De Risi, Vincenzo (Author)
This book offers a general introduction to the geometrical studies of Gottfried Wilhelm Leibniz (1646-1716) and his mathematical epistemology. In particular, it focuses on his theory of parallel lines and his attempts to prove the famous Parallel Postulate. Furthermore it explains the role that Leibniz’s work played in the development of non-Euclidean geometry. The first part is an overview of his epistemology of geometry and a few of his geometrical findings, which puts them in the context of the seventeenth-century studies on the foundations of geometry. It also provides a detailed mathematical and philosophical commentary on his writings on the theory of parallels, and discusses how they were received in the eighteenth century as well as their relevance for the non-Euclidean revolution in mathematics. The second part offers a collection of Leibniz’s essays on the theory of parallels and an English translation of them. While a few of these papers have already been published (in Latin) in the standard Leibniz editions, most of them are transcribed from Leibniz’s manuscripts written in Hannover, and published here for the first time. The book provides new material on the history of non-Euclidean geometry, stressing the previously neglected role of Leibniz in these developments.This volume will be of interest to historians in mathematics, philosophy or logic, as well as mathematicians interested in non-Euclidean geometry.
...MoreReview Jesseph, Douglas Michael (2017) Review of "Leibniz on the Parallel Postulate and the Foundations of Geometry: The Unpublished Manuscripts". Isis: International Review Devoted to the History of Science and Its Cultural Influences (pp. 695-696).
Article
Sebastián Xambó Descamps;
(2018)
From Leibniz's characteristica geometrica to contemporary Geometric Algebra
(/isis/citation/CBB725109115/)
Article
M. Rosa Massa-Esteve;
(2017)
Mengoli's Mathematical Ideas in Leibniz's Excerpts
(/isis/citation/CBB736043920/)
Article
Debuiche, Valérie;
(2013)
Perspective in Leibniz's Invention of Characteristica Geometrica: The Problem of Desargues' Influence
(/isis/citation/CBB001213655/)
Book
Leibniz, G. W.;
(2004)
Quadrature Arithmétique du Cercle, de l'ellipse et de l'hyperbole et la Trigonométrie sans tables Trigonométriques qui en est le Corollaire
(/isis/citation/CBB000750904/)
Article
Parmentier, Marc;
(2001)
Démonstration et infiniment petits dans la Quadratura arithmetica de Leibniz
(/isis/citation/CBB000770921/)
Article
Blåsjö, Viktor;
(2012)
The Rectification of Quadratures as a Central Foundational Problem for the Early Leibnizian Calculus
(/isis/citation/CBB001251213/)
Book
Glimp, David;
Warren, Michelle R.;
(2004)
Arts of Calculation: Quantifying Thought in Early Modern Europe
(/isis/citation/CBB000771864/)
Book
De Risi, Vincenzo;
(2007)
Geometry and Monadology: Leibniz's Analysis Situs and Philosophy of Space
(/isis/citation/CBB000830164/)
Article
Arthur, Richard T. W.;
(2013)
Leibniz's Syncategorematic Infinitesimals
(/isis/citation/CBB001211764/)
Article
Lützen, Jesper;
(2014)
Seventeenth Century Arguments for the Impossibility of the Indefinite and the Definite Circle Quadrature
(/isis/citation/CBB001550679/)
Article
Giovanelli, Marco;
(2010)
Urbild und Abbild: Leibniz, Kant und Hausdorff über das Raumproblem
(/isis/citation/CBB001230056/)
Article
Andrea Del Centina;
(2020)
Pascal’s mystic hexagram, and a conjectural restoration of his lost treatise on conic sections
(/isis/citation/CBB200348751/)
Article
Timmermans, Benoît;
(2005)
La similitude des figures chez Leibniz: entre géométrie et rhétorique
(/isis/citation/CBB000670810/)
Article
Knobloch, Eberhard;
(2002)
Leibniz's Rigorous Foundation of Infinitesimal Geometry by Means of Riemannian Sums
(/isis/citation/CBB000300359/)
Chapter
Sutherland, Daniel;
(2010)
Philosophy, Geometry, and Logic in Leibniz, Wolff, and the Early Kant
(/isis/citation/CBB001033539/)
Article
Lærke, Mogens;
(2014)
Leibniz, the Encyclopedia, and the Natural Order of Thinking
(/isis/citation/CBB001201304/)
Chapter
Miguel, Bernardino Orio de;
(2008)
Some Hermetic Aspects of Leibniz's Mathematical Rationalism
(/isis/citation/CBB001023821/)
Article
Arthur, Richard T. W.;
(2013)
Leibniz's Theory of Space
(/isis/citation/CBB001320866/)
Article
Mayer, Uwe;
(2013)
Kein tummelplatz, darauff gelehrte leut Kugeln wechseln. Principles and Practice of Mencke's Editorship of the Acta eruditorum in the Light of Mathematical Controversies
(/isis/citation/CBB001552262/)
Book
Andersen, Kirsti;
(2007)
The Geometry of an Art: The History of the Mathematical Theory of Perspective from Alberti to Monge
(/isis/citation/CBB000850432/)
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