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 .

# Study's Theorem

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## References

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

## Referenced on Wolfram|Alpha

Study's Theorem## Cite this as:

Weisstein, Eric W. "Study's Theorem."
From *MathWorld*--A Wolfram Web Resource. https://mathworld.wolfram.com/StudysTheorem.html