Sets of Points Self-Conjugate with regard to a Quadric in n Dimensions

Extract

§ 1. In space of three dimensions the properties of self-conjugate tetrads, pentads and hexads with regard to a quadric are well known (see Baker's Principles of Geometry, vol. iii). The general theorem in space of n dimensions S_n is to establish the existence of a set of n + p + 1 points A₀, A₁, …, A_n+p (0 ≤ p ≤ n−1) such that the pole, with respect to a given quadric, of the (n−1)-flat determined by any set of n of the points lies in the p-flat determined by the remaining p + 1 points.