Bézout's Theorem

Theorem
Suppose that $$X$$ and $$Y$$ are two plane projective curves defined over a field $$F$$ that do not have a common component.

(This condition is true if both $$X$$ and $$Y$$ are defined by different irreducible polynomials. In particular, it holds for a pair of "generic" curves.)

Then the total number of intersection points of $$X$$ and $$Y$$ with coordinates in an algebraically closed field $$E$$ which contains $$F$$, counted with their multiplicities, is equal to the product of the degrees of $$X$$ and $$Y$$.

Proof
He published it in his 1779 paper Théorie générale des équations algébriques.