The principle of virtual velocities
This chapter is almost entirely devoted to Johann Bernoulli, who considers the equilibrium for a set of infinitesimal displacements and forces. In the first part the different conceptions of the force of the XVIII century, including those of dead and living forces, are summarized. In the central part Bernoulli’s VWL is presented which enforces equality of positive and negative energies, the energy being defined as the scalar product of the force by the displacement of its application point, named virtual velocity. He offers a number of applications to the various cases including the fluid but does not provide any demonstration. In the final part a comparison of Varignon’s mechanics, based on composition of forces and Bernoulli’s mechanics based on his VWL is considered.