Article ID: CBB945634443

Infinite analytical procedures for the computation of logarithms in works by Benito Bails (1731–1797) (2023)


During the Spanish eighteenth century, a process of modernization took place in scientific knowledge, partly driven by the circulation and appropriation of new scientific ideas. In this context, the Spanish mathematician Benito Bails (1731–1797) published his course Elementos de Matemática (Elements of Mathematics) consisting of ten volumes (1779–1799), in which, among other subjects, he presented one of the most complete mathematical developments of logarithmic calculation methods of his time, by using the infinity through infinite series. The aim of our article is to demonstrate how algebraic analytical reasoning enabled Bails to obtain new and more efficient infinite algorithms that converge more quickly in the computation of logarithms in any system. We show how Euler's number ‘e’ is calculated, probably for the first time in Spanish teaching, in an eighteenth century mathematical text. Our analysis concludes that Bails’ course constituted an innovation and provides evidence of its creativity, originality and ingenuity.

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Authors & Contributors
Navarro Loidi, Juan
Ausejo Martínez, Elena
Hill, Ted
Stawiska, Małgorzata
Domoradzki, Stanisław
Sanz, Miguel
Quaderns d'Història de l'Enginyeria
Llull: Revista de la Sociedad Española de Historia de las Ciencias y de las Técnicas
Historia Mathematica
Studia Historiae Scientiarum
Science in Context
Science and Education
Docent Press
Universidad de Alicante
Princeton University Press
El Colegio de Mexico
American Mathematical Society
Mathematics education
Teaching; pedagogy
Euler, Leonhard
Zaragoza, José de
Bails, Benito
Stifel, Michael
Spence, William
Rudolff, Christoff
Time Periods
18th century
20th century
19th century
17th century
20th century, early
United States
Imperial University of Peking
Jesuits (Society of Jesus)

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