IsisCB Explore

Article ID: CBB986988543

Leibniz on the Requisites of an Exact Arithmetical Quadrature (2018)

Raffo Quintana, Federico (Author)

Studies in History and Philosophy of Science
Volume: 67
Pages: 65-73

URI: http://www.sciencedirect.com/science/article/pii/S0039368117301553

DOI: 10.1016/j.shpsa.2017.12.003

Outside Links

WorldCat

Google Scholar

JSTOR

Academia.edu

Induction Arithmetic Mathematics 18th century 17th century Wallis, John Leibniz, Gottfried Wilhelm von

In this paper we will try to explain how Leibniz justified the idea of an exact arithmetical quadrature. We will do this by comparing Leibniz's exposition with that of John Wallis. In short, we will show that the idea of exactitude in matters of quadratures relies on two fundamental requisites that, according to Leibniz, the infinite series have, namely, that of regularity and that of completeness. In the first part of this paper, we will go deeper into three main features of Leibniz's method, that is: it is an infinitesimal method, it looks for an arithmetical quadrature and it proposes a result that is not approximate, but exact. After that, we will deal with the requisite of the regularity of the series, pointing out that, unlike the inductive method proposed by Wallis, Leibniz propounded some sort of intellectual recognition of what is invariant in the series. Finally, we will consider the requisite of completeness of the series. We will see that, although both Wallis and Leibniz introduced the supposition of completeness, the German thinker went beyond the English mathematician, since he recognized that it is not necessary to look for a number for the quadrature of the circle, given that we have a series that is equal to the area of that curvilinear figure.

...More

Citation URI

https://data.isiscb.org/isis/citation/CBB986988543/

Citations Indexes

Similar Citations

Book Wardhaugh, Benjamin; (2012)
The History of the History of Mathematics: Case Studies for the Seventeenth, Eighteenth, and Nineteenth Centuries (/isis/citation/CBB001251196/)

Book Lloyd Strickland; Harry R. Lewis; (2022)
Leibniz on Binary: The Invention of Computer Arithmetic (/isis/citation/CBB215936036/)

Thesis Abram Kaplan; (2018)
The Myth of Greek Algebra: Progress and Community in Early-Modern Mathematics (/isis/citation/CBB202265617/)

Book Goldenbaum, Ursula; Jesseph, Douglas; (2008)
Infinitesimal Differences: Controversies between Leibniz and His Contemporaries (/isis/citation/CBB000950297/)

Article Lützen, Jesper; (2014)
Seventeenth Century Arguments for the Impossibility of the Indefinite and the Definite Circle Quadrature (/isis/citation/CBB001550679/)

Article Davies, E. B.; (2009)
Some Reflections on Newton's Principia (/isis/citation/CBB000932110/)

Book Hacking, Ian; (2006)
The Emergence of Probability: A Philosophical Study of Early Ideas aboutProbability, Induction, and Statistical Inference (/isis/citation/CBB000830028/)

Article MacKenzie, Scott R.; (2014)
Sexual Arithmetic: Appetite and Consumption in The Way of the World (/isis/citation/CBB001201791/)

Book Leo Corry; (2022)
British Versions of Book II of Euclid’s Elements: Geometry, Arithmetic, Algebra (1550–1750) (/isis/citation/CBB193067062/)

Article Luo, Jianjin; (2003)
On the Development of the Formulae for Sums of Integers (/isis/citation/CBB000774899/)

Article Goldstein, Joel A.; (2000)
A Matter of Great Magnitude: The Conflict over Arithmetization in 16th-, 17th-, and 18th-Century English Editions of Euclid's Elements Books I Through VI (1561-1795) (/isis/citation/CBB000110930/)

Article Francisco Gómez-García; Pedro J. Herrero-Piñeyro; Antonio Linero-Bas; Ma. Rosa Massa-Esteve; Antonio Mellado-Romero; (2021)
The six books of Diophantus’ Arithmetic increased and reduced to specious: the lost manuscript of Jacques Ozanam (1640–1718) (/isis/citation/CBB347141746/)

Book Koetsier, Teun; Bergmans, Luc; (2005)
Mathematics and the Divine: A Historical Study (/isis/citation/CBB000500288/)

Article Dutka, Jacques; (1982)
Wallis's product, Brouncker's continued fraction, and Leibniz's series (/isis/citation/CBB000025519/)

Book (1995)
Geometria, flussioni e differenziali: Tradizione e innovazione nella matematica del Seicento (/isis/citation/CBB000076004/)

Book Beeley, Philip; Scriba, Christoph J.; (2012)
Correspondence of John Wallis (1616--1703). Vol. III, October 1668--December 1673 (/isis/citation/CBB001200116/)

Article Knobloch, Eberhard; (2013)
Analiticidad, equipolencia y teoría de curvas en Leibniz (/isis/citation/CBB001214081/)

Book Davide Gullotto; (2023)
La Repubblica dei Matematici. Storia dell’analisi matematica nell’età di Euler e Leibniz (/isis/citation/CBB269641386/)

Article Zaytsev, Evgeny; (2008)
Euler's Problem of Königsberg Bridges and Leibniz' Geometria Situs (/isis/citation/CBB001021140/)

Article Dunlop, Katherine; (2013)
Mathematical Method and Newtonian Science in the Philosophy of Christian Wolff (/isis/citation/CBB001320268/)

Comments

{{ comment.created_by.username }} on {{ comment.created_on | date:'medium' }}