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

0484610 - FLÚ 2018 RIV GB eng M - Monography Chapter
Crippa, Davide
Leibniz and the Impossibility of Squaring the Circle.
The dialogue between sciences, philosophy and engineering. New historical and epistemological insights. Homage to Gottfried W. Leibniz 1646-1716. London: College Publications, 2017 - (Pisano, R.), s. 93-120. Dialogues and games of logic, 5. ISBN 978-1-84890-227-5
Institutional support: RVO:67985955
Keywords : Gregory * Huygens * Leibniz * impossibility * quadrature of the circle * infinite series
OECD category: Philosophy, History and Philosophy of science and technology

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.
Permanent Link: http://hdl.handle.net/11104/0279875