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xii
PROBLEM
46. To describe a parabola with given axis and to pass through two
given points
47. To describe a parabola with given axis, to pass through a given
point and to touch a given line
48.
CONTENTS.
51.
To describe a parabola to pass through three points and the
axis to be in a given direction
53.
To describe a parabola with given axis and to touch two given
lines
54.
49.
To describe a parabola to touch two given lines at given points
50. To describe a parabola to touch three given lines, one of them
at a given point .
52. To describe a parabola to touch three given lines and the axis
to be in a given direction
•
To describe a parabola to pass through two given points and to
touch two given lines
To describe a parabola to pass through three given points and to
touch a given line
55. To describe a parabola to pass through a given point and to
touch three given lines
56. To describe a parabola to pass through four given points .
57. To describe a parabola to touch four given lines
58. To determine the centre of curvature at any point of a given
parabola
59. To describe a parabola to touch two given circles, the axis being
the line joining their centres
CHAPTER IV.
THE ELLIPSE.
60.
To describe an ellipse with given axes (three methods)
Tangent and normal
61. To describe approximately by means of circular arcs an ellipse
having given axes (two methods)
Sundry properties of the ellipse.
62. To determine the axes of an ellipse from a given pair of con-
jugate diameters
63. To describe an ellipse with given conjugate diameters (four
methods)
64. To describe an ellipse with a given axis and to pass through a
given point
65.
66.
67.
68.
69. To describe an ellipse, the centre, the directions of a pair of
conjugate diameters, a tangent and a point on the curve
being given
70. To describe an ellipse, the centre, two tangents and a point on
the curve being given
71.
To describe an ellipse, the centre and three tangents being given
72. To describe an ellipse, the centre, two points on the curve and
a tangent being given
74.
73. To describe an ellipse, the centre and three points on the curve
75.
76.
77.
To describe an ellipse with a given axis and to touch a given line
To describe an ellipse, the directions of a pair of conjugate dia-
meters, a tangent and its point of contact being given
To describe an ellipse, the centre, two points on the curve and the directions of a pair of conjugate diameters being given
To describe an ellipse, the centre, the direction of the major
axis and two tangents being given
78.
82.
83.
To describe an ellipse, the foci and a point on the curve being
given
To describe an ellipse, the foci and a tangent to the curve being given.
To describe an ellipse, a focus, a tangent with its point of
contact and a second point on the curve being given.
To describe an ellipse, a focus, a tangent and two points on the
curve being given
To describe an ellipse, a focus, a point on the curve and two tangents being given
79. To describe an ellipse, a focus and three tangents being given
80. To describe an ellipse, a focus and three points being given
81. To describe an ellipse, two tangents with their points of contact
and a third point being given
To describe an ellipse, two tangents and three points being given
To describe an ellipse, three tangents and two points being given
PAGE
111
114
115
116
ib.
118
119
121
122
123
124
125
126
127
129
131
133
134
xiv
84.
85.
86.
87.
89.
91.
92,
To describe an ellipse, five tangents being given
To describe an ellipse, four tangents and a point being given
To describe an ellipse, five points being given
To describe an ellipse, four points and a tangent being given
Pole and Polar
93.
Harmonic Properties.
88. To determine the centre of curvature at any point of a given
ellipse
CHAPTER V.
THE HYPERBOLA.
90. To describe an hyperbola, an asymptote, focus and a point on the curve being given .
To describe an hyperbola, the foci and a vertex, the vertices and a focus, or the axes, being given
To describe an hyperbola, an asymptote, focus and tangent
To describe an hyperbola, an asymptote, directrix and a point
To describe an hyperbola, the asymptotes and a point being
94. To describe an hyperbola, the asymptotes and a tangent being
given.
Sundry properties of hyperbola .
95. To describe an hyperbola, transverse axis and a point being
96. To describe an hyperbola, transverse axis and tangent being
97. To describe an hyperbola, a pair of conjugate diameters being
136
137
138
139
140
141
145
153
157
158
159
160
166
98. To describe an hyperbola, the centre, directions of a pair of con-
jugate diameters and two points being given
99. To describe an hyperbola, the centre, directions of a pair of con-
jugate diameters, a tangent and a point being given
100. To describe an hyperbola, the centre, two tangents and a point
101.
102.
To describe an hyperbola, the centre, a tangent and two points
103. To describe an hyperbola, the centre and three points being given
104. To describe an hyperbola, the foci and a point on the curve being
To describe an hyperbola, the centre and three tangents being
105. To describe an hyperbola, the foci and a tangent being given
106. To describe an hyperbola, a focus, tangent with its point of contact and a second point on the curve being given.
107. To describe an hyperbola, a focus, a tangent and two points
109.
110.
108. To describe an hyperbola, a focus, two tangents and a point
111.
To describe an hyperbola, a focus and three tangents being given
To describe an hyperbola, a focus and three points on the curve
To describe an hyperbola, two tangents with their points of
contact and a third point on the curve being given
112. To describe an hyperbola, three tangents and two points on the
113. To describe an hyperbola, two tangents and three points on the
114. To describe an hyperbola, five tangents being given
115. To describe an hyperbola, five points on the curve being given .
116. To describe an hyperbola, four tangents and one point being
117. To describe an hyperbola, four points and one tangent being
118. To determine the centre of curvature at any point of a given
hyperbola
168
170
171
172
173
174
175
176
178
179
181
182
183
184
185
186
187
188
119. To find the polar reciprocal of one circle with regard to another
CHAPTER VIII.
ANHARMONIC RATIO.
120. Given the anharmonic ratio of four points, and the position of
three of them, to determine the fourth
191-195
121. Given any number of points on a straight line, and three points
on a second line corresponding to a given three on the first,
to complete the homographic division of the second line
122. Given a pencil of rays, and three rays of a second pencil corresponding to a given three of the first, to complete the second so that the two shall be homographic
123. Given two homographic ranges in the same straight line, to
determine the double points
126. Given two straight lines
draw Rab so that
124. Given two pairs of conjugate points and a fifth point of the
involution, to determine its conjugate
125. Given A, a and B, b in a straight line, to find in the same line a
point M such that
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226
228
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