Nous resultats i procediments en les matemàtiques del segle XVII: càlcul de màxims a Pietro Mengoli (1626/1627-1686)

Abstract

The publication in 1591 of In artem analyticen isagoge by François Viète (1540 1603) constituted an important step forward in the development of a symbolic language. As Viètes work came to prominence at the beginning of the 17th century, other authors, like Pietro Mengoli (1626/16271686), also began to consider the benefit of algebraic procedures for solving all kind of problems. Mengoli followed the algebraic research of Viète in order to construct geometry of species, Geometriae Speciosae Elementa (1659), which allowed him to use algebra in geometry in complementary ways to solve quadrature problems. Mengoli, like Viète, considered his algebra as a technique in which symbols are used to represent not just numbers but also values of any abstract magnitudes. He dealt with species, forms, triangular tables, quasi ratios and logarithmic ratios. However, the most innovative aspect of his work was his use of letters to directly study geometric figures via their algebraic expressions. In this article, I analyze the algebraic construction of these geometric figures, the use of triangular tables and the singular proof developed by Mengoli for finding the maxima of these geometric figures before the development of Newtons and Leibnizs calculus. This analysis illustrates Mengolis mathematical ideas on the specific role of symbolic language as a means of expression and as an analytic tool.