The Origins of Infinitesimal Calculus

Margaret E. Baron

• Publisher: Pergamon
• Year: 2014
• Print ISBN: 9780080125138
• eBook ISBN: 9781483280929
• Topic: Mathematics
• Subtopic: Calculus
• Index: Mathematics

The Origins of Infinitesimal Calculus focuses on the evolution, development, and applications of infinitesimal calculus. The publication first ponders on Greek mathematics, transition to Western Europe, and some center of gravity determinations in the later 16th century. Discussions focus on the growth of kinematics in the West, latitude of forms, influence of Aristotle, axiomatization of Greek mathematics, theory of proportion and means, method of exhaustion, discovery method of Archimedes, and curves, normals, tangents, and curvature. The manuscript then examines infinitesimals and indivisibles in the early 17th century and further advances in France and Italy. Topics include the link between differential and integral processes, concept of tangent, first investigations of the cycloid, and arithmetization of integration methods. The book reviews the infinitesimal methods in England and Low Countries and rectification of arcs. The publication is a vital source of information for historians, mathematicians, and researchers interested in infinitesimal calculus.

Table of contents

• Front Cover
• The Origins of the Infinitesimal Calculus
• Copyright Page
• Table of Contents
• PREFACE
• INTRODUCTION
• CHAPTER 1. GREEK MATHEMATICS
• CHAPTER 2. THE TRANSITION TO WESTERN EUROPE
• CHAPTER 3. SOME CENTRE OF GRAVITY DETERMINATIONS IN THE LATER SIXTEENTH CENTURY
• CHAPTER 4. INFINITESIMALS AND INDIVISIBLES IN THE EARLY SEVENTEENTH CENTURY
• CHAPTER 5. FURTHER ADVANCES IN FRANCE AND ITALY
• CHAPTER 6. CONSOLIDATION OF GAINS: FRANCE, ENGLAND AND THE LOW COUNTRIES
• CHAPTER 7. EPILOGUE: NEWTON AND LEIBNIZ
• BIBLIOGRAPHY
• INDEX