The names of these shapes are based on the following: Arbelos — a shoemaker's knife, Salinon — a salt cellar, and Lune — the moon. Notice that when we make a lune from two circles, we in fact make 2 lunes — one on each side. The shape formed in the middle, from the intersection of the two circles, is called a Lens.

The arbelos and salinon were first introduced in Aristotle's Book of Lemmas — we've already seen Aristotle here: Aristotle's Wheels

The problem of Squaring the Circle is one of the most famous problems from antiquity, and was only proved impossible when π was proven transcendental by Lindemann in 1882. Hippocrates of Chios (not to be confused with Hippocrates of Kos — famous for the Hippocratic Oath in medicine) showed a lune of the particular type in the activity above is equal in area to an associated triangle. This was the first exact calculation of the area of a circular shape!

Try and visualise similar shapes made from the intersections of spheres in 3D.