The rectification of quadratures as a central foundational problem for the early Leibnizian calculus

Autor:	Blasjo, Viktor, History and Foundations of Science, Sub Fundamental Mathematics
Přispěvatelé:	History and Foundations of Science, Sub Fundamental Mathematics
Jazyk:	angličtina
Rok vydání:	2012
Předmět:	History Mathematics(all) Extension (metaphysics) Reduction (recursion theory) Transcendental curves General Mathematics Leibnizian calculus Calculus Transcendental number Rectification of quadratures Rigour Period (music) Mathematics
Zdroj:	Historia Mathematica, 39(4), 405. Academic Press Inc.
ISSN:	0315-0860
Popis:	Transcendental curves posed a foundational challenge for the early calculus, as they demanded an extension of traditional notions of geometrical rigour and method. One of the main early responses to this challenge was to strive for the reduction of quadratures to rectifications. I analyse the arguments given to justify this enterprise and propose a hypothesis as to their underlying rationale. I then go on to argue that these foundational concerns provided the true motivation for much ostensibly applied work in this period, using Leibniz’s envelope paper of 1694 as a case study.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_dedup___::e9dd43e0fe1cc13df28325138bf43dab https://dspace.library.uu.nl/handle/1874/262527 Zobrazit plný text záznamu Full Text from ScienceDirect