Convergence and Formal Manipulation of Series from the Origins of Calculus to About 1730.
In this paper I illustrate the evolution of series theory from Leibniz and Newton to the first decades of the eighteenth century. Although mathematicians used convergent series to solve geometric problems, they manipulated series by a mere extension of the rules valid for finite series, without cons...
| Publicado en: | Annals of Science Vol. 59; no. 2; pp. 179 - 200 |
|---|---|
| Autor principal: | |
| Formato: | Artículo |
| Publicado: |
Taylor & Francis Ltd
Apr2002
|
| Materias: | |
| Acceso en línea: | Ver este registro en EBSCOhost |
| fields | @attributes: recordID: 1 pdfLink: plink: https://search.ebscohost.com/login.aspx?direct=true&db=hlh&AN=6547454&site=ehost-live header: @attributes: shortDbName: hlh uiTerm: 6547454 longDbName: Humanities International Complete uiTag: AN controlInfo: bkinfo: jinfo: jid: 00033790 7J1 jtl: Annals of Science issn: 00033790 maglogo: Y pubinfo: dt: Apr2002 vid: 59 iid: 2 pid: 377 pub: Taylor & Francis Ltd artinfo: ui: 6547454 10.1080/00033790010028179 ppf: 179 ppct: 21 formats: fmt: @attributes: type: P size: 348KB tig: atl: Convergence and Formal Manipulation of Series from the Origins of Calculus to About 1730. aug: au: Ferraro, Giovanni affil: Via Nazionale, 38, I-821 Afragola, Naples, Italy su: Arithmetic series Calculus sug: subj: Arithmetic series Calculus ab: In this paper I illustrate the evolution of series theory from Leibniz and Newton to the first decades of the eighteenth century. Although mathematicians used convergent series to solve geometric problems, they manipulated series by a mere extension of the rules valid for finite series, without considering convergence as a preliminary condition. Further, they conceived of a power series as a result of a process of the expansion of a finite analytical expression and thought that the link between series and analytical expression was not restricted to the interval of convergence. This gave rise to formal aspects that became progressively more evident while the complexity of the theory increased. Asymptotic and recurrence series emerged as the result of the natural evolution of theory, without the difference between these infinite processes with respect to ordinary series being highlighted. The various aspects of dealing with series can be viewed today as derived from different definitions of the sum. However, mathematicians of that time always considered them as different approaches to a single theory that was based on a unique notion of the sum (even though, later in the eighteenth century, they disagree about what this notion was). pubtype: Academic Journal doctype: Article src: R language: English refInfo: copyright: @attributes: flag: Y custom: Copyright of Annals of Science is the property of Taylor & Francis Ltd and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. item: Annals of Science holder: Taylor & Francis Ltd dt: @attributes: year: 2002 holdings: @attributes: islocal: N |
|---|