Maria Rosa

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

La publicacio, l’any 1591, de l’obra In artem analyticen isagoge de Francois Viete (1540–1603) va constituir un pas endavant important en el desenvolupament del llenguatge simbolic. A comencaments del segle xvii la difusio de l’obra de Viete va pro- vocar que altres autors, com ara Pietro Mengoli (1626/1627–1686), tambe consideressin la utilitat dels procediments algebraics per resoldre tot tipus de problemes. Mengoli va seguir el cami de Viete tot construint una geometria d’especies, Geometriae speciosae elementa (1659), que li va permetre emprar conjuntament l’algebra i la geometria per resoldre problemes de quadratura. Mengoli, com Viete, va considerar la seva algebra una tecnica en la qual els simbols eren utilitzats no unicament per representar nombres sino tambe valors de qualsevulla magnitud. Va tractar amb especies, formes, taules triangulars, quasi raons i raons logaritmiques. Tanmateix, l’aspecte mes innovador del seu treball va ser l’us de les lletres per tractar directament les figures geome- triques mitjancant les seves expressions algebraiques. En aquest article, analitzo la construccio algebraica d’aquestes figures geometriques, l’us de les taules triangulars i la demostracio molt original que va fer Mengoli per trobar el maxim d’aquestes figures geometriques abans del desenvolupament del calcul de Newton i Leibniz. Aquestes analisis i l . l ustren les idees matematiques de Mengoli sobre la funcio especifica del llenguatge simbolic com a mitja d’expressio i com a eina analitica

Mengoli's mathematical ideas in Leibniz's excerpts

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 Viete, 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 Mengolis works, and again later in 1676, when he wrote some excerpts from Mengolis Circolo. The aim of this paper is to show how in these excerpts Leibniz dealt with Mengolis ideas as well as to provide new insights into Leibnizs mathematical interpretations and commentsDedicated 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 Mengolis works, and again later in 1676, when he wrote some excerpts from Mengolis Circolo. The aim of this paper is to show how in these excerpts Leibniz dealt with Mengolis ideas as well as to provide new insights into Leibnizs mathematical interpretations and comments.