 In the zetetic (analytic) stage of Viète’s analysis, we follow Pappus’s directive to treat “what is sought as if it has been achieved” precisely by naming the unknowns by variables. Then, by assuming the equivalence between proportions (as Viète does), we can solve for the variables \(x\) and \(y\) and establish that \(x\) and \(y\) have the following relationship to \(a\) and \(b\):