"One of the most celebrated geometrical problems of antiquity was the trisection of an angle. It stands side by side with those other famous problems,—the squaring of the circle and the duplication of the cube. ...modern analysis shows that the trisection of an angle is an insoluble problem if in our constructions we confine ourselves to the use of circles and straight lines. i.e. to Euclidean geometry. ...By the use of the conic sections, however, the problem is readily solved in many ways. Pappus... has given us the following beautiful reduction of the problem... "Since we can trisect a right angle," says Pappus, "it follows that the trisection of any angle can be effected if we can trisect an acute angle." ..While the geometricians quoted by Pappus could not solve the problem, Pappus himself, who lived at a time when the conic sections had been developed to some extent, fixed the position of the point E by means of an hyperbola. Pappus also claims, as his own, a solution by means of the conchoid of Nicomedes."
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William Whitehead Rupert, Famous Geometrical Theorems and Problems with Their History (1901) Part 3
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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