	84

30	90

CHAPTER VIII	97

Equation of Circle circumscribing Triangle a ß	104

Centres of Similitude	110

CHAPTER X	118

Given four Points on a Conic Locus of Pole of a fixed Point or Envelope of Polar	132

CHAPTER XI	138

Eccentricity of a Conic given by general Equation	140

15	142

Supplemental Chords	156

17	157

Sum or difference of Focal Radii constant	162

Polar Equation of Parabola	167

Angle subtended at the Focus by a Chord bisected by Line joining Focus to its Pole	168

19	171