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

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.

Archimedes Book of Lemas numero 4 Arbelos

Books of Lemmas Index

Proposition 1
Proposition 2
Proposition 3
Proposition 4
Proposition 5
Proposition 6
Proposition 7
Proposition 8
Proposition 9
Proposition 10
Proposition 11
Proposition 12
Proposition 13
Proposition 14
Proposition 15

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