Rieger's differential calculus courses at the Colegio Imperial de Madrid

Abstract

One of the mathematicians and teachers who introduced Differential and Integral Calculus in Spain in the mid–18th century was Christian Rieger (1714–1780). This Jesuit mathematician moved from Vienna to the Imperial College in Madrid in 1761, and was the first professor of mathematics at this college until 1765. Two manuscripts, introductory to Differential Calculus, have been found among the documents belonging to the Jesuits of the Imperial College, which can be attributed to Rieger: “In methodum fluxionum” and “Introducción fácil al algoritmo de fluxiones”. Both texts are written under Newton’s geometrical–kynematical vision and the one written in Spanish which, in principle, is the translation from Latin, does not reflect all the content of the first one nor does it strictly follow the Latin text, incorporating many sections of Thomas Simpson’s (1710–1761) book, The Doctrine and Application of Fluxions. All this suggests that Miguel Benavente (1726–?), the translator of Rieger’s work, probably played an important role in the writing of “Introducción fácil al algoritmo de fluxiones”. Analyzing this text, where diverse influences converge, is a way to know how the first teachings of Differential and Integral Calculus were developed in Spain.