BOOK ONE 71 in the results. We therefore lose no generality by taking this approach; it contributes to making things clearer. Application of the preceding theory to equations in three unknowns (119.) The eight expressions we have found for P in (91 ff) do simplify, when there are three unknowns only. This is because C = T , and terms containing T - C vanish: Indeed, N (u . . . n) T -C-1 , N (u . . . n) T -C-2 and N (u . . . n) T -C-3 become N (u . . . n) -1 , N (u . . . n) -2 , N (u . . . n) -3 , and these quantities are all 0 by (39). We can use this observation to simplify the expression of P ; differentiating as we just said in (118), we find the various values of D and the corresponding conditions for each of the eight forms. First form (120.) We assume the polynomial multiplier satisfies C - B < B - A; C - B < B - A ; C - B < B - A .