Article ID: CBB000933319

El número e en los textos matemáticos españoles del siglo XVIII (2008)


Loidi, Juan Miguel Navarro (Author)

Quaderns d'Història de l'Enginyeria
Volume: 9
Pages: 145--166

ISSN: 1135-934X

Publication Date: 2008
Edition Details: Part of a special issue: 300 Aniversari de Leonhard Euler (1707--2007)

In books on Mathematics published in Spain from 1750, subjects dealing with differential and integral calculus began to appear. The influence of L. Euler was apparent in many of these texts; for example, P. Padilla Arcos cites Euler in his Curso militar de mathemáticas (Military Course on Mathematics) (1753, II). In this paper, the treatment given in these treatises to the number e, often associated with Euler, is traced. This number is commented on in these treatises in two different sections. First in the part devoted to logarithms or series, and later in the chapters devoted to integral and differential calculus. At the beginning it is defined as the base of Neperian logarithms or the number that has the Neperian logarithm 1. It is often calculated by means of series, although some authors such as T. Cerdá in his Liciones de Matematica (1758, I) confines themselves to finding its decimal logarithm M = loge = 1/ln10 = 0,43429448, which enables one to go from natural logarithms to vulgar logarithms. Most of those who manage to find its value give eight decimal figures (2,71828183), while B. Bails in his Tabla de Logaritmos (1787) arrives at 23 exact decimals (M gives it with 25 decimals). One observes that this constant still remains to be well founded, since while P. Giannini in his Curso matemático (1795, III) calls it the number e, Bails refers to it with n, J. J. García in his Elementos de Aritmetica Álgebra y Geometría (1782) uses c and F. Villalpando in his Tractatus praeliminaris (1778) prefers the letter a. In the section devoted to differential and integral calculus, the number e appears again. It is frequently mentioned when treating the derivation as that basis of logarithms that makes dlog x = dx/x, or as the basis of the exponentials that fulfilled dex = exdx. It receives a similar treatment in the chapters devoted to integrals.

Included in

Article Massa Esteve, Maria Rosa (2008) Congrés Internacional “300 Aniversari Leonhard Euler (1707--2007)”. Barcelona, 20--21 de setembre de 2007. Quaderns d'Història de l'Enginyeria (p. 307). unapi

Article Lusa Monforte, Guillermo (2008) Congrés Internacional “300 Aniversari Leonhard Euler (1707--2007)”. Una presentación informal. Quaderns d'Història de l'Enginyeria (p. 3). unapi

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Authors & Contributors
Ferraro, Giovanni
Havil, Julian
Domingo Martínez-Verdú
Jouve, Guillame
Giovanni Capobianco
Linero-Bas, Antonio
Historia Mathematica
Quaderns d'Història de l'Enginyeria
Bollettino di Storia delle Scienze Matematiche
British Journal for the History of Mathematics
Ziran Kexueshi Yanjiu (Studies in the History of Natural Sciences)
Centaurus: International Magazine of the History of Mathematics, Science, and Technology
Princeton University Press
Publicaciones de la Universidad de Alicante
Città del Silenzio
Differential equations
Sequences and series (mathematics)
Euler, Leonhard
Lagrange, Joseph Louis
Gauss, Carl Friedrich
Alembert, Jean le Rond d'
Leibniz, Gottfried Wilhelm von
Laplace, Pierre Simon
Time Periods
18th century
17th century
19th century
21st century
St. Petersburg Academy of Sciences

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