A point X of a projective space Pn (over a commutative field of characteristic ≠ 2) is called an outer point of a quadric Qn−1 if and only if X is not a point of Qn−1 and the polar hyperplane ΓX contains a maximal subspace of Qn−1; the points of PnQn−1 which are not outer points of Qn−1 are called inner points of Qn−1. This definition is motivated by special cases in classical projective geometry; it improves earlier definitions.