ABSTRACT
The first group of works by Ibn al-Haytham on infinitesimal mathematics was on the quadrature of lunes and circles. The problem he wanted to solve was how to calculate in a rigorous way the area enclosed between the arcs of circles and to find out in every case — whether with lunes or circles — the exact quadrature of these curvilinear areas. The problem of the infinitesimal is ever-present in the proportion of circles under consideration or in the proportion of the squares of their diameters. No other mathematician, before or since Ibn al-Haytham, writing in Greek, Arabic or Latin, has contributed as much to this area of study, or to advance this kind of research, right up until the last decades of the seventeenth century. We are aware that this may come as a surprise, especially as the works of Ibn al-Haytham are still largely unknown.
