  This article has his origin in some lectures given at the University of
Bologna, inside an interdisciplinary program of mathematics, history of
science, physics and philosophy. Since they are at the junction of these
fields, movement and infinitesimal calculus are good instances to understand
some fundamental questions in history of sciences, the diversity of the
conceptions stretching across it and more generally the philosophy background
of theses researches. It is the field where the 'struggle of giants' takes
place. In this article we consider the general foundations needed for this
study, in particular its philosophical background. While the principal question
concerns 'the one and the multiple' it is treated through the study of the
'discreet and the continuous' considered under both his philosophical and
mathematical aspect. In a second article we will consider the relation between
the theorization of the movement and the infinitesimal calculus, and their
historical background where they were able to grow
