Mathematical Career of Pierre de Fermat, 1601-1665

Michael Sean Mahoney is Professor of History at Princeton University.

• Preface (1994) ix Introduction xi Acknowledgments xvii I. The Personal Touch 1 1. Mathematics in 1620 2. Fermat's Life and Career in Parlement 3. Motivation to Mathematics II. Nullum Non Problema Solvere: Viete's Analytic Program and Its Influence on Fermat 26 1. Algebra, Analysis, and the Analytic Art 2. Following the "Precepts of the Art" 3. Fermat's Style of Work and His Influence on His Contemporaries III. The Royal Road 72 1. Introduction 2. Fermat's Analytic Geometry, the Ad locos pianos et solidos isagoge 3. The Origins of the Isagoge: Apollonius' Plane Loci and Conics 4. Extensions of the System of the isagoge: The Isagoge ad locos ad superficiern 5. Uses of the System of the Isagoge: Graphic Solution and Classification of Equations IV. Fashioning One's Own Luck 143 1. Introduction 2. The Roots of an Equation and the Roots of a Method 3. Of Dubious Parentage: The Method of Tangents 4. Looking Under the Bed: Descartes vs. Fermat, 1637-38 5. The Aftermath: Proceeding By Touch 6. Learning New Tricks: The Letter to Brulart 7. Fine Tuning: The Path Toward Quadrature and Rectification V. Archimedes and The Theory of Equations 214 1. Introduction 2. From Spirals to Conoids 3. The Method of Centers of Gravity 4. The Treatise on Quadrature (ca. 1658) 5. The Treatise on Rectification (1660) 6. Fermat and the Calculus VI. Between Traditions 283 1. Introduction 2. Numbers, Perfect and Not So Perfect 3. Triangles and Squares 4. Reclaiming the Patrimony: The Challenges of 1657 5. One Final Attempt: The "Relation" to Carcavi (1659) and the Method of Infinite Descent 6. Infinite Descent and the "Last Theorem" Epilogue: Fermat in Retrospect 361 Appendix I: Sidelights on A Mathematical Career 368 1. Mechanics 2. Optics 3. Probability Appendix II: Bibliographical Essay and Chronological Conspectus of Fermat's Works 411 Index 425

"Mahoney's sensitive handling of the material, his sharp appreciation of conceptual and notational subtleties, and his willingness to detail or reconstruct proofs and procedures, now make possible an appreciation of the real power and variety of Fermat's invention."--Alan Gabbey, British Journal for the History of Science "A remarkably satisfying and cogent analysis."--Carl B. Boyer, Science