This edition does not include all the works of I. Bernoulli on mechanics. Here, first of all, there are several articles on the sacred task of brachistochron. In addition, we took two large works devoted to the propaganda of Leibniz's concept of living forces: the first is devoted to the theory of the impact of elastic bodies, the second is actually an analysis of the concept of "living force." A special addition about the reason for elasticity is attached to the first work. All compositions are arranged in chronological order. The translation was made according to Opera Omnia, published in 1742, during the life of the author and with his participation. The appendix contains an excerpt from Varignon's "New Mechanics," published in 1725, which contains a letter from I. Bernoulli to his friend about the principle of virtual speeds. Translation from German.