The mathematical career of Pierre de Fermat (1601-1665)

Machine derived contents note: Table of contents for The mathematical career of Pierre de Fermat (1601-1665)

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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

Library of Congress subject headings for this publication: Fermat, Pierre de, 1601-1665, Mathematicians France Biography