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    Cover
    Title Page
    Table of Contents
    Translator's Foreword
    Dedication from the 1779 edition
    Preface to the 1779 edition
    Definitions and preliminary notions
    About the way to determine the differences of quantities
    A general and fundamental remark
    Reductions that may apply to the general rule to differentiate quantities when several differentiations must be made.
    Remarks about the differences of decreasing quantities
    About sums of quantities
    Remarks
    About sums of rational quantities with no variable divider
    Book One
    Section I
    Section II
    About incomplete polynomials and first-order incomplete equations
    Problem IV
    Problem V
    Problem VII: We ask for the degree of the final equation resulting from an arbitrary number n of equations of the form (ua . . . n)t = 0 in the same number of unknowns
    Remark
    Problem VIII
    Problem X
    Problem XI
    (3) The other unknowns do not exceed a given degree (different or the same for each), but, when combined groups of two or three among themselves as well as with the first two, they reach all possible dimensions until that of the polynomial or the equation
    Problem XII
    Problem XIII
    Problem XIV
    Problem XVI
    We further assume that the degrees of the n 3 other unknowns do not exceed given values we also assume that the combination of two, three, four, etc. of these variables among themselves or with the first three reaches all possible dimensions, up to the
    Problem XVII
    Problem XVIII
    Summary and table of the different values of the number of terms sought in the preceding polynomial and in related quantities
    Problem XIX
    Problem XX
    Problem XXII
    About the largest number of terms that can be cancelled in a given polynomial by using a given number of equations, without introducing new terms
    Determination of the symptoms indicating which value of the degree of the final equation must be chosen or rejected, among the different available expressions
    Expansion of the various values of the degree of the final equation, resulting from the general expression found in (104), and expansion of the set of conditions that justify these values
    Application of the preceding theory to equations in three unknowns
    General considerations about the degree of the final equation, when considering the other incomplete equations similar to those considered up until now
    Problem XXIII
    General method to determine the degree of the final equationfor all cases of equations of the form (ua . . . n)t = 0
    General considerations about the number of terms of other polynomials that are similar to those we have examined
    Conclusion about first-order incomplete equations
    Section III
    Book Two
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    Section II > Problem XVII - Pg. 46

    46 A A B A A B C A BOOK ONE until now. The kind of polynomial under consideration is represented by the expression ([(u A , x ) B , (u A , y ) , (x , y ) ] , z . . . n) T This expression means the three unknowns u, x, and y satisfy the following: 1. u does not exceed the degree A, x does not exceed the degree A , y does not exceed the degree A . 2. The combination of u and x does not exceed the dimension B, u and y do not exceed the dimension B , x and y do not exceed the dimension B ; 3. The combination of u and x and y together cannot exceed a dimension larger than C. Each of the n - 3 other unknowns does not exceed a given degree; for example, z does not exceed the degree A , u does not exceed the degree A , IV x does not exceed the degree A , but the combination of two, three, four, V etc. of the variables z, u , x , etc. among themselves as well as with u, x, and y reaches all possible dimensions up to T , which is the degree of the polynomial. Problem XVII (83.) We ask for the expression of general conditions to guarantee the