On an algebraic curve, the sum of the number of coincidences at a noncuspidal point 
is the sum of the orders of the infinitesimal distances from
a nearby point 
to the corresponding points when the distance 
is taken as the principal infinitesimal.
Zeuthen's Rule
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References
Coolidge, J. L. A Treatise on Algebraic Plane Curves. New York: Dover, p. 131, 1959.Referenced on Wolfram|Alpha
Zeuthen's RuleCite this as:
Weisstein, Eric W. "Zeuthen's Rule." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/ZeuthensRule.html