La influencia del "Cursus Mathematicus" de Hérigone en la algebrización de la matemática

Résumé

The process of algebraization of mathematics consists, roughly, in the progressive acceptance of algebraic procedures as a method of solving arithmetic and geometric problems. This process led to transformations in mathematics, as well as a change from a geometric to an algebraic way of thinking. Although algebra had an important evolution during the 16th century, gaining relevance due to its effectiveness in solving problems, the most important change towards this new way of thinking occurred with the publication of the work Introduction to Analytical Art (1591) by François Viète (1540-1603) and the development of his new algebra applied to geometry. Historically, the next milestone has been the publication of Geometry (1637) by René Descartes (1596-1650) where the author introduced the geometric unit and, thus, was able to construct an algebra of segments in which the algebraic operations of addition, subtraction, multiplication, division, potentiation, and roots extraction have both an arithmetic and a geometric interpretation. In this interlude between Viète and Descartes is the work of Pierre Hérigone (ca.1580-1643), a bilingual mathematical course, written in two columns in Latin and French, made up of six volumes, of which the first four were published in 1634, the fifth in 1637 and the sixth in 1642. The Course has a special feature: the use of a totally symbolic language to transmit mathematics that, according to Hérigone, can be understood by anyone without the use of their mother language. In the Course, in relation to the algebrization process, algebra is exposed following the Analytical Art, which makes it an important object of analysis in terms of the diffusion of Viète's new algebra in the time before Descartes. In this work we study the Mathematical Course of Hérigone, which has not been studied in depth until now, with the aim of analyzing the mathematical, methodological and structural contributions of the work of this mathematician in the process of algebrization of mathematics, as well as his influence on it.