François De Gandt
Translated by Curtis Wilson

Translator's Introduction
Preface
Conventions and Abbreviations
Preamble 3
Ch. I The De motu of 1684 10
The Elements of Newton's Solution 10
Ch. II Aspects of Force before the Principia 58
The Diffusion of the Solar Virtue: Kepler and the Calculation of Forces 63
Weight and Acceleration: Force and Time in the Galilean Tradition 85
Gravity and Centrifugal Force: The Analysis of Effort in the Cartesian Tradition 117
Newton and Circular Motion before the Principia 139
Ch. III The Mathematical Methods 159
Indivisibles or Ultimate Ratios? 159
The Methods of Indivisibles 168
Motion in Geometry: The Kinematics of Curves and the Method of Fluxions 202
The Methods of the Principia (1): Ultimate Ratios and Finite Witnesses 221
The Methods of the Principia (2): The Inverse Problem and the Emergence of a New Style 244
Conclusions 265
Notes 273
Bibliography 287
Index 295

In this book François De Gandt introduces us to the reading of Newton's Principia in its own terms. The path of access that De Gandt proposes leads through the study of the geometrization of force. The result is a highly original meditation on the sources and meaning of Newton's magnum opus.
In Chapter I De Gandt presents a translation of and detailed commentary on an earlier and simpler version of what in 1687 became Book I of the Principia; here in clearer and starker outline than in the final version, the basic principles of Newton's dynamics show forth. Chapter II places this dynamics in the intellectual context of earlier efforts--the first seeds of celestial dynamics in Kepler, Galileo's theory of accelerated motion, and Huygens's quantification of centrifugal force--and evaluates Newton's debt to these thinkers. Chapter III is a study of the mathematical tools used by Newton and their intellectual antecedents in the works of Galileo, Torricelli, Barrow, and other seventeenth-century mathematicians. The conclusion discusses the new status of force and cause in the science that emerges from Newton's Principia.
Originally published in 1995.
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