Khayyam seems to have been attracted to cubic equations originally through his consideration of the following geometric problem: in a quadrant of a circle, drop a perpendicular from some point on the circumference to one of the radii so that the ratio of the perpendicular to the radius is equal to the ratio of the two parts of the radius on which the perpendicular falls. In a short, untitled treatise, Khayyam leads us from one case of this problem to the equation   x3 + 200x = 20x2 + 2000.13 An approximation to the solution of this equation is not difficult to find, but Khayyam also generates a direct geometric solution: he uses the numbers in the equation to determine intersecting curves of two conic sections (a circle and a hyperbola), and demonstrates that the solution x is equal to the length of a particular line segment in the diagram.