Descartes's mathematical thought

Abstract

Preface. List of Abbreviations and a Note on the Quotation and Translation. Introduction. Rene Descartes and Modern European Mathematics. 1: The Formation of Descartes's Mathematical Thought. 1. Descartes and Jesuit Mathematical Education. 1. Descartes and the Jesuit College of La Fleche. 2. The Curriculum at La Fleche. 3. Mathematical Studies in the Ratio Studiorum 4. Motives for the Teaching of Mathematics in the Jesuit Colleges. 2: The Mathematical Thought of Christoph Clavius. 1. Descartes and Clavius. 2. The Philosophy of Mathematics of Clavius. 3. Pappus in the Works of Clavius. 4. Diophantus in the Works of Clavius. 5. Descartes's Mathematical Background before the Encounter with Beeckman. 3: The First Attempt at Reforming Mathematics. 1. 'An Entirely New Science': The Idea for the Unification of Arithmetic and Geometry. 2. The Mathematics in the Cogitationes privatae. 3. The De Solidorum Elementis. 4. Descartes's Mathematical and Philosophical Dream of 1619. 4: The Mathematical Background of the Regulae Ad Directionem Ingenii. 1. The Old Algebra: The First Fruit of 'An Entirely New Science'. 2. The Mathematics in the Regulae ad Directionem Ingenii. 3. Mathesis Universalis. 5. The Geometrieof 1637. 1. The Pappus Problem. 2. The Composition of the Geometrie. 3. Descartes's Place in the Formative Period of the Modern Analytic Tradition. 4. Beyond Cartesian Mathematics. Interim Consideration. Descartes and the Beginnings ofMathematicism in Modern Thought. II: The Concept of 'Mathesis Universalis' in Historical Perspective. 6. 'Universal Mathematics' In Aristotle. 1. Aristotle's Metaphysics and Posterior Analytics. 2. Greek Commentators: Alexander of Aphrodisias and Asclepius of Tralles. 3. Medieval Commentators: Ibn Rushd (Averroes), Albertus Magnus, Thomas Aquinas, and the Scotist Antonius Andreae. 4. Renaissance Commentators: Agostino Nifo and Pedro da Fonseca. 5. The Status of Mathematics in the Aristotelian Scheme of Learning. 7: 'Mathesis Universalis' in the Sixteenth Century. 1. Proclus Diadochus and Francesco Barozzi. 2. Adriaan van Roomen. 8: 'Mathesis Universalis' in the Seventeenth Century. 1. Reviewing Descartes's Concept of 'Mathesis Universalis' from His Philosophy of Mathematics. 2. The Leibnizian Synthesis. Conclusion: Descartes and the Modern Scheme of Learning. Bibliography. Indices. Name Index. Subject Index. Treatise Index.