Ibn al-Haytham's lemmas for solving ``Alhazen's problem'' (Q1168294)

The problem is defined as that of finding the point of reflection on the surface of a spherical mirror, convex or concave, given the two points related to one another as eye and visible object. In the first part of the paper, the solution is given as it appears in Ibn Al-Haytham's \textit{Optics}. It is long and wearisome compared to Huygens's solution, but the latter is based on the same idea. Moreover, Ibn Al-Haytham's solution is part of a long series of investigations leading to a theory of reflections from different surfaces. Its importance for the history of mathematics in Europe, down to the seventeenth century is recognisable. Ibn Al-Haytham supported his solution with eight lemmas. Section II of the paper is concerned with the statement and proofs of these lemmas. They are naturally all geometrical.