One of the most famous problems in Greek antiquity wassquaring the circle, that is

Chapter 10, Problem 57

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One of the most famous problems in Greek antiquity wassquaring the circle, that is, using a straightedge and compassto construct a square whose area is equal to that of agiven circle. It was proved in the nineteenth century thatno such construction is possible. However, show that theshaded areas in the accompanying figure are equal, therebysquaring the crescent.

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