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

Front Cover
D. Van Nostrand, 1880 - Geometry, Analytic - 287 pages
 

Contents

Determination of a Point in Polar Coordinates
11
Definitions Locus Constants Variables
12
Constructing Equations
13
Independent Variable Dependent Variable Functions
14
Continuous and Discontinuous Curves
15
Discussion of Equations
16
Discussion of Equation of First Degree
23
CHAPTER II
28
Intersection of Two Lines
49
CHAPTER III
57
Locus Unchanged by Transformation
63
CHAPTER IV
69
ART PAGE 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
CHAPTER V
90
Definition of a Parabola
91
Equation of the Parabola
92
Tangent to the Parabola
94
Normal to the Parabola
96
Intersection of Tangent and Focal Perpendicular
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
104
Parameter of any Diameter
105
Definition
106
Focal Chords
107
Examples
109
CHAPTER VI
112
Tangent to the Circle xa² + yb²
113
Transformation to New Axes
114
Focal Distance of Point on Ellipse
119
Circle described on Major Axis
120
Tangent to the Ellipse
121
ART PAGE 76 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 referred to Conjugate Diameters
138
Tangents at Extremities of a Chord
139
Rectangle of Focal Perpendiculars
141
Polar Equation of Ellipse
142
Polar Equation of Ellipse referred to Centre
143
Focal Chords
144
Examples
145
CHAPTER VII
151
Equation of the Hyperbola
152
Equation with Lefthand Vertex as Origin
153
Equation referred to Centre
154
Focal Distance of a Point
158
The Conjugate Hyperbola
160
Construction of Conjugate Hyperbolas
162
Tangent to the Hyperbola
163
Intersection of Tangent and Focal Perpendicular
164
Point of Contact of Tangent
165
Equation of Hyperbola referred to Conjugate Diameters
176
Tangents at Extremities of a Chord
178
Focal Chords
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
Noncentral Locus
205
Examples
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
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
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
250
Examples
252
CHAPTER III
255
Traces of a Plane
256
The Equation of the First Degree
257
Equations in Terms of Intercepts
258
Length of Perpendicular from a Given Point
260
Angle between Two Planes
261
Angle between a Line and a Plane
263
Examples
264
CHAPTER IV
268
Equation of a Right Circular Cone
269
Equation of a Cylinder
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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