The Cambridge Companion to Newton

By I. Bernard Cohen; George E. Smith | Go to book overview

15
Newton versus Leibniz: from
geometry to metaphysics
A. RUPERT HALL

In the course of a long life Isaac Newton made many enemies: Francis Linus (or Hall), Robert Hooke, John Flamsteed, Gottfried Wilhelm Leibniz, Johann I Bernoulli. Of these Leibniz was by far the greatest intellect and above all an outstanding mathematician and philosopher. Newton defeated them all and outlived them all except the last, twenty-five years his junior.

It was a sad chronology that brought two such inventive mathematicians as Newton and Leibniz to live in the same age; never were temperaments and intellectual characters more at odds. Almost the only feature that they had in common was Protestant piety, yet even in appealing to God the Creator they could not agree. In mathematics and its applications to celestial mechanics, and more particularly in the development of the calculus, though the methods promulgated by the two men were equivalent, they had been reached and were justified by wholly distinct arguments. Newton was by choice a geometer, Leibniz an algebraist; the difference does not of course imply that they could not tackle the same problems. J. E. Hofmann has written that Leibniz's “first major [mathematical] discovery in Paris [in 1673] originated in thoughts strongly influenced by considerations of logic and philosophy-and as so often with Leibniz, was not fully established but came as the fruit of a particular insight observed in simple examples and generalised by a stroke of genius. ” 1 At this stage Leibniz was working with numerical series, for example:

a particular case of his general theorem that even infinite series of numbers can be summed. Later of course Leibniz would extend

-431-

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The Cambridge Companion to Newton
Table of contents

Table of contents

  • Title Page *
  • Contents v
  • Figures vii
  • Contributors ix
  • Preface xiii
  • Introduction 1
  • Notes *
  • 1 - Newton's Philosophical Analysis of Space and Time 33
  • Notes *
  • 2 - Newton's Concepts of Force and Mass, with Notes on the Laws of Motion 57
  • Notes *
  • 3 - Curvature in Newton's Dynamics 85
  • Notes *
  • 4 - The Methodology of the Principia 138
  • Notes *
  • 5 - Newton's Argument for Universal Gravitation 174
  • Notes *
  • 6 - Newton and Celestial Mechanics 202
  • Notes *
  • 7 - Newton's Optics and Atomism 227
  • Notes *
  • 8 - Newton's Metaphysics 256
  • Notes *
  • 9 - Analysis and Synthesis in Newton's Mathematical Work 308
  • Notes *
  • 10 - Newton, Active Powers, and the Mechanical Philosophy 329
  • Notes *
  • 11 - The Background to Newton's Chymistry 358
  • Notes *
  • 12 - Newton's Alchemy 370
  • Notes *
  • 13 - Newton on Prophecy and the Apocalypse 387
  • Notes *
  • 14 - Newton and Eighteenth-Century Christianity 409
  • Notes *
  • 15 - Newton Versus Leibniz: from Geometry to Metaphysics 431
  • Notes *
  • 16 - Newton and the Leibniz-Clarke Correspondence 455
  • Notes *
  • Bibliography 465
  • Index 481
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