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The Origins of Infinitesimal Calculus.

Author: Margaret E Baron
Publisher: Kent : Elsevier Science, 2014.
Edition/Format:   eBook : Document : English
Summary:
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  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Baron, Margaret E.
Origins of Infinitesimal Calculus.
Kent : Elsevier Science, ©2014
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Margaret E Baron
ISBN: 9781483280929 1483280926
OCLC Number: 1041737249
Description: 1 online resource (313 pages)
Contents: Front Cover; The Origins of the Infinitesimal Calculus; Copyright Page; Table of Contents; 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 ofproportion 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 EUROPE2.0 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 Luca Valerio (1552-1618). CHAPTER 4. INFINITESIMALS AND INDIVISIBLES IN THE EARLY SEVENTEENTH CENTURY4.1 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 COUNTRIES6.0 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.

Abstract:

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 i.

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