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General Theory of Algebraic Equations by Etienne Bézout, Eric Feron

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SECTION III

About incomplete polynomials and second-, third-,fourth-, etc., order incomplete equations

(165.) No matter how general the polynomials we have dealt with in the previous section are, they do not yet cover all possible polynomials and all possible equations. Their form is not as general as necessary for us to claim that we can determine the lowest degree of the final equation for any algebraic equation.

It is not enough to specify the highest dimensions reached by the unknowns, taken either alone or in combinations of 2, 3, etc., to capture all the variations that may influence the degree of the final equation. While these have a very significant influence on the degree of the final equation, there are many other equations for ...

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