Cayley-Bacharach theorem
= Cayley-Bacharach theorem
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In its classical nine-point cubic form, the <Cayley-Bacharach theorem> says that a cubic through eight of the nine distinct intersections of two plane cubics must contain the ninth. The <eight-point cubic completion for two triples of lines> is the elementary case needed for triangular-strip propagation in <incidence geometry>. The phenomenon explains why interpolation conditions at such a complete intersection are dependent.