dc.contributor.author Massa Esteve, Maria Rosa dc.contributor.other Universitat Politècnica de Catalunya. Departament de Matemàtiques dc.date.accessioned 2018-10-03T12:01:26Z dc.date.available 2018-10-03T12:01:26Z dc.date.issued 2018-06-22 dc.identifier.citation Massa, M. The harmonic triangle in Mengoli 's and Leibniz's works. "Quaderns d'història de l'enginyeria", 22 Juny 2018, vol. XVI, p. 233-258. dc.identifier.issn 1135-934X dc.identifier.other https://upcommons.upc.edu/handle/2117/118709 dc.identifier.uri http://hdl.handle.net/2117/121858 dc.description.abstract The harmonic triangle was defined by Gottfried Wilhelm Leibniz (1646- 1716) in 1673, and its definition was related to the successive differences of the harmonic series. Leibniz studied it in many different texts throughout his life. Pietro Mengoli (1627-1686), rather at the same time, used the harmonic triangle as a triangular table to perform quadratures and also the interpola - ted harmonic triangle to calculate the quadrature of the circle. In this article we analyze and compare the independent treatment of harmonic triangle by Mengoli and Leibniz in their works, referring to their sources, their aims, and their uses. We show that, on the one hand, Mengoli uses triangular tables as a tool of calculus, and uses the harmonic triangle to perform quadratures through one procedure called by him “homology”. On the other hand, at the same time, Leibniz defines the harmonic triangle from the study on harmonic series, analyses its properties, and uses it to perform the summations of infi - nite series through one procedure called by him “sums of all the differences”. Harmonic triangle has an open visual structure in which the number of terms arranged in this way can be made infinite. The infinite therefore becomes one more element in the mathematical calculations of these authors, which in seventeenth century mathematics opened up a world of possibilities in the series and in their relations with infinitesimal calculus dc.format.extent 26 p. dc.language.iso eng dc.publisher Publicacions UPC dc.rights Attribution-NonCommercial-NoDerivs 3.0 Spain dc.rights.uri http://creativecommons.org/licenses/by-nc-nd/3.0/es/ dc.subject Àrees temàtiques de la UPC::Matemàtiques i estadística dc.subject.lcsh Mathematics--History--17th century dc.subject.lcsh Mengoli, Pietro, 1625-1686 dc.subject.lcsh Leibniz, Gottfried Wilhelm, Freiherr von, 1646-1716 dc.subject.other Harmonic triangle dc.subject.other Pietro Mengoli dc.subject.other Gottfried Wilhelm Leibniz dc.subject.other Seventeenth century. dc.title The harmonic triangle in Mengoli 's and Leibniz's works dc.type Article dc.subject.lemac Matemàtica -- Història -- S. XVII dc.subject.lemac Mengoli, Pietro dc.subject.lemac Leibniz, Gottfried Wilhelm, Freiherr von, 1646-1716 dc.contributor.group Universitat Politècnica de Catalunya. GRHCT - Grup de Recerca d'Història de la Ciència i de la Tècnica dc.relation.publisherversion www.upcommons.upc.edu dc.rights.access Open Access drac.iddocument 23243011 dc.description.version Postprint (author's final draft) upcommons.citation.author Massa, M. upcommons.citation.published true upcommons.citation.publicationName Quaderns d'història de l'enginyeria upcommons.citation.volume XVI upcommons.citation.startingPage 233 upcommons.citation.endingPage 258
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