(ὁ τοῦ κύκλου τετραγωνισμός/ho toû kýklou tetragōnismós, Latin quadratura circuli).
I. The nature of the problem
The quadrature of the circle is one of the three 'classic problems' (the other two being the trisection of an angle, cf. division of angles and circles, and the duplication of the cube) of ancient Greek mathematics. The problem is to find the side x of a square such that its area is equal to the area of a circle with radius r using a geometric procedure; that is, to determin…