On two Cubic Curves in Triangular Relation

F. Morley
1907 Proceedings of the London Mathematical Society  
Two plane cubic curves-one of points and one of lines-can be so related that there is an infinity of triangles with points on the former and lines on the latter. I shall say that two such cubics are in triangular relation. This problem, which is investigated here, stands, in a way, between Poncelet's problem, with its various developments, and Klein's tetrahedra whose points and planes are on a Kummer quartic. The case when the two cubics are in apolarity occurs in the memoir by Prof. White, "
more » ... by Prof. White, " On Twisted Cubic Curves that have a Directrix," Trans. Amer. Math. Soc, Vol. iv., p. 186. The problem belongs to the theory of two connexes, but I shall first give its genesis from a single cubic. The identification of the pairs of cubics arrived at in the two ways is made in § 8. * This theory is best set out in Glebsch's lectures (see Vol. in., chap, ii., of the ¥n uch translation). Here (at) is written in place of Clebsch's symbol a* for a row product.
doi:10.1112/plms/s2-4.1.384 fatcat:hum5k2hylvbubo7kpmim6apmdm