Chasles and the Systems of Forces

The way in which a system of forces modifies the kinetic state of a physical system was a serious issue in the first 30 years of the nineteenth century. Mathematicians and physicists knew how to solve single problems, but the foundations of the theory were not solid. In 1830, Chasles offered a remarkable contribution to this question. His results were not new from a physical standpoint, but they are expressed in a way which can supply a precise geometrical foundation to the study of the system of forces. Therefore, in the first of the two sections in which this chapter is divided, I provide the reader with the mathematical context in which Chasles’ work on the system of forces is inscribed. In the second section, his results are analysed and the thesis that they are a significant part of his global foundational programme is claimed.