Displacement of a Rigid Body

This chapter is devolved to the analysis of the way in which Chasles’ foundational programme was extended beyond geometry. The problem of the movement of a rigid body is addressed. An initial brief historical introduction is followed by five sections, which explore the work of Chasles by dividing it into three main periods. Section 3.1 is dedicated to the first one, which corresponds to the year 1830. Section 3.2 regards, instead, the second period, which dates from 1831 to the publication of the Aperçu in 1837. The third section concerns a comparison between Chasles’ conceptions and those developed by other mathematicians on this same subject as well as a contribution he gave in 1843. The influence exerted by his ideas and methods is also addressed in this section, which is useful to understand the complex relations between synthetic and analytical methods in geometry at that time. Chasles offered a complete and advanced treatment of the movement of a rigid body in a series of papers published between 1860 and 1861. This connotes the third phase of his thought on such a topic, to which the fourth section is devoted. Chasles offered almost no demonstrations of the propositions he conceived in this third phase, but other mathematicians embarked in such an enterprise. In this section we also provide an overview of their work. The Conclusive considerations follow as fifth section.