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General Theory of Algebraic Equations by Etienne Bézout, Eric Feron

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Book Two

In which we give a process for reaching the final equation resulting from an arbitrary number of equations in the same number of unknowns, and in which we present many general properties of algebraic quantities and equations

General observations

(194.) The method expressed in the first book for determining the degree of the final equation strongly indicates that the art of eliminating all variables but one reduces altogether to the elimination method in first-order equations, with an arbitrary number of unknowns. In appearance, it would seem that little remains to be said about this matter, since we know of methods that lead us quickly to the value of all unknowns in first-order equations. But even if these methods had all the perfection ...

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