"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..."
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George Pólya, How to Solve It (1945)
https://en.wikiquote.org/wiki/Pappus_of_Alexandria
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Pappus of Alexandria
Pappus of Alexandria (c. 290 - c. 350 AD) was one of the last great Greek mathematicians of Antiquity, known for his Synagoge (Συναγωγή) or Collection (c. 340), and for Pappus's hexagon theorem in projective geometry. Nothing is known of his life, except (from his own writings) that he had a son named Hermodorus, and was a teacher in Alexandria. Collection, his best-known work, is a compendium of mathematics in eight volumes, the bulk of which survives. It covers a wide range of topics, includin
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