Study's Theorem

Given three curves phi_1, phi_2, phi_3 with the common group of ordinary points G (which may be empty), let their remaining groups of intersections g_(23), g_(31), and g_(12) also be ordinary points. If phi_1^' is any other curve through g_(23), then there exist two other curves phi_2^', phi_3^' such that the three combined curves phi_iphi_i^' are of the same order and linearly dependent, each curve phi_k^' contains the corresponding group g_(ij), and every intersection of phi_i or phi_i^' with phi_j or phi_j^' lies on phi_k or phi_k^'.

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

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Study's Theorem

Cite this as:

Weisstein, Eric W. "Study's Theorem." From MathWorld--A Wolfram Web Resource.

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