Mètodes analítics en el s.XVII: l’Hospital i el problema d’Alhazen

Abstract

In his book on optics Alhazen (965-1040) considered the following problem: to determine the point of reflection on a spherical mirror. Alhazen’s solution was a rather cumbersome geometrical construction. The so-called “Alhazen’s problem” was studied in the 17th century, in which analytical methods and calculus emerged. The use of these new mathematical tools resulted in more ingenious solutions of Alhazen’s problem. The aim of this paper is to analyse and compare the solutions given by some authors, namely, Isaac Barrow (1630-1677), Christiaan Huygens (1629-1695), René de Sluse (1622-1685) and, more especially, Guillaume F. A. Marquis de L’Hospital (1661-1704). The study of Alhazen’s problem in the 17th century contributes evidences of the algebraisation of mathematics.