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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.
49.
To describe a parabola with given axis and to touch two given
lines
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 .
51.
To describe a parabola to pass through three points and the
axis to be in a given direction
52. To describe a parabola to touch three given lines and the axis
to be in a given direction
•
53.
To describe a parabola to pass through two given points and to
touch two given lines
82
54.
To describe a parabola to pass through three given points and to
touch a given line
84
55. To describe a parabola to pass through a given point and to
touch three given lines
85
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
87
88
89
59. To describe a parabola to touch two given circles, the axis being the line joining their centres
CHAPTER IV.
91
THE ELLIPSE.
To describe an ellipse with given axes (three methods)
Tangent and normal
99
102
61. To describe approximately by means of circular arcs an ellipse
having given axes (two methods)
103
Sundry properties of the ellipse.
105
62. To determine the axes of an ellipse from a given pair of con-
jugate diameters
110
PROBLEM
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
PAGE
111
114
65.
66.
67.
68.
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
115
116
ib.
118
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
119
70. To describe an ellipse, the centre, two tangents and a point on
the curve being given
121
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
122
123
73. To describe an ellipse, the centre and three points on the curve
124
74.
To describe an ellipse, the foci and a point on the curve being
given
125
75.
To describe an ellipse, the foci and a tangent to the curve being given.
76.
To describe an ellipse, a focus, a tangent with its point of
contact and a second point on the curve being given.
126
77.
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
133
134
85.
To describe an ellipse, four tangents and a point being given
87.
To describe an ellipse, four points and a tangent being given
Pole and Polar
Harmonic Properties.
139
140
141
88. To determine the centre of curvature at any point of a given
ellipse
CHAPTER V.
THE HYPERBOLA.
145
89.
To describe an hyperbola, the foci and a vertex, the vertices and
a focus, or the axes, being given
90. To describe an hyperbola, an asymptote, focus and a point on the curve being given .
91.
To describe an hyperbola, an asymptote, focus and tangent
158
92,
To describe an hyperbola, an asymptote, directrix and a point
93.
To describe an hyperbola, the asymptotes and a point being
94. To describe an hyperbola, the asymptotes and a tangent being
given.
160
Sundry properties of hyperbola .
95. To describe an hyperbola, transverse axis and a point being
166
96. To describe an hyperbola, transverse axis and tangent being
97. To describe an hyperbola, a pair of conjugate diameters being
98. To describe an hyperbola, the centre, directions of a pair of con-
jugate diameters and two points being given
168
99. To describe an hyperbola, the centre, directions of a pair of con-
jugate diameters, a tangent and a point being given
170
100. To describe an hyperbola, the centre, two tangents and a point
171
101.
To describe an hyperbola, the centre, a tangent and two points
172
102.
To describe an hyperbola, the centre and three tangents being
173
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
174
175
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
176
108. To describe an hyperbola, a focus, two tangents and a point
178
109.
110.
To describe an hyperbola, a focus and three tangents being given
To describe an hyperbola, a focus and three points on the curve being given
179
111.
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
183
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
187
118. To determine the centre of curvature at any point of a given
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
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
201
214
218
123. Given two homographic ranges in the same straight line, to
determine the double points
220
124. Given two pairs of conjugate points and a fifth point of the
involution, to determine its conjugate
226
125. Given A, a and B, b in a straight line, to find in the same line a
point M such that