In my contribution I would like to study the debate on vis viva (forces vives) between Émilie Du Châtelet and Jean-Jacques Dortous de Mairan. The polemics took place after the publication of Du Châtelet's work Institutions de physique in 1740 and became an important element in the intellectual biography of the two scholars. I propose to analyze the Du Châtelet/Mairan debate from the perspective of argumentation, focusing on the approaches to the appeals to authority.