"The circle being after rectilineal figures, the most simple in appearance, geometricians very naturally soon began to seek for its measure. Thus we find that the philosopher Anaxagoras occupied himself with the question in prison. Then Hippocrates of Chios tried the same problem, and it led him to the discovery of what is called the lune, a surface in the shape of a crescent, bounded by two arcs and exactly equal to a given square. He also found two unequal lines which were together equal to a rectilineal figure, so that if their relation could have been found the solution of the problem would have been obtained. But this no one has yet been able to do, nor is it likely ever to be done."
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Jean-Étienne Montucla, Histoire des recherches sur la quadrature du cercle (1754) as quoted in The Quadrature of the Circle, the Square Root of Two, and the Right-angled Triangle (1873) Tr. J. Babin, ed. William Alexander Myers, Introduction, p. 9-10.
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Hippocrates of Chios
(c. 470 – c. 410 BCE) was an ancient Greek mathematician, geometer, and astronomer. He was born on the isle of Chios and may have been a pupil of the mathematician and astronomer of Chios. Hippocrates was originally a merchant. The work of Hippocrates is known only through second-hand sources. There are no known extant quotes by him.
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