The Book of Lemmas: Proposition 4
Let AB be the diameter of a semicircle and C any point on AB, and semicircles be described within the first semicircle and having AC, CB as diameters respectively. The figure included between the circumferences of the three semicircles was described as an arbelos (shoemaker's knife) by Archimedes. Its area is equal to the circle having DC as diameter, where DC is perpendicular to AB and meets the original semicircle at D.
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