A linear form is a weighted sum such as 2x+y; its weights are coefficients. The paper replaces each variable occurrence in a clause polynomial with a linear form whose coefficients are polynomials in a parameter T. A polynomial in T is a finite sum of terms with nonnegative whole-number powers of T and rational coefficients, such as 3T^2-2T+1. Replacing x by (1-T)x+Ty restores x at T=0 but gives y at T=1. Different occurrences may get different forms; each must restore its original variable at zero. At other T values, outputs need not be 0 or 1, so a transformed clause need not indicate satisfaction.