The Book of Lemmas: Proposition 14
Main Concept
Let AEB be a semicircle with AB as its diameter, and let AC and BD be equal lengths measured along AB from A and B respectively. Let AC and BD as diameters describe semicircles on the side towards E, while CD as a diameter describes a semicircle on the opposite side. The figure contained by the circumferences of these four semicircles is what Archimedes called a salinon (which means "salt cellar" in Greek). Let the perpendicular to AB through O, the center of the first semicircle, meet the opposite semicircles in E and F respectively. Then, the area of the salinon is equal to the area of the circle with EF as its diameter.
Adjust the slider, or click and drag on the plot to change the value of r, the radius of the two semicircles with AC and BD as their diameters. Observe the calculated values demonstrating that the area of the light blue salinon is equivalent to the area of the green circle with the diameter of EF.
AB = 2
AC =
BD =
CD =
EF =
Area of the Salinon =
Area of the Circle with Diameter EF =
Radius white semicircles, r =
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