Zerfallende Quadrikenschnitte und stereographische Projektion

If the intersection of two quadrics Q₁^n-1, Q₂^n-1 in projective space Pⁿ contains a quadric Q₃^n-2 which is different from its singularity space, then the intersection Q₁^n-1 ∩ Q₂^n-1 is the union of two quadrics Q₃^n-2, Q₄^n-2. This theorem leads to a geometric characterization of those hyperquadrics of a hyperplane π of Pⁿ that are images of quadrics on a given quadric Q^n-1 by a given stereographic projection of Q^n-1 onto π.