Un lemme d'analyse dont use Ibn al-Haytham en gnomonique, dioptrique et cin\'ematique c\'eleste

Abstract

In several places and for different purposes, Ibn al-Haytham has studied the variations of a well-known function. The context of these applications reveals some characteristics of Ibn al-Haytham's mathematical and physical thought. An in-depth study of his mathematical proofs of monotony show how close he was from an elaborate concept of the continuous.