Etienne B\'ezout on Elimination Theory

Understand

B\'ezout's name is attached to his famous theorem.

• B\'ezout's Theorem states that the degree of the eliminand of a system a $n$ algebraic equations in $n$ unknowns, when each of the equations is generic of its degree, is the product of the degrees of the equations.
• The eliminand is, in the terms of XIXth century algebra, an equation of smallest degree resulting from the elimination of $(n-1)$ unknowns.
• B\'ezout demonstrates his theorem in 1779 in a treatise entitled "Th\'eorie g\'en\'erale des \'equations alg\'ebriques".