Introducing differential calculus in Spain: The fluxion of the product and the quadrature of curves by Tomàs Cerdà

Abstract

Differential calculus was introduced into eighteenth-century Spain through the teaching of several authors in different scientific institutions. One of the more noteworthy of these Spanish authors was the Jesuit Tomàs Cerdà (1715–1791), who taught mathematics at the College of Cordelles in Barcelona and at the Imperial College in Madrid. This mathematician introduced differential calculus through the manuscript entitled ‘Tratado de Fluxiones’ (1757–1759), which had as a main source The Doctrine and Application of Fluxions (1750) by Thomas Simpson (1710–1761). Our aim in this paper is to analyse Cerdà’s special contribution to the introduction into Spain of the Newtonian theory of fluxions based on Simpson’s definition of a fluxion. Specifically, the paper shows that Cerdà deduced the fluxion of the product of two variables and the area under a curve by previously establishing the fluxion of a curvilinear surface, a particular and different approach to that employed by other contemporaneous mathematicians in Spain.