Utilize este identificador para referenciar este registo:
https://hdl.handle.net/1822/85016
Título: | Geometry and analysis in Anastácio da Cunha's calculus |
Autor(es): | Domingues, João Caramalho |
Palavras-chave: | José Anastácio da Cunha 18th-century calculus Geometry/analysis Nominalism |
Data: | 8-Jun-2023 |
Editora: | Springer |
Revista: | Archive for History of Exact Sciences |
Resumo(s): | It is well known that over the 18th century the calculus moved away from its geometric origins; Euler, and later Lagrange, aspired to transform it into a "purely analytical" discipline. In the 1780s, the Portuguese mathematician José Anastácio da Cunha developed an original version of the calculus whose interpretation in view of that process presents challenges. Cunha was a strong admirer of Newton (who famously favoured geometry over algebra) and criticized Euler's faith in analysis. However, the fundamental propositions of his calculus follow the analytical trend. This appears to have been possible due to a nominalistic conception of variable that allowed him to deal with expressions as names, rather than abstract quantities. Still, Cunha tried to keep the definition of fluxion directly applicable to geometrical magnitudes. According to a friend of Cunha's, his calculus had an algebraic (analytical) branch and a geometrical branch, and it was because of this that his definition of fluxion appeared too complex to some contemporaries. |
Tipo: | Artigo |
URI: | https://hdl.handle.net/1822/85016 |
DOI: | 10.1007/s00407-023-00313-1 |
ISSN: | 0003-9519 |
e-ISSN: | 1432-0657 |
Versão da editora: | https://link.springer.com/article/10.1007/s00407-023-00313-1 |
Arbitragem científica: | yes |
Acesso: | Acesso aberto |
Aparece nas coleções: | CMAT - Artigos em revistas com arbitragem / Papers in peer review journals |
Ficheiros deste registo:
Ficheiro | Descrição | Tamanho | Formato | |
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geometry+analysis_JAC_AM.pdf | 632,32 kB | Adobe PDF | Ver/Abrir |
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