1、ISAAC NEWTONTHE PRINCIPIAMathematical Principles of Natural PhilosophyA New Translationby I. Bernard Cohen and Anne Whitmanassisted by Julia BudenzPreceded byA GUIDE TO NEWTONS PRINCIPIAby I. Bernard CohenUNIVERSITY OF CALIFORNIA PRESSBerkeley Los Angeles LondonTHE PRINCIPIAThe publication of this w
2、orf has been made possible in part by a grant from theNational Endowment for the Humanities, an independent federal agency. Thepublisher also gratefully acknowledges the generous contribution to this booprovided by the General Endowment Fund of the Associates of the Universityof California Press.Por
3、trait of Isaac Newton at about the age of sixty, a drawing presentedby Newton to David Gregory. For details see the following page.Portrait of Isaac Newton at about the age of sixty, presented by Newton to David Gregory(16611708). This small oval drawing (roughly 33/4 in. from top to bottom and 31A
4、in. fromleft to right) is closely related to the large oval portrait in oils made by Kneller in 1702, whichis considered to be the second authentic portrait made of Newton. The kinship between thisdrawing and the oil painting can be seen in the pose, the expression, and such unmistakabledetails as t
5、he slight cast in the left eye and the button on the shirt. Newton is shown in boththis drawing and the painting of 1702 in his academic robe and wearing a luxurious wig,whereas in the previous portrait by Kneller (now in the National Portrait Gallery in London),painted in 1689, two years after the
6、publication of the Principia, Newton is similarly attiredbut is shown with his own shoulder-length hair.This drawing was almost certainly made after the painting, since Knellers preliminarydrawings for his paintings are usually larger than this one and tend to concentrate on theface rather than on t
7、he details of the attire of the subject. The fact that this drawing showsevery detail of the finished oil painting is thus evidence that it was copied from the finishedportrait. Since Gregory died in 1708, the drawing can readily be dated to between 1702 and1708. In those days miniature portraits we
8、re commonly used in the way that we today woulduse portrait photographs. The small size of the drawing indicates that it was not a copy madein preparation for an engraved portrait but was rather made to be used by Newton as a gift.The drawing captures Knellers powerful representation of Newton, show
9、ing him as aperson with a forceful personality, poised to conquer new worlds in his recently gained positionof power in London. This high level of artistic representation and the quality of the drawingindicate that the artist responsible for it was a person of real talent and skill.The drawing is mo
10、unted in a frame, on the back of which there is a longhand notereading: “This original drawing of Sir Isaac Newton, belonged formerly to Professor Gregoryof Oxford; by him it was bequeathed to his youngest son (Sir Isaacs godson) who was laterSecretary of Sion College; March 8th 1870.“David Gregory
11、first made contact with Newton in the early 1690s, and although theirrelations got off to a bad start, Newton did recommend Gregory for the Savilian Professorshipof Astronomy at Oxford, a post which he occupied until his death in 1708. As will be evident toreaders of the Guide, Gregory is one of our
12、 chief sources of information concerning Newtonsintellectual activities during the 1690s and the early years of the eighteenth century, the periodwhen Newton was engaged in revising and planning a reconstruction of his Principia. Gregoryrecorded many conversations with Newton in which Newton discuss
13、ed his proposed revisionsof the Principia and other projects and revealed some of his most intimate and fundamentalthoughts about science, religion, and philosophy. So far as is known, the note on the back ofthe portrait is the only record that Newton stood godfather to Gregorys youngest son.ISAAC N
14、EWTONTHE PRINCIPIAMathematical Principles of Natural PhilosophyA New Translationby I. Bernard Cohen and Anne Whitmanassisted by Julia BudenzPreceded byA GUIDE TO NEWTONS PRINCIPIAby I. Bernard CohenUNIVERSITY OF CALIFORNIA PRESSBerkeley Los Angeles LondonUniversity of California PressBerkeley and Lo
15、s Angeles, CaliforniaUniversity of California PressLondon, EnglandCopyright 1999 by The Regents of the University of CaliforniaLibrary of Congress Cataloging-in-Publication DataNewton, Isaac, Sir, 1642-1727.Principia. EnglishThe Principia : mathematical principles of natural philosophy /Isaac Newton
16、 ; a new translation by I. Bernard Cohen and Anne Whitmanassisted by Julia Budenz ; preceded by a guide to Newtons Principiaby I. Bernard Cohen,p. cm.Includes bibliographical references and index.ISBN 978-0-520-08816-0 (alk. paper).ISBN 978-0-520-08817-7 (alk. paper)1. Newton, Isaac, Sir, 1642-1727.
17、 Principia. 2. MechanicsEarlyworks to 1800. 3. Celestial mechanicsEarly works to 1800.I. Cohen, I. Bernard, 1914- . II. Whitman, Anne Miller,1937-1984. III. Title.QA803.N413 1999531dc21 99-10278CIPPrinted in the United States of America1314 13 12 11 10 9The paper used in this publication meets the m
18、inimum requirements ofANSI/NISO Z39.48-1992 (R 1997) (Permanence of Paper). This translation isdedicated toD. T. WHITESIDEwith respect and affectionThis page intentionally left blank ContentsPreface xiA GUIDE TO NEWTONS PRINCIPIA 1Contents of the Guide 3Abbreviations 9CHAPTER ONE: A Brief History of
19、 the Principia 11CHAPTER TWO: Translating the Principia 26CHAPTER THREE: Some General Aspects of the Principia 43CHAPTER FOUR: Some Fundamental Concepts of the Principia 85CHAPTER FIVE: Axioms, or the Laws of Motion 109CHAPTER six: The Structure of Book 1 128CHAPTER SEVEN: The Structure of Book 2 16
20、1CHAPTER EIGHT: The Structure of Book 3 195CHAPTER NINE: The Concluding General Scholium 274CHAPTER TEN: How to Read the Principia 293CHAPTER ELEVEN: Conclusion 369THE PRINCIPIA (Mathematical Principles of Natural Philosophy) 371Halleys Ode to Newton 379Newtons Preface to the First Edition 381Newton
21、s Preface to the Second Edition 384Cotess Preface to the Second Edition 385Newtons Preface to the Third Edition 400Definitions 403Axioms, or the Laws of Motion 416BOOK 1: THE MOTION OF BODIES 431BOOK 2: THE MOTION OF BODIES 631BOOK 3: THE SYSTEM OF THE WORLD 791General Scholium 939Index 947This page
22、 intentionally left blank PrefaceALTHOUGH NEWTONs PRINCIPIA has been translated into many languages, thelast complete translation into English (indeed, the only such complete translation)was produced by Andrew Motte and published in London more than two and ahalf centuries ago. This translation was
23、printed again and again in the nineteenthcentury and in the 1930s was modernized and revised as a result of the effortsof Florian Cajori. This latter version, with its partial modernization and partialrevision, has become the standard English text of the Principia.Mottes version is often almost as o
24、paque to the modern reader as NewtonsLatin original, since Motte used such older and unfamiliar expressions as “sub-sesquialterate“ ratio. Additionally, there are statements in which the terms are nolonger immediately comprehensible today, such as book 3, prop. 8, corol. 3, inwhich Motte writes that
25、 “the densities of dissimilar spheres are as those weightsapplied to the diameters of the spheres,“ a statement unaltered in the Motte-Cajoriversion. Of course, a little thought reveals that Newton was writing about thedensities of nonhomogeneous spheres and was concluding with a reference to thewei
26、ghts divided by the diameters. The Motte-Cajori version, as explained in 2.3of the Guide to the present translation, is also not satisfactory because it too isfrequently difficult to read and, what is more important, does not always presentan authentic rendition of Newtons original. The discovery of
27、 certain extraordinaryexamples in which scholars have been misled in this regard was a chief factor inour decision to produce the present translation.When we completed our Latin edition, somewhat awed by the prospect ofundertaking a wholly new translation, we thought of producing a new edition ofMot
28、tes English version, with notes that either would give the reader a modernequivalent of difficult passages in Mottes English prose or would contain someaids to help the reader with certain archaic mathematical expressions. That is,since Mottes text had been a chief means of disseminating Newtons sci
29、ence forover two centuries, we considered treating it as an important historical documentXIXii PREFACEin its own right. Such a plan was announced in our Latin edition, and we evenprepared a special interleaved copy of the facsimile of the 1729 edition to serve asour working text.*After the Latin edi
30、tion appeared, however, many colleagues and some review-ers of that edition insisted that it was now our obligation to produce a completelynew translation of the Principia, rather than confine our attentions to Mottes olderpioneering work. We were at first reluctant to accept this assignment, not on
31、lybecause of the difficulty and enormous labor involved, but also because of ourawareness that we ourselves would thereby become responsible for interpretationsof Newtons thought for a long period of time.Goaded by our colleagues and friendly critics, Anne Whitman and I finallyagreed to produce a wh
32、olly new version of the Principia. We were fortunate in ob-taining a grant from the National Science Foundation to support our efforts. Manyscholars offered good advice, chief among them our good friends D. T. Whitesideand R. S. Westfall. In particular, Whiteside stressed for us that we should payno
33、 attention to any existing translation, not even consulting any other version onoccasions when we might be puzzled, until after our own assignment had beenfully completed. Anyone who has had to translate a technical text will appreciatethe importance of this advice, since it is all too easy to be in
34、fluenced by othertranslations, even to the extent of unconsciously repeating their errors. Accord-ingly, during the first two or three rounds of translation and revision, we recordedpuzzling or doubtful passages, and passages for which we hoped to produce afinal version that would be less awkward th
35、an our preliminary efforts, reservingfor some later time a possible comparison of our version with others. It should benoted that in the final two rounds of our revision, while checking some difficultpassages and comparing some of our renditions with others, the most useful worksfor such purpose wer
36、e Whitesides own translation of an early draft of what corre-sponds to most of book 1 of the Principia and the French translation made in the*An Index Verborum of the Latin edition of the Principia has been produced by Anne Whitmanand I. Bernard Cohen in association with Owen Gingerich and Barbara W
37、elther. This index includes thecomplete text of the third edition (1726) and also the variant readings as given in the Latin edition of thePrincipia (edited by Alexandre Koyre, I. Bernard Cohen, and Anne Whitman), published in 1972 by theHarvard University Press and the Cambridge University Press. T
38、hus the Index includes the complete textof the three authorized Latin editions (1687, 1713, 1726) as well as the MS annotations in both Newtons“annotated“ and “interleaved“ personal copies of the first and second editions. The Index is on depositin the Burndy Library of the Dibner Institute (Cambrid
39、ge, Mass.), where it may be consulted. Microfilmcopies can be purchased.Very useful tools for scholars and students are the planned Octavo editions of the first and thirdLatin editions of Newtons Principia; the latter will include this English translation. The high-resolutionfacsimiles on CD-ROM all
40、ow readers to view the original book and search the complete Latin texts andtranslation. For publication information, see the Octavo web site: .PREFACE xiiimid-eighteenth century by the marquise du Chatelet. On some difficult points, wealso profited from the exegeses and explanations in the Le Seur
41、and Jacquier Latinedition and the Krylov Russian edition. While neither Anne Whitman nor I couldread Russian, we did have the good fortune to have two former students, RichardKotz and Dennis Brezina, able and willing to translate a number of Krylovs notesfor us.The translation presented here is a re
42、ndition of the third and final edition ofNewtons Principia into present-day English with two major aims: to make New-tons text understandable to todays reader and yet to preserve Newtons form ofmathematical expression. We have thus resisted any temptation to rewrite Newtonstext by introducing equati
43、ons where he expressed himself in words. We have, how-ever, generally transmuted such expressions as “subsesquiplicate ratio“ into moresimply understandable terms. These matters are explained at length in 10.310.5of the Guide.After we had completed our translation and had checked it against NewtonsL
44、atin original several times, we compared our version with Mottes and foundmany of our phrases to be almost identical, except for Mottes antique mathematicalexpressions. This was especially the case in the mathematical portions of books 1and 2 and the early part of book 3. After all, there are not ma
45、ny ways of sayingthat a quantity A is proportional to another quantity B. Taking into account thatMottes phrasing represents the prose of Newtons own day (his translation waspublished in 1729) and that in various forms his rendition has been the standardfor the English-reading world for almost three
46、 centuries, we decided that we wouldmaintain some continuity with this tradition by making our phrasing conform tosome degree to Mottes. This comparison of texts did show, however, that Mottehad often taken liberties with Newtons text and had even expanded Newtonsexpressions by adding his own explan
47、ationsa result that confirmed the soundnessof the advice that we not look at Mottes translation until after we had completedour own text.This translation was undertaken in order to provide a readable text for stu-dents of Newtons thought who are unable to penetrate the barrier of NewtonsLatin. Follo
48、wing the advice of scholarly friends and counselors, we have not over-loaded the translation with extensive notes and comments of the sort intended forspecialists, rather allowing the text to speak for itself. Much of the kind of editorialcomment and explanation that would normally appear in such no
49、tes may be foundin the Guide. Similarly, information concerning certain important changes in thetext from edition to edition is given in the Guide, as well as in occasional textualnotes. The table of contents for the Guide, found on pages 37, will direct thereader to specific sections of the Principia, or even to particular propositions.xiiiXIV PREFACEThe Guide to the present translation is intended to be just thata kind ofextended road map through the sometimes labyrinthine pathways of the Principia.Some propositions
