The Mathematical Career of Pierre de Fermat

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