## Study's Theorem

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.