 Budan explains in his book how, given a monic polynomial p(x), the coefficients of p(x+1) can be obtained by developing a "Pascal-like triangle" with first row the coefficients of p(x), rather than by expanding successive powers of x+1, as in Pascal's triangle proper, and then summing; thus, the method has the flavour of lattice path combinatorics.Taken together with Descartes' "Rule of Signs", this leads to an upper bound on the number of the real roots a polynomial has inside an open interval.Although Budan's Theorem, as this result was known, was taken up by, among others, (1779-1854), in his celebrated algebra textbook, it tended to be eclipsed by an equivalent result due to Joseph Fourier, as the consequence of a priority dispute.