Mahoney, Michael Sean 　著

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Preface (1994) ix Introduction xi Acknowledgments xvii I. ThePersonal Touch 1 1. Mathematics in 1620 2. Fermat's Life and Career inParlement 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. TheRoyal Road 72 1. Introduction 2. Fermat's Analytic Geometry, the Ad locospianos et solidos isagoge 3. The Origins of the Isagoge: Apollonius' PlaneLoci and Conics 4. Extensions of the System of the isagoge: The Isagoge adlocos ad superficiern 5. Uses of the System of the Isagoge: Graphic Solutionand 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. OfDubious 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 TowardQuadrature and Rectification V. Archimedes and The Theory of Equations 2141. Introduction 2. From Spirals to Conoids 3. The Method of Centers ofGravity 4. The Treatise on Quadrature (ca. 1658) 5. The Treatise onRectification (1660) 6. Fermat and the Calculus VI. Between Traditions 2831. Introduction 2. Numbers, Perfect and Not So Perfect 3. Triangles andSquares 4. Reclaiming the Patrimony: The Challenges of 1657 5. One FinalAttempt: The "Relation" to Carcavi (1659) and the Method of Infinite Descent6. Infinite Descent and the "Last Theorem" Epilogue: Fermat in Retrospect361 Appendix I: Sidelights on A Mathematical Career 368 1. Mechanics 2.Optics 3. Probability Appendix II: Bibliographical Essay and ChronologicalConspectus of Fermat's Works 411 Index 425