Article ID: CBB945634443

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

unapi

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
Ausejo Martínez, Elena
Navarro Loidi, Juan
Blanco, Mónica
Cervara, José Antonio
Craik, Alex D. D.
Fischer, Joachim
Journals
Historia Mathematica
Llull: Revista de la Sociedad Española de Historia de las Ciencias y de las Técnicas
Quaderns d'Història de l'Enginyeria
British Society for the History of Mathematics Bulletin
Chinese Journal for the History of Science and Technology
La Gaceta de la Real Sociedad Matemática Española
Publishers
American Mathematical Society
El Colegio de Mexico
Princeton University Press
Springer
Universidad de Alicante
Docent Press
Concepts
Mathematics
Mathematicians
Mathematics education and teaching
Logarithms
Calculus
Functions (mathematics)
People
Euler, Leonhard
Bails, Benito
Zaragoza, José de
Bézout, Étienne
Caramuel, Juan
Juan, Jorge
Time Periods
18th century
19th century
20th century
17th century
20th century, early
21st century
Places
Spain
China
Turkey
Scotland
Austro-hungary
Ottoman Empire
Institutions
Jesuits (Society of Jesus)
Imperial University of Peking
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