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