The study of modern mathematics in the military course of mathematics (1753-1756) of Pedro Padilla

Abstract

In 18th-century Spain, military institutions played an essential role in the teaching of higher mathematics. Toward the end of 1750, an Academy of Mathematics was established at the Royal Guards Barracks in Madrid and was ruled by Pedro Padilla (1724-1807?) until it was dissolved in 1760. In 1753-1756, Padilla authored and published his Curso Militar de Mathematicas [Military Course of Mathematics] for the specific use by this Academy. According to the preface of his first volume, Padilla’s primary aim was to show that understanding the basic principles of each branch of mathematics could be useful to not only infantry and cavalry regiments, but could serve engineers, artillery and navy personnel. Besides, the publication of Padilla’s course was also an early initiative done so during a time when the tradition of dictating was still very strong. Of the twenty mathematical treatises that Padilla originally intended to develop, only the first five would be published in the end (in four volumes). The treatises IV and V are the most innovative, since they contain the earliest educational works on higher geometry and calculus published in Spain, respectively. The aim of this paper is to explore how the study of higher geometry and calculus was approached by Padilla in his course and, in particular, to identify the sources on which it could be based. The analysis of the treatises IV and V in Padilla’s mathematical course contributes evidences of the study of modern mathematics in 18th-century Spain.