Groundbreaking Scientific Experiments, Inventions, and Discoveries of the 18th Century

By Jonathan Shectman | Go to book overview

C

Calculus of Finite Differences and
Differential Equations

Brooke Taylor, Methodus Incrementorum, 1715

Leonhard Euler, Mechanica, 1736

Joseph-Louis Lagrange, Theory of Analytic Functions, 1797

The main ideas that underpin differential equations developed over a very long period of time. Indeed, they depended on calculus, which came about during the seventeenth century and matured in the eighteenth, after a very long history of finite differences. The ancient mathematician Archimedes (ca. 287–212 B.C.) greatly extended a way of determining areas of figures with curved boundaries, known as the method of exhaustion. Thousands of years later, mathematicians would rework this method into the mathematical field of calculus. Archimedes used it and similar methods to figure curved surface areas, like those of spheres and cones. In the seventh century, Indian and Arab mathematicians successfully used finite differences to calculate astronomical sinus tables.

Little further significant work was done in this area until the explosion of mathematical knowledge during the seventeenth century. In 1624, English mathematician Henry Briggs (1561–1630) used differential equations to calculate tables of logarithms. Briggs was first to introduce logarithms to base 10, and he began constructing a 14-base table of common logarithms. Later in the century, Dutch mathematician Adriaen Vlacq (1600–1667) finished Briggs's work. During this period, Blaise Pascal (1623–1662) undertook important work toward the understanding of infinite series in relation to the mathematics that would later become important to both differential and integral calculus. The prior revolutions in physics and astronomy led to the seventeenth-century birth of analytic geometry, number theory, probability theory and calculus.

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Groundbreaking Scientific Experiments, Inventions, and Discoveries of the 18th Century
Table of contents

Table of contents

  • Recent Titles in Groundbreaking Scientific Experiments, Inventions and Discoveries through the Ages ii
  • Groundbreaking Scientific Experiments, Inventions and Discoveries of the 18th Century iii
  • Contents vii
  • Alphabetical List of Entries xi
  • Series Foreword xiii
  • Acknowledgments xvii
  • Introduction xix
  • Timeline of Important Events xxvii
  • Experiments, Inventions and Discoveries 1
  • A 3
  • B 16
  • C 31
  • D 72
  • E 80
  • F 92
  • H 105
  • I 119
  • L 124
  • M 133
  • N 161
  • O 170
  • P 180
  • R 211
  • S 216
  • T 247
  • U 256
  • V 261
  • W 265
  • Appendix: Entries Listed by Scientific Field 281
  • Glossary of Technical Terms 283
  • Bibliography 303
  • Index 311
  • About the Author 319
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