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Foreword; Contents; I Leibniz on the Parallel Postulateand the Foundations of Geometry; 1 Introduction; 2 The Theory of Parallel Lines in the Age of Leibniz; 2.1 From Antiquity to the Renaissance.; 2.2 Jesuit and French Attempts in the Seventeenth Century.; 2.3 Italian and British Attempts in the Seventeenth Century.; 3 Leibniz' Epistemology of Geometry and the Parallel Postulate; 3.1 Proving Axioms.; 3.2 Leibniz' Theory of Definition.; 3.3 Geometry as the Science of Space.; 3.4 Philosophy and the Parallel Postulate.; 4 Leibniz' Attempts to Prove the Parallel Postulate.
4.1 Preliminary Definitions. 4.2 Leibniz' Youth and the Parisian Years (Texts 1-4).; 4.3 The First Studies on the Parallel Postulate: 1677-1689 (Texts 5-16).; 4.4 Leibniz' Studies in the 1690s (Texts 17-29 and 34).; 4.5 Leibniz' Late Studies (Texts 30-39).; 5 Reception and Legacy; 5.1 Toward a Geometry of Space in the Eighteenth Century.; 5.2 Wolff, Kästner and the Early Reactions.; 5.3 The Concept of Lage, Direction, and the Actual Infinite.; 5.4 The Principle of Reason.; II Leibniz' Texts on Parallel Lines; 6 Leibniz' Texts on Parallel Lines.
6.1 From Characteristica geometrica. Reading Notes to Fabri's "Synopsis geometrica" (1673)6.2 From De secandis parallelis (1676).; 6.3 From Linea infinita & extensio interminata (January-April 1676); 6.4 From Dissertationis de arithmetica circuli quadratura propositiones septem and Quadraturae circuli arithmetica pars prima (April-June 1676); 6.5 From Leibniz' Marginal Notes to Barrow's Edition of Euclid (1676-1677); 6.6 From Characteristica geometrica (January 1677); 6.7 From Characteristica geometrica, Scheda 1 (1679); 6.8 From Linea est via puncti ... (1679).
6.9 Axioma 13 Euclidis ... (Around 1679)6.10 From De calculo algebraico et constructiones lineares optime conciliandis (January 1680); 6.11 From Elementa nova matheseos universalis (Summer 1683); 6.12 From Definitiones (1685); 6.13 From Si linea recta moveatur ... (1685); 6.14 From De curvis similibus et similiter positis et parallelis (1685); 6.15 From Logica de notionibus. Annotata circa schedas Jungianas (1685); 6.16 From Phoranomus (1689); 6.17 From Demonstrationes Euclideas (Around 1690); 6.18 Parallelae (1690); 6.19 From Generalia de natura linearum (Acta eruditorum, September 1692).
6.20 Rectae parallelae (around 1692)6.21 From Lineam specie datam describere (Around 1693); 6.22 From Leibniz' Notes to Arnauld's Nouveaux elemens de geometrie (Around 1693); 6.23 From Elementa geometriae generalia (Around 1694); 6.24 From De novo usu centri gravitatis (Acta eruditorum, November 1695); 6.25 From Expediendi Laboris causa ... (Around 1695); 6.26 From Duae rectae parallelae ... (1695); 6.27 Leibniz to Johann Bernoulli (January 29th/February 8th, 1697); 6.28 From Specimen analyseos anagogicae (1698).
4.1 Preliminary Definitions. 4.2 Leibniz' Youth and the Parisian Years (Texts 1-4).; 4.3 The First Studies on the Parallel Postulate: 1677-1689 (Texts 5-16).; 4.4 Leibniz' Studies in the 1690s (Texts 17-29 and 34).; 4.5 Leibniz' Late Studies (Texts 30-39).; 5 Reception and Legacy; 5.1 Toward a Geometry of Space in the Eighteenth Century.; 5.2 Wolff, Kästner and the Early Reactions.; 5.3 The Concept of Lage, Direction, and the Actual Infinite.; 5.4 The Principle of Reason.; II Leibniz' Texts on Parallel Lines; 6 Leibniz' Texts on Parallel Lines.
6.1 From Characteristica geometrica. Reading Notes to Fabri's "Synopsis geometrica" (1673)6.2 From De secandis parallelis (1676).; 6.3 From Linea infinita & extensio interminata (January-April 1676); 6.4 From Dissertationis de arithmetica circuli quadratura propositiones septem and Quadraturae circuli arithmetica pars prima (April-June 1676); 6.5 From Leibniz' Marginal Notes to Barrow's Edition of Euclid (1676-1677); 6.6 From Characteristica geometrica (January 1677); 6.7 From Characteristica geometrica, Scheda 1 (1679); 6.8 From Linea est via puncti ... (1679).
6.9 Axioma 13 Euclidis ... (Around 1679)6.10 From De calculo algebraico et constructiones lineares optime conciliandis (January 1680); 6.11 From Elementa nova matheseos universalis (Summer 1683); 6.12 From Definitiones (1685); 6.13 From Si linea recta moveatur ... (1685); 6.14 From De curvis similibus et similiter positis et parallelis (1685); 6.15 From Logica de notionibus. Annotata circa schedas Jungianas (1685); 6.16 From Phoranomus (1689); 6.17 From Demonstrationes Euclideas (Around 1690); 6.18 Parallelae (1690); 6.19 From Generalia de natura linearum (Acta eruditorum, September 1692).
6.20 Rectae parallelae (around 1692)6.21 From Lineam specie datam describere (Around 1693); 6.22 From Leibniz' Notes to Arnauld's Nouveaux elemens de geometrie (Around 1693); 6.23 From Elementa geometriae generalia (Around 1694); 6.24 From De novo usu centri gravitatis (Acta eruditorum, November 1695); 6.25 From Expediendi Laboris causa ... (Around 1695); 6.26 From Duae rectae parallelae ... (1695); 6.27 Leibniz to Johann Bernoulli (January 29th/February 8th, 1697); 6.28 From Specimen analyseos anagogicae (1698).