Hippocrates Lunes

three figures pointed out by Hippocrates of Chios, each of which is enclosed by the arcs of two circles and for each of which, using a ruler and compass, it is possible to construct figures enclosed by straight lines and having equal areas. The construction of one of the Hippocrates’ lunes is evident from Figure 1. The area of the shaded Hippocrates’ lune is equal to the area of the isosceles triangle ABC. Other Hippocrates’ lunes are constructed in a more complicated fashion.

Figure 1