An Elementary Course in Analytic Geometry

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American book Company, 1898 - Geometry, Analytic - 390 pages
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Awwwwwsum!!!!...book.... helped me a lot.:)

Contents

Properties of the quadratic equation 12 The quadratic equation involving two unknowns
12
Trigonometric Conceptions and Formulas 13 Directed lines Angles
15
Trigonometric ratios
17
Functions of related angles
18
Other important formulas
19
ARTICLE
20
Orthogonal projection
21
15
23
CHAPTER II
24
LESSON
25
To find the co÷rdinates of the point which divides in a given
37
ARTICLE PAGE 44 Equation of straight line through given point and in given
44
Loci by polar co÷rdinates
46
a by any trans
52
41
56
44
63
Equation of a circle polar co÷rdinates
64
Equation of locus traced by a moving point
65
second method
66
The conic sections
67
4
70
The use of curves in applied mathematics
73
Through a given external point two tangents to a conic
74
52
76
11
79
CHAPTER V
81
Equation of straight line in terms of the intercepts which it makes on the co÷rdinate axes
83
Equation of straight line through a given point and in a given direction
84
Equation of straight line in terms of the perpendicular from the origin upon it and the angle which that perpendicular makes with the xaxis
86
second method
87
Summary
88
Every equation of the first degree between two variables has for its locus a straight line
89
Reduction of the general equation Ax + By + C 0 to the standard forms Determination of a b m p and a in terms of A B and C
91
To trace the locus of an equation of the first degree
94
Special cases of the equation of the straight line Ax+By+C0
95
To find the angle made by one straight line with another
97
Condition that two lines are parallel or perpendicular
98
Line which makes a given angle with a given line
101
18
105
Bisectors of the angles between two given lines
108
The equation of two lines
110
Condition that the general quadratic expression may be factored
111
co÷rdinate axes oblique
115
19
116
polar co÷rdinates
118
Cartesian Co÷rdinates Only
124
Equation of a chord of contact
126
Polar Co÷rdinates
130
In rectangular co÷rdinates every equation of the form x2 +
137
Equation of tangent to the circle in terms of the co÷rdinates
144
ARTICLE PAGE 85 Equation of a normal to a given circle
147
Lengths of tangents and normals Subtangents and sub normals
149
Tangent and normal lengths subtangent and subnormal for the circle
150
To find the length of a tangent from a given external point to a given circle
151
From any point outside of a circle two tangents to the circle can be drawn
152
Chord of contact
154
Poles and polars
156
Fundamental theorem
157
Geometrical construction for the polar of a given point and for the pole of a given line with regard to a given circle
158
Circles through the intersections of two given circles
160
Radical axis radical center
161
polar co÷rdinates
162
Equation of a circle referred to oblique axes
163
Every equation of the form
186
Intrinsic property of the hyperbola Second standard equa
195
Normal to the conic Ax2 + By2 + 2 Gx + 2 Fy + C 0 at
203
21
205
Construction of the parabola
220
Diameters
230
equation
231
CHAPTER X
237
Construction of the ellipse
240
The tangent and normal bisect externally and internally
246
Diameters
253
ARTICLE
257
Supplemental chords
259
CHAPTER XI
265
Conjugate hyperbolas
271
Equilateral or rectangular hyperbola
277
ARTIOLE PAGE 171 Diameters
284
Properties of conjugate diameters of the hyperbola
285
Supplemental chords
287
Equations representing an hyperbola but involving only one variable
288
CHAPTER XII
292
Illustrative examples
294
Test for the species of a conic
297
Center of a conic section
298
Transformation of the equation of a conic to parallel axes through its center
299
The invariants A + B and H2 AB
301
1
303
Summary
306
The equation of a conic through given points a
307
CHAPTER XIII
309
The conchoid of Nicomedes
312
The witch of Agnesi
314
The lemniscate of Bernouilli
315
a The limašon of Pascal
318
b The cardioid
319
The Neilian or semicubical parabola
320
Transcendental Curves 191 The cycloid
321
The hypocycloid
323
Spirals ARTICLE PAGR 193 Definition
325
The reciprocal or hyperbolic spiral
326
The parabolic spiral
328
The logarithmic spiral
329
SOLID ANALYTIC GEOMETRY CHAPTER I
331
Rectangular co÷rdinates
332
Polar co÷rdinates
333
203
334
Distance and direction from one point to another rectangu lar co÷rdinates
336
The point which divides in a given ratio the straight line from one point to another
337
Angle between two radii vectores Angle between two lines
338
Transformation of co÷rdinates rectangular systems
339
CHAPTER II
342
Equations in one variable Planes parallel to co÷rdinate planes
343
Equations in two variables Cylinders perpendicular to co÷r dinate planes
344
Equations in three variables Surfaces
346
Curves Traces of surfaces
347
Surfaces of revolution
348
EQUATIONS OF THE FIRST DEGREE AX + By + C2 + D 0
353
Distance of a point from a plane
359
CHAPTER IV
367
equation
373
The hyperboloid and its asymptotic cone
379
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Page 120 - The straight line joining the middle points of two sides of a triangle is parallel to the third side, and equal to half of it.
Page 108 - Show that the locus of a point which moves so that the sum of its distances from two h'xed straight lines is constant is a straight line.
Page 170 - Thus a parabola is the locus of a point which moves so that its distance from a fixed point is equal to its distance from a fixed straight line (see fig.
Page 179 - F') ; the diameter drawn through them is called the major axis, and the perpendicular bisector of this diameter the minor axis. It is also defined as the locus of a point which moves so that the ratio of its distance from a fixed point...
Page 67 - A conic section or conic is the locus of a point which moves so that its distance from a fixed point is in a constant ratio to its distance from a fixed straight line...
Page 240 - Art. 144 is sometimes given as the definition of the ellipse ; viz. the ellipse is the locus of a point the sum of whose distances from two fixed points is constant.
Page 122 - The line joining the middle points of two sides of a triangle is parallel to the third side and equal to half of the third side.
Page 211 - To draw that diameter of a given circle which shall pass at a given distance from a given point. 9. Find the locus of the middle points of any system of parallel chords in a circle.
Page 169 - A point moves so that the square of its distance from the base of an isosceles triangle is equal to the product of its distances from the other two sides.
Page 79 - A point moves so that the difference of the squares of its distances from two fixed points is constant. Show that the locus is a straight line. Hint. Draw XX' through the fixed points, and YY/ through their middle point.

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