Some mathematical aspects of Newton's Principia

International audienceIn this paper, I investigate some of the preliminary lemmas of Princip-ia and deal with two important aspects of Newton's mathematics: the method of first and last ratios and the role of figures in the mathemati-cal reasoning. In particular, I tackle the question of the relationship between the method of first and ultimate ratios and the modern theory of limits; then, I show that in Newton's mathematics, the figure continued to play one of the fundamental functions of the figure in Greek geometry: a part of the reasoning was unloaded on to it