George Pólya on Pappus of Alexandria

“Many elementary textbooks of geometry contain a few remarks about analysis, synthesis, and "assuming the problem as solved." There is little doubt that this almost ineradicable tradition goes back to Pappus, although there is hardly a current textbook whose writer would show any direct acquaintance with Pappus. The circumstance alone that it is restricted to textbooks of geometry shows a current lack of understanding...”

“In the seventh book of his Collections, Pappus reports about a branch of study he calls analyomenos. We can render this name in English as "Treasury of Analysis," or as "Art of Solving Problems," or even as "Heuristic"... A good English translation of Pappus's report is easily accessible... Pappus's text is important in many ways. ...the procedures described by Pappus are by no means restricted to geometric problems; they are, in fact, not even restricted to mathematical problems. ...the paraphrase... emphasizes certain curious phrases of the original: "assume what is required to be done as already done, what is sought as found, what you have to prove is true." This is paradoxical; it is not mere self-deception...”