2(a) Archytus developed a construction to find two geometric means between two magnitudes. The longer magnitude is AC, which is the diameter of a circle. That circle is rotated around A to forms a torus. A cylinder is then produced perpendicular to the torus, whose diameter is also AC. The shorter magnitude AB is drawn as a chord of a cross section of the torus. AB is extended until it intersects the cylinder, forming a triangle, which when rotated produces a cone. All three surfaces intersect at point P.