, edited by Paul Cartledge, Cambridge University Press, 1998.)

The arbelos is the blue shaded area below two circles with diameter AD and (AB-AD). The position of the central notch D is arbitrary and can be located anywhere along the diameter AB.

The arc length along the enclosing semicircle AB is the same as the arc length along the two smaller semicircles AD and DB.

If we take the perpendicular at D that intersects the circle at C then there is an associated blue circle shown below that has the same area as the arbelos.

The circles A1 and A2 inscribed in the two parts of the arbelos ADC and CDB are called Archimedian twin circles and their area is the same. The smallest circle S that encloses A1 and A2 has the same area as the arbelos.

Eric W. Weisstein:

"Salinon." From