26 BOOK ONE SECTION II About incomplete polynomials and first-order incomplete equations (49.) We will not insist on the broad impact of the general theorem (47) about complete equations. We will simply remark that it not gives only a precise expression for the degree of the final equation resulting from an arbi- trary number of complete equations with all possible terms and coefficients being present, but also an upper bound on the final degree of any equation, complete or incomplete, which may or may not be reducible due to either the absence of some terms or existing relations among their coefficients. (50.) As useful as this upper bound may already be, it is far more useful to tighten it even more and even to determine the precise degree of the final equation for all possible cases, even when the equations may be reduced because of specific relations among their coefficients. (51.) This subject is so broad that the reader will undoubtedly not expect us to explore it completely. What may be reasonable to expect, however, is to know a generic method to reach this goal in any case: This is what we will attempt to do. (52.) Whatever idea the reader may already have about the extent of the matter we intend to deal with, we believe it will be surpassed by later developments. We must therefore proceed methodically and be first very general so as to prepare the reader to deal with broader subjects. We will therefore introduce the different types of incomplete polynomials