A Treatise on Analytical Geometry: With Applications to Lines and Surfaces of the First and Second Orders

A.S. Barnes, 1876 - 212 Seiten

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ANALYTICAL GEOMETRY OF TWO DIMENSIONS	9

RELATIVE POSITION OF POINTS	15

Constants and Variables	21

Equation of Line Through Two Points	27

TRANSFORMATION OF COORDINATES	37

ABT PAGE 2 1 Passing from One Rectangular System to Another	38

Passing from Rectangular to Polar System	39

Equation of Line Referred to Oblique Axes	40

Conjugate Hyperbolas	128

Asymptotes	131

Hyperbola Referred to Principal Vertex	133

Polar Equation of Hyperbola	134

Discussion of Equations	136

Supplementary Chords and Conjugate Diameters	137

Tangent Bisects Angle Between Focal Lines	139

Hyperbola Referred to Conjugate Diameters	143

OF THE CIRCLE 24 Definition of Terms	42

Equation of Circle Referred to Rectangular Axes	43

Other Forms of the Equation	44

Discussion of the Equations	46

Polar Equation of Circle	49

General Equations of Tangent and Normal	50

Equation of Tangent and Normal to Circle	52

OF THE PARABOLA 31 Definition of Terms	57

Equation of the Parabola	59

Polar Equation of the Parabola	63

Discussion of Polar Equation	65

Tangent Equally Inclined to Axis and Focal Line	67

Ordinates of Point of Contact	70

Parabola Referred to Oblique Axes	72

Discussion of Equation	73

Equation of tangent Referred to Oblique Axes	75

Of Poles and Polars	76

OF THE ELLIPSE 44 Definitions of Terms	82

Construction of the Curve	83

Equation of the Ellipse	85

Discussion of the Equation	87

Equation Referred to Principal Vertex	90

Polar Equation of Ellipse	91

Discussion of the Equations	92

Central Polar Equation	93

Equations of Tangent and Normal	95

ART PAGE 54 Supplementary Chords and Conjugate Diameters	98

Normal Bisects Angle Between Focal Lines	102

Ellipse and Circumscribing Circle 104	104

Ellipse Referred to Conjugate Diameters	107

Discussion of the Equation	108

Relation of Conjugate Diameters	109

Tangent Referred to Conjugate Diameters	113

Of Poles and Polars	114

Of the Hyperbola 62 Definitions of Terms	122

Construction of the Curve	123

Equation of Hyperbola	124

Discussion of the Equation	126

Of Poles and Polars	144

Equation of Hyperbola Referred to Asymptotes	145

Discussion	146

Tangent Referred to Asymptotes	147

Intercepts of Secant	148

LINES OF THE SECOND ORDER 81 Classification of Lines	152

First Transformation	153

i 40c	158

i ac	159

6nac	160

Of Centres	163

PART II	173

Polar Coordinates	175

Of Projections	176

Distance Between Two Points	177

Angle Between Line and Axes	178

OF THE STRAIGHT LINE 95 Equations of Straight Line in Space	179

Discussion of the Equations	180

Line Through One and Two Points	181

Angle Between Two Lines	182

Discussion	185

OF THE PLANE 100 Equation of Plane	188

ION Discussion	189

Angle Between Two Planes	192

OF SURFACES OF REVOLUTION 103 Definitions of Terms	196

Equation of a Surface of Revolution	197

Equation of Sphere	198

Equation of Oblate Spheroid	199

Equation of Hyperboloid of One Nappe	200

Equation of Paraboloid of Revolution	201

Method of Discussion	202

Discussion of Spheroids	203

Discussion of Hyperboloids	204

Discussion of Paraboloids	206

OF CONIC SECTIONS 116 Method of Discussion	207

General Equation of Conic Section	208

Discussion	209

Titel	A Treatise on Analytical Geometry: With Applications to Lines and Surfaces of the First and Second Orders
Autor	William Guy Peck
Verlag	A.S. Barnes, 1876
Original von	Harvard University
Digitalisiert	15. Aug. 2007
Länge	212 Seiten

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