Let AEB be a semicircle on AB as
diameter, and let AC, BD be equal lengths measured along AB from
A, B respectively. On AC, BD as diameters describe semicircles
on the side towards E, and on CD as diameter a semicircle on the
opposite side. The figure included between the circumferences of
the four semicircles is "what Archimedes called salinon". Let the perpendicular to AB through O, the center
of the first semicircle, meet the opposite semicircles in E, F
respectively. Then shall the area of the salinon be equal to the area of
the circle on EF as diameter. "Salinon" means *salt -
cellar*
in Greek. |