 Some of the directives Pappus offers here seem straightforward. The mathematician begins by assuming what is sought after as if it has been achieved until, through analysis, she reaches something that is already known. Then, the mathematician reverses the steps, and through synthesis, sets out “in natural order” the deduction leading from what is known to what is sought after. However, there are ambiguities in Pappus’s discussion. Perhaps most importantly, it is not clear how reversing the steps of analysis could offer a proof, or synthesis, of a stated problem, since the deductions of analysis rely on conditionals (if \(x\), then \(y)\) whereas a reversal would require biconditionals \((x\) iff \(y)\) to achieve synthesis (see Guicciardini 2009, 31–38 for further interpretative problems surrounding Pappus’s remarks; for more on analysis and synthesis in the Renaissance see the classic Hintikka and Remes 1974, the essays in Otte and Panza 1997, and Panza 2007). Ambiguities notwithstanding, for Viète and other early modern mathematicians there was one feature of the discussion that was incredibly important: Pappus makes clear that the ancients had a method of analysis at their disposal, and many early modern mathematicians attempted to align this method from antiquity with the algebraic methods of geometrical analysis that they were using.