I movimenti rigidi da Euler al Programma di Erlangen

This dissertation about the history of geometrical transformation focuses on the roots of the concept of isometry. This study examines the concept of rigid motion and gives a first historical account of its evolution during the period going from the Introduction in analysin infinitorum by Euler (1748) to the Erlangen Programm by Klein (1872). In the second and third part of this dissertation works by Euler (1707-1783), Chasles (1793 - 1880), Jordan (1838-1922) and Klein (1849 - 1925) dealing with rigid motions are studied. The study reveales a long standing connection between rigid motion and kinematics and the absence of the concept of re ection as transformation. Particular attention is devoted to Jordan's revolutionary memoir Memoire sur le groupes de mouvements (1868) in which groups of rigid motion are introduced and applied to crystallography.