"Hippocrates of Chios... attempted the solution [for squaring the circle] and was the first actually to square a curvilinear figure. He constructed semicircles on the three sides of an isosceles right-angled triangle and showed that the sum of the two lunes thus formed is equal to the area of the triangle itself. ...His proof involves the proposition that the areas of circles are proportional to the squares of their diameters,—a proposition which Eudemus... tells us that Hippocrates proved. To the quadrature problem as such, however, his contribution was not important."
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, History of Mathematics (1925) Vol. 1.
https://en.wikiquote.org/wiki/Hippocrates_of_Chios
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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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