Descartes's Mathematical Thought

Descartes's Mathematical Thought

Covering both the history of mathematics and of philosophy, Descartes's Mathematical Thought reconstructs the intellectual career of Descartes most comprehensively and originally in a globalperspective including the history of early modern China and Japan. Especially, it shows what the concept of "mathesis universalis" meant before and during the period of Descartes and how it influenced the young Descartes. In fact, it was the most fundamental mathematical discipline during the seventeenth century, and for Descartes a key notion which may have led to his novel mathematics of algebraic analysis.

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Inhaltsangabe

Preface. List of Abbreviations and a Note on the Quotation and Translation.
Introduction. René 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 Flèche. 2. The Curriculum at La Flèche. 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 Géométrieof 1637. 1. The Pappus Problem. 2. The Composition of the Géométrie. 3. Descartes's Place in the Formative Period of the Modern Analytic Tradition. 4. Beyond Cartesian Mathematics. Interim Consideration. Descartes and the Beginnings of Mathematicism 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 (Averroës), 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: `MathesisUniversalis' 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.