El Concepte de límit de Newton a Cauchy : entre la geometria i l'àlgebra i el paper dels signes [Primera part]

Abstract

The concept of limit is constitutive for the differential and integral calculus. Yet, its historical emergence has not been closely studied. As an alternative to infinitesimal approaches, it had first been introduced by Newton, but without conceptual reflections and without an operational technique; it remained tied to geometrical-kinematical contexts. The paper studies the slow development of the concept during the eighteenth century, and in particular the first definitions and their gradual steps towards algebraization. Thanks to the approach to investigate the contributions within the contemporaneousmathematical communities at large, apparentlymarginal authors reveal to achieve considerable steps towards an algebraized operational theory of limits. Yet, this process proves not to be a continuous one and depending on epistemologies differing over various countries and communities. The analysis finalizes in contrasting two approaches of the 1820s revealing such differing visions: Cauchy in France and Dirksen in Germany. This first part of the paper presents the conceptual frame of that known as the algebraization process and analizes wich way Newton presents this process in the concept of limithow to usesMaclaurin in response to Berkeley and dAlembert in the Enciclopèdie to enter after in the limit as approach. It closes with the start of the algebraization of this new concept: the limit. It opens the door to the second part which will publish them in the next issue.