Force and Geometry in Newton's Principia

Force and Geometry in Newton's Principia

Copyright Date: 1995
Pages: 312
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  • Book Info
    Force and Geometry in Newton's Principia
    Book Description:

    In this book François De Gandt introduces us to the reading of Newton'sPrincipiain 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'smagnum 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 thePrincipia; 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'sPrincipia.

    Originally published in 1995.

    ThePrinceton Legacy Libraryuses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These paperback editions preserve the original texts of these important books while presenting them in durable paperback editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

    eISBN: 978-1-4008-6412-6
    Subjects: History of Science & Technology

Table of Contents

  1. Front Matter
    (pp. i-iv)
  2. Table of Contents
    (pp. v-vi)
    (pp. vii-viii)

    It is with much pleasure and satisfaction that I here present to American and British readers an English translation of Francis De Gandt'sForce et Giometrie: Ies "Principia "de Newton dans Ie XVIIeme siecle. Professor De Gandt proposes this book as an introduction to the reading of Newton'sPrincipia, but the journey of exploration in which he engages us takes unexpected turns and leads to unexpected riches. The method throughout is that ofexplication de texte,long a specialty of French scholars; it combines close reading of texts with historically informed commentary. In applying this method to selected writings both...

    (pp. ix-xii)
    (pp. xiii-2)
    (pp. 3-9)

    This account could begin in the manner of a typical British detective story: an architect, an inventor, and an astronomer had become fascinated with a certain enigma whose complete solution seemed to hover ever within their grasp, but always escaped them.

    The architect, Christopher Wren, and the inventor, Robert Hooke, saw one another frequently. They had collaborated in the vast enterprise of reconstructing London after the great fire of 1666, and they also met in various clubs with colleagues they had known in their Oxford days. In 1662 one of these clubs had assumed a more official form—it became...

  7. CHAPTER I THE DE MOTU of 1684
    (pp. 10-57)

    I turn now to the demonstration actually given by Newton toward the end of 1684 in the little treatise that so delighted Dr Halley

    How to pass beyond the vague idea of an attractive force to its geometrical expression—to its evaluation along a trajectory? Newton saw in the mathematical elaboration of this problem the difference that separated him from Hooke It is one thing to propose a conjecture concerning the variation of force, and quite another to enter into the detail of the geometrical determination, the observations, and the calculations Hooke had spoken and written as if all of...

    (pp. 58-158)

    A collection of exercises that had been designed for the use of students will give an idea of what was commonly understood by force at the time of the De motu Below is an example taken almost at random from one of these collections—it leaves the author’s identity to be guessed

    Problem 7Being given the forces [viribus] of several agents, to determine the time in which they will together produce a given effect d

    Let us suppose that the forces of the agents A, B, C are such that they produce respectively the effectsa,b,c, in the...

    (pp. 159-264)

    In his letters to Hooke of 1679, Newton gave evidence, as we have seen, of a new capacity— that of analyzing trajectories under the influence of a force. The context was that of a fiction which generalized terrestrial gravity. The following year, in his discussion with Flamsteed, Newton exploited the same resource for the study of actual celestial trajectories. He compared heavy bodies projected round the earth with comets in their passage near the sun and implied that planetary motion could be treated similarly. But he did not go beyond rough qualitative determinations concerning the respective situations of the orbit...

    (pp. 265-272)

    “Direct problem,” “inverse problem”: Newton proposed demonstrative means for passing from motions to forces and—in a more uncertain and imperfect way—from forces back to motions. Only the mathematical aspect of these operations has been considered, not the physical significance and scope they have in establishing “the constitution of the System of the World” in Book III.

    The “direct” passage makes it possible to “infer” the unique force that moves the planets, the satellites, projectiles, and so forth. To infer is also “to gather together,” according to the connotation of the Latincolligere—to unify the diversity. Here, briefly,...

  11. NOTES
    (pp. 273-286)
    (pp. 287-294)
  13. INDEX
    (pp. 295-296)
  14. Back Matter
    (pp. 297-297)