"A string, of which both extremities are fixed, passes through a heavy ring. Find the position of equilibrium. Let A and B denote the fixed endpoints of the string and X any position of the ring [on the string]. ...The ring must hang as low as possible. (In fact the ring is heavy; it "wants to come as close to the ground, or to the center of the earth, as possible.) Both parts of the inextensible string, AX and BX, are stretched, and so the ring, sliding along the string, describes and ellipse with foci A and B. Obviously, the position of equilibrium is at the lowest point M of the ellipse where the tangent is horizontal."