Let be cubic plane curves meeting in nine points , ..., . If is any cubic containing , ..., , then contains as well. It is related to Gorenstein rings, and is a generalization of Pappus's hexagon theorem and Pascal's theorem.

Eisenbud, D.; Green, M.; and Harris, J. "Cayley-Bacharach Theorems and Conjectures." Bull. Amer. Math. Soc. 33, 295-324, 1996.

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Weisstein, Eric W. "Cayley-Bacharach Theorem." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/Cayley-BacharachTheorem.html