It is well known that over the eighteenth century the calculus moved away from its geometric origins; Euler, and later Lagrange, aspired to transform it into a “purely analytical” discipline. In the 1780 s, the Portuguese mathematician José Anastácio da Cunha developed an original version of the calculus whose interpretation in view of that process presents challenges. Cunha was a strong admirer of Newton (who famously favoured geometry over algebra) and criticized Euler’s faith in analysis. However, the fundamental propositions of (...) his calculus follow the analytical trend. This appears to have been possible due to a nominalistic conception of variable that allowed him to deal with expressions as names, rather than abstract quantities. Still, Cunha tried to keep the definition of fluxion directly applicable to geometrical magnitudes. According to a friend of Cunha’s, his calculus had an algebraic (analytical) branch and a geometrical branch, and it was because of this that his definition of fluxion appeared too complex to some contemporaries. (shrink)

Vers la fin des années 1750, une Académie de Mathématiques fut créée au sein de l’Académie Militaire de la Garde du Corps à Madrid, dirigée par Pedro Padilla (1724-1807?) jusqu’à sa fermeture en 1760. En 1753, Padilla commença à publier son Cours Militaire de Mathématiques (1753 -1756) pour l’usage de cette Académie. Le besoin de textes mathématiques en espagnol dans le domaine militaire a conduit à la création en 1757 de la Société Royale Militaire de Mathématiques à Madrid sous la (...) direction de Pedro de Lucuce (1692-1779), lui aussi directeur de l’Académie Militaire de Mathématiques de Barcelone depuis 1738. Les membres de la Société ont été chargés de l’élaboration d’un cours complet dans lequel les mathématiques étaient considérées comme essentielles à la formation militaire des officiers artilleurs et des ingénieurs militaires. La Société, supprimée en 1760, a réussi à réunir une excellente bibliothèque scientifique et technique servant à son tour à fournir des futures bibliothèques militaires. Le but de cette contribution est d’explorer et de comparer la manière dont l’étude des mathématiques a été abordée dans ces deux cas. Toward the end of 1750, an Academy of Mathematics was established within the Military Academy of Royal Guards of Madrid that was managed by Pedro Padilla (1724-1807?) until it closed in 1760. In 1753, Padilla authored and published his Military Course of Mathematics (1753-1756) for the specific use by this Academy. The further need for mathematical texts in Spanish for military training coursework led to the founding of the Royal Military Society of Mathematics of Madrid in 1757 under the direction of Pedro de Lucuce (1692-1779), the headmaster of the Barcelona Military Academy of Mathematics since 1738. The members of this Society were entrusted with producing a comprehensive course program in which mathematics was considered and presented as essential to training of military engineers and gunners. The Society of Mathematics was dissolved in 1760 but had succeeded in building an extensive scientific and technical book depository that later served as a valuable resource supplying other military libraries. The aim of this contribution is to explore and compare how the study of mathematics was approached in these two cases. (shrink)