The quadratures of lunes, which were considered to belong to an uncommon class of propositions on account of the close relation of lunes to the circle, were first investigated by Hippocrates, and his exposition was thought to be correct; we will therefore deal with them at length and describe them. ... This he affected by circumscribing a semicircle about an isosceles right-angled triangle and a segment of a circle similar to those cut off by the sides. Then, since the segment about the base is equal to the sum of those about the sides, it follows that, when part of the triangle above the se...

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