During the 19th century the development of analysis and mechanics led mathematicians to the use of expressions with many degrees of freedom. The formulation of notions like kinetic energy as a quadratic form and the principle of least action as a variational problem raised the possibility of applying geometric methods to mechanical problems in higher dimensions. As has been argued by Scholz (1980) and Lützen (1995), the acceptance of non-Euclidean geometry in the second half of the 19th century, together with the development of higher dimensional phenomena in mechanics and projective geometry, set the stage for the introduction of higher dimensional geometry as a framework to represent and solve naturally arising problems. By freeing geometry from its Euclidean origins it was possible to imagine a study of geometric objects in any dimension on which complex mechanical systems moved according to well known principles.