The debate at the École polytechnique
This chapter is devoted to the debate at the École polytechnique on the principle of virtual velocities as presented in Lagrange’s Méchanique analitique of 1788, assuming a reductionist approach. In the first part, after a brief mention of Gaspard de Prony’s contribution, three interesting demonstrations by Fourier of the principle of virtual velocities are presented. Fourier considers the case of unilateral constraints also. In the second part the demonstration of Ampère is presented. Note the use of purely geometric virtual velocities, following the lead of Lazare Carnot. In the third part the probably less interesting demonstration of Pierre Simon Laplace is reported.