An elementary treatise on cubic and quartic curves, by A. B. Basset.

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CONTENTS.

ART.
29-35. Various properties of polar curves.
36-38. The Hessian of a curve and its properties.
39. The Steinerian of a curve..
40. Asymptotes.
41. General equation of a curve in trilinear coordinates
42. The Hessian passes through every point of inflexion
43-46. Further propositions connected with multiple points on a
curve, its Hessian and its polars...
47-49. Singularities at infinity....
50. Condition that the line at infinity should be a tangent
51. Imaginary singularities...
CHAPTER III.
TANGENTIAL COORDINATES.
52. The Boothian system of tangential coordinates
53. Tangential equation of a curve whose Cartesian equation is given
54. Cartesian equation of a curve whose tangential equation is given
55. On the curve (x/a)n+ (y/b)-1=l....
56. Examination of the different terms of a tangential equation
57-58. Reciprocal polars, inverse and pedal curves
59. A node corresponds to a double tangent on the reciprocal polar
60. A cusp corresponds to a stationary tangent on the reciprocal
polar.....
61. The line at infinity...
62-63. Method of finding the multiple tangents to a curve
64-66. Pedal curves. The tangential polar equation of a curve
67. On the curves r =an cos n..
68. Orthoptic and isoptic loci....
69-70. The circular points at infinity..
71-72. The trilinear system of tangential coordinates
73. Tangential equation of a circle...
74. Tangential equation of the circular points.
75. Foci of curves....
76. Plicker's definition of a focus..
77. Number of foci when the line at infinity is a multiple tangent
78. do. when a curve passes through the circular points.
79. do. when the circular points are nodes.
80. do. do. cusps or points of
inflexion....
81. The inverse of a focus is a focus of the inverse curve
82. Equation of tangents drawn from a point (A, k) to a curve
83. Locus of the points of intersection of tangents at the extremities
of a line drawn through a fixed point....

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