On the determination of the degree of an equation obtained by elimination (translation with commentary)

Ueber die Bestimmung des Grades einer durch Elimination hervorgehenden Gleichung (On the determination of the degree of an equation obtained by elimination)

[Inserted by J. Maurice Rojas] We give a formula for the number of complex roots of a generic system of two polynomial equations in two unknowns. The formula is completely combinatorial, ultimately depending just on the convex hull of the exponent vectors of the equations. This formula presents the first known pre-cursor to David N. Bernstein's theorem relating mixed volumes and the number of roots in the complex algebraic torus of a system of polynomial equations. More precisely, our formula is a special case of a formula derived in 1994 by T. Y. Li and Xiaoshen Wang.