Definitions: Cone, Flock, Baseline

Theorem 5.1: Let be one of a set F of q planes, none passing through the point V. If T is any nonempty subset of the complement of the union of the baselines of F in , then F is a flock of the cone C(V, T).

Pf: Let P be a point in T, thus P is on no baseline of F. Suppose that the line VP meets a line of intersection, l, of two planes of F. Then VP would lie in the plane determined by V and l. The intersection of this plane with is a baseline of F, and since P is in , it would lie on this baseline. This contradiction shows that the lines of intersection of planes of F can not meet any line joining V to a point of T. Thus, F is a flock of the cone C(V, T) since it contains q planes.

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