Home >
Archimedes' Book of Lemmas >
Previous, 1, 2,
3, 4, 5,
6,
7, 8,
9, 10,
11, 12,
13, 14,
15, Next
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. 

