An Elementary Course in Analytic Geometry

Front Cover
American book Company, 1898 - Geometry, Analytic - 390 pages
 

Contents

LESSON
11
Properties of the quadratic equation
12
The quadratic equation involving two unknowns
13
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
CHAPTER II
24
Analytic Geometry
25
Rectangular coördinates
27
4 234 5 6 9 11
28
Slope of a line
33
12
35
13
36
Fundamental problems of analytic geometry
40
19
42
Equation of straight line through given point and in given
44
Loci by polar coördinates
46
a by any trans
52
24
53
42
61
direction
63
Equation of a circle polar coördinates
64
Equation of locus traced by a moving point
65
second method
66
The conic sections
67
Introductory
70
The use of curves in applied mathematics
73
83
76
31
77
13
80
CHAPTER V
81
Equation of straight line in terms of the intercepts which it makes on the coördinate axes
83
Equation of straight line through a given point and in a given direction
84
2288
85
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 œ 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 91
101
The distance of a given point from a given line
107
Bisectors of the angles between two given lines
108
The equation of two lines 108
110
Condition that the general quadratic expression may be factored
111

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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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