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E-grāmata: Leibniz on the Parallel Postulate and the Foundations of Geometry: The Unpublished Manuscripts

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Leibniz on the Parallel Postulate and the Foundations of Geometry: The Unpublished ManuscriptsPalielināt
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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.

1.Introduction.- 2.The Theory of Parallel Lines in the Age of Leibniz.- 3.Leibniz" Epistemology of Geometry and the Parallel Postulate.- 4.Leibniz" Attempts to prove the Parallel Postulate.- 5.Reception and Legacy.- Leibniz" Texts on Parallel Lines.- Bibliography.

Recenzijas

By bringing together all of the known relevant Leibnizian writings on the subject, De Risi has rendered a very valuable service to Leibniz scholars and historians of seventeenth-century mathematics. This volume is indispensable for anyone interested in the development of non-Euclidean geometry or the mathematical thought of Leibniz. (Douglas M. Jesseph, Isis, Vol. 108 (3), September, 2017)

1 Introduction
3(4)
2 The Theory of Parallel Lines in the Age of Leibniz
7(14)
2.1 From Antiquity to the Renaissance
7(4)
2.2 Jesuit and French Attempts in the Seventeenth Century
11(3)
2.3 Italian and British Attempts in the Seventeenth Century
14(7)
3 Leibniz' Epistemology of Geometry and the Parallel Postulate
21(36)
3.1 Proving Axioms
21(10)
3.2 Leibniz' Theory of Definition
31(9)
3.3 Geometry as the Science of Space
40(9)
3.4 Philosophy and the Parallel Postulate
49(8)
4 Leibniz' Attempts to Prove the Parallel Postulate
57(46)
4.1 Preliminary Definitions
57(8)
4.2 Leibniz' Youth and the Parisian Years (Texts 1--4)
65(5)
4.3 The First Studies on the Parallel Postulate: 1677--1689 (Texts 5--16)
70(10)
4.4 Leibniz' Studies in the 1690s (Texts 17--29 and 34)
80(11)
4.5 Leibniz' Late Studies (Texts 30--39)
91(12)
5 Reception and Legacy
103(22)
5.1 Toward a Geometry of Space in the Eighteenth Century
103(2)
5.2 Wolff, Kastner and the Early Reactions
105(4)
5.3 The Concept of Lage, Direction, and the Actual Infinite
109(6)
5.4 The Principle of Reason
115(10)
6 Leibniz' Texts on Parallel Lines
125(56)
6.1 From Characteristica geometrica. Reading Notes to Fabri's "Synopsis geometrica" (1673)
125(1)
6.2 From De secandis parallelis (1676)
125(2)
6.3 From Linea infinita & extensio interminata (January--April 1676)
127(2)
6.4 From Dissertationis de arithmetica circuit quadratura propositiones septem and Quadraturae circuli arithmetica pars prima (April--June 1676)
129(1)
6.5 From Leibniz' Marginal Notes to Barrow's Edition of Euclid (1676-1677)
129(1)
6.6 From Characteristica geometrica (January 1677)
129(1)
6.7 From Characteristica geometrica, Scheda 1 (1679)
129(2)
6.8 From Linea est via puncti ... (1679)
131(1)
6.9 Axioma 13 Euclidis ... (Around 1679)
131(2)
6.10 From De calculo algebraico et constructiones lineares optime conciliandis (January 1680)
133(2)
6.11 From Elementa nova matheseos universalis (Summer 1683)
135(2)
6.12 From Definitiones (1685)
137(2)
6.13 From Si linea recta moveatur (1685)
139(1)
6.14 From De curvis similibus et similiter positis et parallelis (1685)
139(2)
6.15 From Logica de notionibus. Annotata circa schedas Jungianas (1685)
141(2)
6.16 From Phoranomus (1689)
143(1)
6.17 From Demonstrationes Euclideas (Around 1690)
143(1)
6.18 Parallelae (1690)
143(2)
6.19 From Generalia de natura linearum (Acta eruditorum, September 1692)
145(1)
6.20 Rectae parallelae (around 1692)
145(2)
6.21 From Lineam specie datam describere (Around 1693)
147(1)
6.22 From Leibniz' Notes to Arnauld's Nouveaux elemens de geometrie (Around 1693)
147(6)
6.23 From Elementa geometriae generalia (Around 1694)
153(1)
6.24 From De novo usu centri gravitatis (Acta eruditorum, November 1695)
153(1)
6.25 From Expediendi Laboris causa... (Around 1695)
153(2)
6.26 From Duae rectae parallelae... (1695)
155(2)
6.27 Leibniz to Johann Bernoulli (January 29th/February 8th, 1697)
157(2)
6.28 From Specimen analyseos anagogicae (1698)
159(1)
6.29 From Justification du Calcul des infinitesimales par celuy de l'Algebre ordinaire (1702)
159(1)
6.30 From Attentius examinans ... (Around 1702)
159(2)
6.31 From Calculum situs (Around 1702)
161(4)
6.32 From Table de definitions (1702--1704)
165(1)
6.33 From Nouveaux Essais sur l'entendement humain, II, xxxi, § 3; and III, iii, § 18 (1703--1705)
165(2)
6.34 From De lineae super linea incessu (Acta eruditorum, January 1706), and Letter to Johann Bernoulli (July 15th, 1706)
167(1)
6.35 From Demonstratio omnimoda (1712)
167(2)
6.36 From In Euclidis πρωτα (1712)
169(10)
6.37 From Spatium absolutum (August--September 1714)
179(1)
6.38 From Rectam definio ... (1715)
179(1)
6.39 From Calculi situs fundamenta (1745)
179(2)
Bibliography 181(10)
Index of Names 191
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