Related quadrics and systems of a rational quartic curve

Abstract

1·1. The points, tangents, osculating planes, …, osculating primes of a curve may be said to form a system which is characterised by the number of these elements which are incident with a prime, …, line, point, respectively. For the normal rational quartic curve the system is (4, 6, 6, 4); projection of this system from a general point gives the system (4, 6, 6) in [3]; section by a general prime gives the system (6, 6, 4). These two systems in [3], which are the systems with which we are concerned in this paper, are duals of one another, and will be called systems of the first and second kinds respectively.