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PROBLEM
30. On a given straight line to describe a segment of a circle which
shall contain a given angle
PAGE
40
41
42
32. To describe a circle to touch two given circles and to pass
through a given point
33. To describe a circle to touch two given circles and a given
straight line
34. To describe a circle to touch three given circles.
35. To draw a circular arc through three given points without using
36.
To describe a parabola with given focus and directrix
Tangent and normal.
37.
To draw a parabola with given axis and vertex and to pass
61
38.
To draw a parabola with given focus and axis and to pass
62
39. To describe approximately by means of circular arcs a parabola
with given focus and vertex
To describe a parabola with given focus and to pass through
two given points
64
41.
To describe a parabola with given focus, to pass through a given
point and to touch a given line.
65
42. To describe a parabola with given focus and to touch two given
lines
43. To describe a parabola with given directrix and to pass through
68
44.
To describe a parabola with given directrix, to pass through a
given point and to touch a given line
ib.
45. To describe a parabola with given directrix and to touch two
given lines.
69
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
71
48.
To describe a parabola with given axis and to touch two given
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.
53.
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
54. 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
87
88
58. To determine the centre of curvature at any point of a given
parabola
89
59. To describe a parabola to touch two given circles, the axis being
the line joining their centres
91
CHAPTER IV.
THE ELLIPSE.
60. To describe an ellipse with given axes (three methods)
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
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
111
114
65. To describe an ellipse with a given axis and to touch a given line
66. To describe an ellipse, the directions of a pair of conjugate dia-
meters, a tangent and its point of contact being given
67. To describe an ellipse, the centre, two points on the curve and
the directions of a pair of conjugate diameters being given
68. To describe an ellipse, the centre, the direction of the major
axis and two tangents being given
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
122
123
73. To describe an ellipse, the centre and three points on the curve
74.
To describe an ellipse, the foci and a point on the curve being
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.
To describe an ellipse, a focus, a tangent and two points on the
curve being given
127
To describe an ellipse, a focus, a point on the curve and two tangents being given
80.
79. To describe an ellipse, a focus and three tangents being given
To describe an ellipse, a focus and three points being given
129
81.
To describe an ellipse, two tangents with their points of contact
and a third point being given
131
82. To describe an ellipse, two tangents and three points being given
83. To describe an ellipse, three tangents and two points being given
133
134
84. To describe an ellipse, five tangents being given
136
85.
To describe an ellipse, four tangents and a point being given
86. To describe an ellipse, five points being given
138
87. To describe an ellipse, four points and a tangent being given
Pole and Polar
Harmonic Properties.
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
92. To describe an hyperbola, an asymptote, directrix and a point
158
93. To describe an hyperbola, the asymptotes and a point being
94. To describe an hyperbola, the asymptotes and a tangent being
95. To describe an hyperbola, transverse axis and a point being
given.
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
170
99. To describe an hyperbola, the centre, directions of a pair of con-
jugate diameters, a tangent and a point being given
To describe an hyperbola, the centre, two tangents and a point
100.
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
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
105. To describe an hyperbola, the foci and a tangent being given 175
106. To describe an hyperbola, a focus, tangent with its point of
107. To describe an hyperbola, a focus, a tangent and two points
To describe an hyperbola, a focus, two tangents and a point
109. To describe an hyperbola, a focus and three tangents being given
110. To describe an hyperbola, a focus and three points on the curve
111. To describe an hyperbola, two tangents with their points of
contact and a third point on the curve being given
181
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
186
187
118. To determine the centre of curvature at any point of a given
hyperbola.
188