The article "Controversies on Nature as Legality (1680-1710)" is a first complement to the article "Les lois de la nature : le problème terminologique", for in it I examine the texts of which what I called the physico-mathematical and the metaphysical usages of the word "law" meet. These texts can be divided into two constellations. The first corresponds to the polemic between Antoine Arnauld and Nicolas Malebranche, in which intervened Bernard Le Bovier de Fontenelle, Pierre Bayle, Jacques-Bénigne Bossuet and François de Salignac de la Motte-Fénelon (1685-1715). The second constellation is made up of the exchanges between Leibniz, Bayle, Jean Christophe Sturm and Gunther Christoph Schelhammer (1695-1707). If the notion of law of Nature is ...