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

CONTENTS. Xii
ART. PAGE
180. Reciprocal of a point of undulation...... 117
181-185. Properties of quartics having twelve points of undulation 118
186-187. Double tangents......... 122
188-189. Singularities at infinity....... 124
190. Binodal quartics......... 125
191-195. Trinodal quartics. Discussion of the systems of conics
which can be described through certain points on a
trinodal quartic......... 126
196. Tricuspidal quartics......... 132
CHAPTER IX.
BICIRCULAR QUARTICS.
197. Definition of bicircular quartics and cartesians... 133
198. Equation of a bicircular quartic..... 133
199. Equation of a cartesian........ 134
200. Casey's geometrical construction for bicircular quartics, cartesians and circular cubics... 135
201. Inverse of bicircular quartic. 136
202. Classification of bicircular quartics. Inverse of a conic. 137
203. Bicircular quartics having a pair of flecnodes at the circular
points...... 137
204. Pedal of a conic is a bicircular quartic. 138
205. The generating circle........ 139
206-207. Locus of points of intersection of the tangents and
normals at two inverse points...... 139
208-211. Other methods of generating a bicircular quartic. The
focal conic. 141
212. Properties of the focal conic and its corresponding circle of
inversion.......... 143
213-214. Properties of a certain orthogonal system of circles. 144
215. Equations of a bicircular quartic and a circular cubic in
trilinear coordinates...... 146
216. Centres of inversion........ 147
217-219. Focal conics and foci..... 147
220. The foci of the focal conic are double foci of the quartic. 150
221-222. A linear relation exists between the distances of a point
on the quartic from any three foci..... 150
223-224. Circular cubics.. 152
225-240. Various properties of circular cubics, considered as a
special case of bicircular quartics.. 153
241. Points of inflexion of a circular cubic... 159
242. A certain envelope.....160