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abstract: VÍCTOR
NAVARRO BROTÓNS
Teaching mathematical disciplines in Spain in the 16th century This essay examines some aspects of the teaching of the mathematics disciplines and its applications in some of the principal Spanish universities of the 16th century (Salamanca, Alcalá, Valencia) and in other institutions sponsored by the monarchy, such as the Casa de la Contratación (House of Trade) of Seville and the so-called Academy of Mathematics of Madrid. The three cited universities (two of they, Alcalá and Valencia, created in the beginning of the 16th century) had a chair of mathematics whose teaching contents evolved along the century, arriving to include a fairly wide range of subjects: arithmetic, geometry, trigonometry, geometric optics or perspective, survey, astronomy, astrology, cartography and geography, navigation, military art and use of astronomic tables and instruments. In the Casa de la Contratación and other nautical schools the teachings were oriented to provide the minimal bases for the navigation (nautical astronomy, instruments and maps, etc.). The initial project of the Academy of Mathematics was to provide a good mathematical training to a wide spectrum of professionals (cosmographers, engineers, architects, sculptors and painters, etc.), but in practice was apparently oriented mainly towards the subjects related to cosmography and navigation. In the universities, the propaedeutical function of the mathematical disciplines, regarding the studies of logic, philosophy (and theology) and medicine, was combined with a practical and applied orientation, that it was gaining ground along the century. Nevertheless, some of the most outstanding teachers, as Jerónimo Muñoz (professor in Valencia and Salamanca), they did not avoid the discussion of questions of natural philosophy, and intervened actively in the cosmological debates that were developed in Europe in the last decades of the 16th century. 
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