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

## TL;DR

This paper explores Ibn al-Haytham's mathematical and physical ideas through his study of a function's variations, revealing his advanced understanding of continuity and monotony in historical context.

## Contribution

It provides an in-depth analysis of Ibn al-Haytham's proofs of monotony, highlighting his early conceptualization of the continuous in mathematical thought.

## Key findings

- Ibn al-Haytham's work demonstrates an advanced understanding of monotony.
- His proofs reveal a conceptual approach to the continuous.
- The study sheds light on the historical development of mathematical ideas.

## 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.