TY - JOUR
AU - Taylor, H. M.
AB - On the Intersections of Two Oubics. 265 On the Intersections of Two Oubics. By H. M. TAYLOR. Received January 6th, 1898. Bead January 13th, 1898. Received, in amended form, May 5th, 1898. I t has long been a well-known theorem that every cubic drawn through eight given points passes through a ninth fixed point. Geometrical methods have been given for finding this ninth point by means of conies, and also by means of straight lines only.* In this paper expressions will be found for the coordinates of the ninth point in terms of the other eight. It will appear that (I.) the coordinates of the ninth point are functions of the eighth degree in the coordinates of each of the other points; (II.) that when seven of the points are given, if the eighth point lies upon a straight line, the locus of the ninth point is -an octavic curve having a triple point at each of the seven given points : and that, if the straight line on which the eighth point lies passes through one or two of the seven points, the locus of the ninth point degenerates and contains respectively one or two nodal cubics, having 
TI - On the Intersections of Two Cubics
JO - Proceedings of the London Mathematical Society
DO - 10.1112/plms/s1-29.1.265
DA - 1897-11-01
UR - https://www.deepdyve.com/lp/wiley/on-the-intersections-of-two-cubics-0LNHx09mxL
SP - 265
EP - 274
VL - s1-29
IS - 1
DP - DeepDyve
ER -