Problem 643: Archimedes' Book of Lemmas: Proposition 4, Arbelos

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Let C be any point on a semicircle of diameter AB, and let CD be perpendicular to AB. If semicircles be described within the first semicircle and having AD and DB as diameters respectively, the figure included between the circumferences of the three semicircles is "what Archimedes called arbelos". Then the area of the arbelos is the same as the area of the circle with diameter CD.
"Arbelos" means shoemaker's knife in Greek.


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