Mathematical Compendium, by Tomás Vicente Tosca (1707-1715)

Tomás Vicente Tosca is perhaps the summit reference of Santiago de Cárdenas, because he was one of the most important Spanish intellectuals of the time. This mathematician and philosopher lived between the seventeenth and eighteenth centuries, developing two important works, mathematics and philosophy, which became a fundamental part of the Spanish Pre-Enlightenment. The Mathematical Compendium is an extensive treatise composed of nine volumes in which he explains topics that today would be considered within mathematics (such as arithmetic, geometry, algebra, music, among others), of physics (including static, hydrostatic, optics), engineering (machinery, architecture, hydrotechnology), astronomy and nautical, and even occultism. This almost encyclopedic work differs substantially from the other references used by Cárdenas because it is a discursive as well as a technical document: numerical and graphic examples abound, as well as hand development of calculations and applications.

There is no doubt that Cardenas was able to find in this author and in this bibliographical reference the greatest source of technical knowledge that he needed. The trace of his influence is seen not only in the number of quotations he has – although they are three explicit in all his treatise, it is the most frequently mentioned reference – but in the clear way he applies the knowledge extracted from there. The handling of the operations, the treatment of calculations and even the style to propose examples are obligatory references to Tosca, which Cardenas also stands out to give an academic support to his self-training.

Although we have said that the nine volumes of the Compendium of Tosca treated about so many topics, from here we propose that it is possible that Cárdenas did not have access to all, only two of them: Volume I and Volume IV. From these two books come the best associations can be extracted between what was elaborated by Cardenas and what reported by Tosca. In particular, the lack of an algebraic knowledge of equations in Cárdenas suggests that he did not study – or did not reach – Volume II, which deals precisely with algebra, “higher” arithmetic -series and powers- and music. The three topics are scarcely developed in a very elementary and weak formulation by Cardenas, which much differs from his processing of other topics. How much was the lack of interest? How much the lack of time? Or, How much was the lack of access to these treaties? We do not know.

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