An Elementary Treatise on Cubic and Quartic Curves (Google eBook)

Front Cover
Deighton, Bell, 1901 - Curves, Cubic - 255 pages
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Contents

The evolute of an ellipse
223
Its radius of curvature
224
Tangential equation of the evolute of the evolute of an ellipse
225
Connection between the evolute of an ellipse and a fourcusped hypocycloid
226
The involute of a circle
227
Roulette of the centre of a circle whose involute rolls on a straight line is a parabola
228
Roulette of the focus of a parabola which rolls on a straight line is a catenary
229
ABT PAGE 347 The tractrix or tractory
230
The equiangular spiral
231
The spiral of Archimedes The hyperbolic spiral The lituus
232
CHAPTER XII
233
A projection introduces five independent constants
234
Projection of a triangle
235
Formulae for projection
236
Any two real points can be projected into the circular points
238
Advantages of projection
239
Some projective properties of nodal cubics
240
Equation of cubic when the circular points are points of inflexion
241
Projection of a tricuspidal quartic into a threecusped hypocy cloid or a cardioid
242
Projection of a quartic having a node and a pair of cusps into a limacon
243
Projective properties of quartics of the ninth species
244
Projection of a quartic having three biflecnodes into the lemnis cate of Bernoulli
245
373377 Simple forms of quartics having certain given singularities
246
Geometrical interpretation of the general expression for a ternary quartic
247
380381 Discussion of the quartic a23+32y+y2a 0
248
Generalization of the results by projection
251
ADDENDA AND CORRIGENDA I Addition to 2728
253
The six stationary tangents of a trinodal quartic touch a conic
254
Famous problems of antiquity
255

Common terms and phrases

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