The Origins of Infinitesimal Calculus

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.

Preface

Introduction

Chapter 1. Greek Mathematics

1.0 Introduction

1.1 The Influence of Greek Mathematics in the Seventeenth Century

1.2 A Brief Chronology of Greek Mathematics

1.3 Early Greek Mathematics and the Physical World

1.4 The Axiomatisation of Greek Mathematics

1.5 The Theory of Proportion and Means

1.6 The Squaring of the Circle

1.7 The Method of Exhaustion

1.8 The Discovery Method of Archimedes

1.9 Curves, Normals, Tangents and Curvature

Chapter 2. The Transition to Western Europe

2.0 Introduction

2.1 On Hindu Mathematics

2.2 The Arabs

2.3 The Influence of Aristotle

2.4 The Continuum, Indivisibles and Infinitesimals

2.5 The Growth of Kinematics in the West

2.6 The Latitude of Forms

2.7 The Function Concept in the Fourteenth and Fifteenth Centuries

2.8 Conclusion

Chapter 3. Some Centre of Gravity Determinations in the Later Sixteenth Century

3.0 Introduction

3.1 Francesco Maurolico (1494-1575)

3.2 Federigo Commandino (1509-1575)

3.3 Simon Stevin (1548-1620)

3.4 LucaValerio (1552-1618)

Chapter 4. Infinitesimals and Indivisibles in the Early Seventeenth Century

4.1 Johann Kepler (1571-1630)

4.2 Indivisibles in Italy

4.3 Bonaventura Cavalieri (1598-1647)

4.4 Grégoire de Saint-Vincent (1584-1667)

Chapter 5. Further Advances in France and Italy

5.0 Introduction

5.1 The Arithmetisation of Integration Methods

5.2 First Investigations of the Cycloid

5.3 Another Integration Method

5.4 The Concept of Tangent

5.5 The Composition of Motions

5.6 The Link Between Differential and Integral Processes

5.7 Evangelista Torricelli : Tangent and Quadrature

Chapter 6. Consolidation of Gains: France, England and the Low Countries

6.0 Introduction

6.1 Blaise Pascal (1623-1662)

6.2 Infinitesimal Methods in England

6.3 Infinitesimal Methods in the Low Countries

6.4 The Rectification of Arcs

6.5 James Gregory (1638-1675)

6.6 Isaac Barrow (1630-1677)

Chapter 7. Epilogue: Newton and Leibniz

7.0 Introduction

7.1 Isaac Newton (1642-1727)

7.2 Gottfried Wilhelm Leibniz (1646-1716)

Bibliography

Index