The Origins of Infinitesimal Calculus

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Elsevier, 09/05/2014 - 312 páginas
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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.
 

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Índice

INTRODUCTION
1
CHAPTER 1 GREEK MATHEMATICS
11
CHAPTER 2 THE TRANSITION TO WESTERN EUROPE
60
CHAPTER 3 SOME CENTRE OF GRAVITY DETERMINATIONS IN THE LATER SIXTEENTH CENTURY
90
CHAPTER 4 INFINITESIMALS AND INDIVISIBLES IN THE EARLY SEVENTEENTH CENTURY
108
CHAPTER 5 FURTHER ADVANCES IN FRANCE AND ITALY
149
FRANCE ENGLAND AND THE LOW COUNTRIES
195
NEWTON AND LEIBNIZ
253
BIBLIOGRAPHY
291
INDEX
299
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