Leibniz and the Impossibility of Squaring the Circle

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985955%3A_____%2F17%3A00484610" target="_blank" >RIV/67985955:_____/17:00484610 - isvavai.cz</a>

Výsledek na webu

—

DOI - Digital Object Identifier

—

Jazyk výsledku

angličtina

Název v původním jazyce

Leibniz and the Impossibility of Squaring the Circle

Popis výsledku v původním jazyce

In this paper, I shall study the last proposition of the De Quadratura Arithmetica (1676) of G.W. Leibniz, where we find a proof that it is impossible to solve algebraically the quadrature of an arbitrary sector of the circle, the hyperbola and the ellipse. I shall deal with the quadrature of the circle only, and I shall put this mathematical result into its proper context, that is to say the controversy that had opposed James Gregory and Christiaan Huygens several years earlier. Probably under Huygens’ guidance, Leibniz studied the documents related to the controversy and wrote interesting observations about it. These observations show that Leibniz was led to investigate the issue of impossibility with the hope of correcting some flaws in Gregory’s reasoning, and eventually come up with an original impossibility theorem. Keywords: Infinitesimal Geometry, Gregory, Huygens, Leibniz, impossibility, quadrature of the circle, infinite series.

Název v anglickém jazyce

Leibniz and the Impossibility of Squaring the Circle

Popis výsledku anglicky

In this paper, I shall study the last proposition of the De Quadratura Arithmetica (1676) of G.W. Leibniz, where we find a proof that it is impossible to solve algebraically the quadrature of an arbitrary sector of the circle, the hyperbola and the ellipse. I shall deal with the quadrature of the circle only, and I shall put this mathematical result into its proper context, that is to say the controversy that had opposed James Gregory and Christiaan Huygens several years earlier. Probably under Huygens’ guidance, Leibniz studied the documents related to the controversy and wrote interesting observations about it. These observations show that Leibniz was led to investigate the issue of impossibility with the hope of correcting some flaws in Gregory’s reasoning, and eventually come up with an original impossibility theorem. Keywords: Infinitesimal Geometry, Gregory, Huygens, Leibniz, impossibility, quadrature of the circle, infinite series.

Druh

C - Kapitola v odborné knize

CEP obor

—

OECD FORD obor

60301 - Philosophy, History and Philosophy of science and technology

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2017

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název knihy nebo sborníku

The dialogue between sciences, philosophy and engineering. New historical and epistemological insights. Homage to Gottfried W. Leibniz 1646-1716

ISBN

978-1-84890-227-5

Počet stran výsledku

28

Strana od-do

93-120

Počet stran knihy

434

Název nakladatele

College Publications

Místo vydání

London

Kód UT WoS kapitoly

—