scholarly journals Some Ideas on the Genesis of the Infinitesimal Calculus

2021 ◽  
Vol 8 (1) ◽  
pp. 173-195
Author(s):  
Alejandro Ortiz Fernández
Keyword(s):  
Infinitesimal Calculus

LE LETTERE DI GIUSEPPE PEANO NELLA CORRISPONDENZA DI ERNESTO CESÀRO

Nuncius ◽  
1993 ◽  
Vol 8 (1) ◽  
pp. 249-281
Author(s):  
FRANCO PALLADINO
Keyword(s):  
United States ◽  
Nineteenth Century ◽  
The United States ◽  
Cost Of Living ◽  
Infinitesimal Calculus ◽  
Italian School ◽  
Actuarial Mathematics ◽  
Important Member ◽  
The Cost ◽  
Giuseppe Peano

Abstract<title> SUMMARY </title>We have gathered here twenty-six writings from the correspondence of Giuseppe Peano, as well as letters by Alexander Macfarlane and Alexander Ziwet.Peano's letters were addressed to Ernesto Cesaro, an important member of the great Italian school of mathematics founded in the second half of the Nineteenth century. In these writings, Peano discusses various topics: Infinitesimal calculus and Barycentric calculus, the «Rivista di Matematica» and the «Formulario» of which he was editor; didactics and a question about Actuarial mathematics. Some of the writings are confidential in nature: in one letter, Peano proposes exchanging his professorial chair with Cesaro's, and hence transferring from Turin to Naples.The letters written by Macfarlane and Ziwet were sent to Peano; they contain, at the request of Cesaro, information concerning university chairs and the cost of living in the United States.

„Niemand kann erklären, was eine Funktion ist“

2019 ◽  
pp. 259-268
Author(s):  
Peter Ullrich
Keyword(s):  
The Other ◽  
Success Story ◽  
Infinitesimal Calculus ◽  
Other Hand ◽  
Hermann Weyl ◽  
The One

Starting from the quote from Hermann Weyl given in the title a ramble is undertaken through the development of the notion of function with special emphasis on the question whether the values are associated following a law. On the one hand, this shows a success story of the interplay of this notion and of infinitesimal calculus. On the other hand, one finds impressive examples of overgeneralizations. Classification: C30, D70, E40, I20, I30, M10. Keywords: notion of function, functional laws, overgeneralization.

The Indivisibles of the Continuum

2020 ◽  
pp. 104-122
Author(s):  
Douglas M. Jesseph
Keyword(s):  
Seventeenth Century ◽  
Internal Structure ◽  
Original Formulation ◽  
Infinitesimal Calculus ◽  
History Of ◽  
John Wallis ◽  
The Continuum

This chapter considers some significant developments in seventeenth-century mathematics which are part of the pre-history of the infinitesimal calculus. In particular, I examine the “method of indivisibles” proposed by Bonaventura Cavalieri and various developments of this method by Evangelista Torricelli, Gilles Personne de Roberval, and John Wallis. From the beginning, the method of indivisibles faced objections that aimed to show that it was either conceptually ill-founded (in supposing that the continuum could be composed of dimensionless points) or that its application would lead to error. I show that Cavalieri’s original formulation of the method attempted to sidestep the question of whether a continuous magnitude could be composed of indivisibles, while Torricelli proposed to avoid paradox by taking indivisibles to have both non-zero (yet infinitesimal) magnitude and internal structure. In contrast, Roberval and Wallis showed significantly less interest in addressing foundational issues and were content to maintain that the method could (at least in principle) be reduced to Archimedean exhaustion techniques.

The Discovery of the Infinitesimal Calculus

Nature ◽  
1951 ◽  
Vol 167 (4261) ◽  
pp. 1048-1050
Author(s):  
H. W. TURNBULL
Keyword(s):  
Infinitesimal Calculus

scholarly journals An Elementary Course of Infinitesimal Calculus

Nature ◽  
1921 ◽  
Vol 107 (2703) ◽  
pp. 775-775
Author(s):  
G. B. M.
Keyword(s):  
Infinitesimal Calculus
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