Mengoli's mathematical ideas in Leibniz's excerpts

Abstract

Dedicated to the memory of Jacqueline Stedall In the seventeenth century many changes occurred in the practice of mathematics. An essential change was the establishment of a symbolic language, so that the new language of symbols and techniques could be used to obtain new results. Pietro Mengoli (1626/7–86), a pupil of Cavalieri, considered the use of symbolic language and algebraic procedures essential for solving all kinds of problems. Following the algebraic research of Viète, Mengoli constructed a geometry of species, Geometriae Speciosae Elementa (1659), which allowed him to use algebra in geometry in complementary ways to solve quadrature problems, and later to compute the quadrature of the circle in his Circolo (1672). In a letter to Oldenburg as early as 1673, Gottfried Wilhelm Leibniz (1646–1716) expressed an interest in Mengoli's works, and again later in 1676, when he wrote some excerpts from Mengoli's Circolo. The aim of this paper is to show how in these excerpts Leibniz dealt with Mengoli's ideas as well as to provide new insights into Leibniz's mathematical interpretations and comments.