The idea of combining theory and practice in mathematics was forged in the seventeenth and eighteenth century as a result of different influences. Several mathematical courses published through the seventeenth century offered extensive material for teaching pure and “mixed” mathematics, such as pure geometry, practical geometry, optics, statics, mechanics, artillery, and fortification. In the eighteenth century, these textbooks were the fundamental source for engineering courses. In particular, we would like to focus our analysis on relevant mathematical courses developed in the Iberian Peninsula by authors such as Luis Serrao Pimentel (1613-1679) and Manuel de Azevedo Fortes (1660-1749) in Portugal, and Sebastián Fernández de Medrano (1646-1705), Jorge Próspero Verboom (1667-1744), Pedro de Lucuce (1692-1779), Tomàs Cerdà (1715-1791), and Pedro Padilla y Arcos (f.1753) in Spain. Most of these courses were designed for the training of military officers. References to them appeared in several treatises produced in Spain, France, or Germany. At the beginning of the eighteenth century, the works of Bernard Forest Bélidor (1698-1761) were particularly influential.
We aim to determine the central subjects for engineering education. Two parts are recognized as essential for the training of an engineer: practical geometry and fortification. Practical geometry consists of trigonometry, logarithms, trigonometric and logarithm tables, instruments and their application in the field. Fortification consists in describing the building of defence lines, fortresses, and bastions. However, analysis of the contents of these treatises raises other questions for discussion related, for example, with the role of pure mathematics. What was the interpretation or the version of Euclid’s Elements used in these textbooks? Does the use of the geometry of Port Royal have any significance? One could also consider other aspects such as to what extent these mathematical courses spread or appropriated the new knowledge in that time, like algebra or infinitesimal calculus. In addition, an international network of mathematical works was assembled to provide a better education for engineers.
The communications on these aspects of mathematical courses will offer new insights into the kind of knowledge available to engineers in the eighteenth century and in consequence its influence on the society. The education of engineers gives us an outstanding example of how international –cosmopolitan- knowledge becomes a local culture, the engineering culture, purportedly “national” in many cases, as explicitly suggested by the title of the notable textbook by Manuel de Azevedo Fortes (“The Portuguese Engineer”).
Mª Rosa Massa Esteve. Universitat Politècnica de Catalunya.
Antónia Fialho Conde. Universidade de Évora.