Given three curves , , with the common group of ordinary points (which may be empty), let their remaining groups of intersections , , and also be ordinary points. If is any other curve through , then there exist two other curves , such that the three combined curves are of the same order and Linearly Dependent, each curve contains the corresponding group , and every intersection of or with or lies on or .

**References**

Coolidge, J. L. *A Treatise on Algebraic Plane Curves.* New York: Dover, p. 34, 1959.

© 1996-9

1999-05-26