The Mathematical Career of Pierre de Fermat

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