An Elementary Treatise on Analytic Geometry, Embracing Plane Geometry and an Introduction to Geometry of Three Dimensions

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D. Van Nostrand, 1880 - 287 páginas
 

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Definitions Locus Constants Variables
12
Constructing Equations
13
Independent Variable Dependent Variable Functions
14
Continuous and Discontinuous Curves
15
Discussion of Equations
18
CHAPTER II
28
Symmetrical Form of Equation
30
Normal Form of Equation
31
Form of Equation referred to Oblique Axes
32
Discussion of Equation of First Degree
34
Perpendicular from a Given Point upon a Given Line
37
Equation of Line through a Given Point
38
Equation of Line through Two Given Points
40
Angle between Two Given Right Lines
43
Equation of Line making Given Angla with Given Line 4G 29 Intersection of Two Lines
49
Line through Intersection of Two Given Lines
50
Polar Equation of Right Line
52
Examples
54
CHAPTER III
57
To New Axes Parallel to Old
58
General Formulae of Transformation
59
From Rectangular to Polar Coordinates
61
Locus Unchanged by Transformation
62
Geometrical Applications
63
CHAPTER IV
69
Tangent to the Circle
73
Normal to the Circle Subnormal Subtangent
75
Tangent to the Circle xa + yft2 rs
76
Intersection of Line and Circle
78
abt A0 46 Length of Tangent from a Given Point
79
Chord of Contact
81
Locus of Intersection of Tangents at Extremities of a Chord
82
Pole and Polar
83
Polar Equation of the Circle
84
Examples 85
85
CHAPTER V
90
Definition of a Parabola
91
Equation of the Parabola
92
Tangent to the Parabola
94
Normal to the Parabola
97
Point of Contact of Tangent
99
Equation of Chord of Contact
100
Applications to the Parabola
101
Diameter of a Curve
102
Equation of Parabola
103
Parameter of any Diameter
105
Polar Equation of Parabola
106
Focal Chords
107
Examples
109
CHAPTER VI
112
Equation of the Ellipse
113
Transformation to New Axes
114
Focal Distance of Point on Ellipse
119
Circle described on Major Axis
120
ABT PAGE 70 Intersection of Tangent and Focal Perpendicular
125
Point of Contact of Tangent
126
Chord of Contact
127
Diameter of an Ellipse
129
Conjugate Diameters
130
Tangent Parallel to a Conjugate Diameter
131
Extremities of a Diameter
132
Perpendicular on the Tangent
133
Eccentric Angle and Conjugate Diameters
134
Supplemental Chords
135
Diameters and Supplemental Chords
136
Ellipse referred to Conjugate Diameters
137
Tangent to the Ellipse 121
138
Tangents at Extremities of a Chord
139
Intersection of Tangents at Right Angles
140
Rectangle of Focal Perpendiculars
141
Polar Equation of Ellipse
142
Polar Equation of Ellipse referred to Centre
143
Focal Chords
144
Tangent to the Hyperbola 102
163
10D Intersection of Tangent and Focal Perpendicular
164
Point of Contact of Tangent
165
Definition of an Asymptote
167
Equation of any Diameter
168
Conjugate Diameters in the Hyperbola
171
Tangent Parallel to a Conjugate Diameter
172
Lengths of Conjugate Diameters
173
Angle between Conjugate Diameters
174
Supplemental Chords
175
Equation of Hyperbola referred to Conjugate Diameters
176
Tangents at Extremities of a Chord
178
Focal Chorda
179
Intersection of Tangents at Right Angles
180
Polar Equation of Hyperbola
181
Polar Equation referred to the Centre
182
Properties peculiar to Hyperbola
184
Equation of Hyperbola referred to Asymptotes
185
Tangent referred to the Asymptotes
187
Intercepts of Secant between Hyperbola and Asymptotes
189
Conjugate Diameters referred to Asymptotes
190
Extremities of Conjugate Diameters
191
Examples
192
CHAPTER VIII
196
First Transformation
197
Second Transformation
199
Relations between Coefficients of Transformation
203
Properties of Transformation
204
Examples 307
207
CHAPTER IX
219
Equation of the Cissoid
220
Conchoid of Nicomedes
221
Equation of the Conchoid
222
The Witch of Agnesi
224
Lemniscate of Bernouilli
225
The Cycloid
227
Equation of the Cycloid
228
Equation of the Cycloid
229
158 Spirals
230
Equation of the Spiral of Archimedes
231
Reciprocal or Hyperbolic Spiral
232
The Lituus
233
The Logarithmic Spiral
235
PART II
237
Coordinate Planes and Axes
238
Positions of Coordinate Planes
239
Theory of Projections
240
Distance between Two Points
241
Direction Cosines of a RadiusVector 242
242
Point in Polar Coordinates
243
ART PAGE 172 Equations of a Right Line
244
Line in Space under Certain Conditions
246
Angle between Two Lines in Space
247
Angle in Terms of Special Constants
248
Intersection of Two Lines 230
252
CHAPTER III
255
Traces of a Plane
257
Equations in Terms of Intercepts
258
Length of Perpendicular from a Given Point 200
260
Angle between Two Planes 201
261
Angle between a Line and a Plane 63
264
CHAPTER IV
268
Equation of a Right Circular Cone
269
Equation of a Cyltoder
270
Equation of a Paraboloid of Revolution
271
Ellipsoids of Revolution
272
The Prolate Spheroid Note
274
The Oblate Spheroid
275
Hyperboloid of Revolution of One Nappe
276
Sections of a Cone
278
Tangent Plane to an Ellipsoid
281
Examples
284
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