The Principia: The Authoritative Translation and Guide: Mathematical Principles of Natural Philosophy

Book Preface

ALTHOUGH NEWToN’s PRINCIPIA has been translated into many languages, the last complete translation into English (indeed, the only such complete translation) was produced by Andrew Motte and published in London more than two and a half centuries ago. This translation was printed again and again in the nineteenth century and in the 1930s was modernized and revised as a result of the efforts of Florian Cajori. This latter version, with its partial modernization and partial revision, has become the standard English text of the Principia.
Motte’s version is often almost as opaque to the modern reader as Newton’s Latin original, since Motte used such older and unfamiliar expressions as “sub­sesquialterate” ratio. Additionally, there are statements in which the terms are no longer immediately comprehensible today, such as book 3, prop. 8, corol. 3, in which Motte writes that “the densities of dissimilar spheres are as those weights applied to the diameters of the spheres,” a statement unaltered in the Motte-Cajori version. Of course, a little thought reveals that Newton was writing about the densities of nonhomogeneous spheres and was concluding with a reference to the weights divided by the diameters. The Motte-Cajori version, as explained in §2.3 of the Guide to the present translation, is also not satisfactory because it too is frequently difficult to read and, what is more important, does not always present an authentic rendition of Newton’s original. The discovery of certain extraordinary examples in which scholars have been misled in this regard was a chief factor in our decision to produce the present translation.

When we completed our Latin edition, somewhat awed by the prospect of undertaking a wholly new translation, we thought of producing a new edition of Motte’s English version, with notes that either would give the reader a modern equivalent of difficult passages in Motte’s English prose or would contain some aids to help the reader with certain archaic mathematical expressions. That is, since Motte’s text had been a chief means of disseminating Newton’s science for over two centuries, we considered treating it as an important historical document m its own right. Such a plan was announced in our Latin edition, and we even prepared a special interleaved copy of the facsimile of the 1729 edition to serve as our working text.*

After the Latin edition appeared, however, many colleagues and some review­ers of that edition insisted that it was now our obligation to produce a completely new translation of the Principia, rather than confine our attentions to Motte’s older pioneering work. We were at first reluctant to accept this assignment, not only because of the difficulty and enormous labor involved, but also because of our awareness that we ourselves would thereby become responsible for interpretations of Newton’s thought for a long period of time.

Goaded by our colleagues and friendly critics, Anne Whitman and I finally agreed to produce a wholly new version of the Principia. We were fortunate in ob­taining a grant from the National Science Foundation to support our efforts. Many scholars offered good advice, chief among them our good friends D. T. Whiteside and R. S. Westfall. In particular, Whiteside stressed for us that we should pay no attention to any existing translation, not even consulting any other version on occasions when we might be puzzled, until after our own assignment had been fully completed. Anyone who has had to translate a technical text will appreciate the importance of this advice, since it is all too easy to be influenced by other translations, even to the extent of unconsciously repeating their errors. Accord­ingly, during the first two or three rounds of translation and revision, we recorded puzzling or doubtful passages, and passages for which we hoped to produce a final version that would be less awkward than our preliminary efforts, reserving  for some later time a possible comparison of our version with others. It should be noted that in the final two rounds of our revision, while checking some difficult passages and comparing some of our renditions with others, the most useful works for such purpose were Whiteside’s own translation of an early draft of what corre­ sponds to most of book l 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 Whitman and I. Bernard Cohen in association with Owen Gingerich and Barbara Welther. This index includes the complete text of the third edition (1726) and also the variant readings as given in the Latin edition of the Principia (edited by Alexandre Koyre, I. Bernard Cohen, and Anne Whitman), published in 1972 by the Harvard University Press and the Cambridge University Press. Thus the Index includes the complete text of the three authorized Latin editions (1687, 1713, 1726) as well as the MS annotations in both Newton’s “annotated” and “interleaved” personal copies of the first and second editions. The Index is on deposit in the Burndy Library of the Dibner Institute (Cambridge, Mass.), where it may be consulted. Microfilm copies can be purchased.

Very useful tools for scholars and students are the planned Octavo editions of the first and third Latin editions of Newton’s Principia; the latter will include this English translation. The high-resolution facsimiles on CD-ROM allow readers to view the original book and search the complete Latin texts and translation. For publication information, see the Octavo web site: www.octavo.com. mid-eighteenth century by the marquise du Chatelet. On some difficult points, we also profited from the exegeses and explanations in the Le Seur and Jacquier Latin edition and the Krylov Russian edition. While neither Anne Whitman nor I could read Russian, we did have the good fortune to have two former students, Richard Kotz and Dennis Brezina, able and willing to translate a number of Krylov’s notes for us.
The translation presented here is a rendition of the third and final edition of Newton’s Principia into present-day English with two major aims: to make New­ton’s text understandable to today’s reader and yet to preserve Newton’s form of mathematical expression. We have thus resisted any temptation to rewrite Newton’s text by introducing equations where he expressed himself in words. We have, how­ever, generally transmuted such expressions as “subsesquiplicate ratio” into more simply understandable terms. These matters are explained at length in §§ 10.3-10.5 of the Guide.

After we had completed our translation and had checked it against Newton’s Latin original several times, we compared our version with Motte’s and found many of our phrases to be almost identical, except for Motte’s antique mathematical expressions. This was especially the case in the mathematical portions of books 1 and 2 and the early part of book 3. After all, there are not many ways of saying that a quantity A is proportional to another quantity B. Taking into account that Motte’s phrasing represents the prose of Newton’s own day (his translation was published in 1729) and that in various forms his rendition has been the standard for the English-reading world for almost three centuries, we decided that we would maintain some continuity with this tradition by making our phrasing conform to some degree to Motte’s. This comparison of texts did show, however, that Motte had often taken liberties with Newton’s text and had even expanded Newton’s expressions by adding his own explanations-a result that confirmed the soundness of the advice that we not look at Motte’s translation until after we had completed our own text.

This translation was undertaken in order to provide a readable text for stu­dents of Newton’s thought who are unable to penetrate the barrier of Newton’s Latin. Following the advice of scholarly friends and counselors, we have not over­loaded the translation with extensive notes and comments of the sort intended for specialists, rather allowing the text to speak for itself. Much of the kind of editorial comment and explanation that would normally appear in such notes may be found in the Guide. Similarly, information concerning certain important changes in the text from edition to edition is given in the Guide, as well as in occasional textual notes. The table of contents for the Guide, found on pages 3-7, will direct the reader to specific sections of the Principia, or even to particular propositions.

The Guide to the present translation is intended to be just that-a kind of extended road map through the sometimes labyrinthine pathways of the Principia. Some propositions, methods, and concepts are analyzed at length, and in some instances critical details of Newton’s argument are presented and some indica­tions are given of the alterations produced by Newton from one edition to the next. Sometimes reference is made to secondary works where particular topics are discussed, but no attempt has been made to indicate the vast range of scholarly information relating to this or that point. That is, I have tended to cite, in the text and in the footnote references, primarily those works that either have been of special importance for my understanding of some particular point or some sections of the Principia or that may be of help to the reader who wishes to gain a more extensive knowledge of some topic. As a result, I have not had occasion in the text to make public acknowledgment of all the works that have been important influences on my own thinking about the Principia and about the Newtonian prob­lems associated with that work. In this rubric I would include, among others, the important articles by J. E. McGuire, the extremely valuable monographs on many significant aspects of Newton’s science and philosophic background by Maurizio Mamiani (which have not been fully appreciated by the scholarly world because they are written in Italian), the two histories of mechanics by Rene Dugas and the antecedent documentary history by Leon Jouguet, the analysis of Newton’s con­cepts and methods by Pierre Duhem and Ernst Mach, and monographic studies by Michel Blay, G. Bathelemy, Pierre Costabel, and A. Rupert Hall, and by Frarn;:ois de Gandt.
I also fear that in the Guide I may not have sufficiently stressed how greatly my understanding of the Principia has profited from the researches of D. T. White­side and Curtis Wilson and from the earlier commentaries of David Gregory, of Thomas Le Seur and Fran?ois Jacquier, and of Alexis Clairaut. The reader will find, as I have done, that R. S. Westfall’s Never at Rest not only provides an admirable guide to the chronology of Newton’s life and the development of his thought in general, but also analyzes the whole range of Newton’s science and presents almost every aspect of the Principia in historical perspective.
All students of the Principia find a guiding beacon in D. T. Whiteside’s essays and his texts and commentaries in his edition of Newton’s Mathematical Papers, esp. vols. 6 and 8 (cited on p. 9 below). On Newton’s astronomy, the concise analysis by Curtis Wilson (cited on p. 10 below) has been of enormous value. Many of the texts quoted in the Guide have been translated into English. It did not seem necessary to mention this fact again and again.

From the very start of this endeavor, Anne Whitman and I were continuously aware of the awesome responsibility that was placed on our shoulders, having mind all too well the ways in which even scholars of the highest distinction have been misled by inaccuracies and real faults in the current twentieth-century English version. We recognized that no translator or editor could boast of having perfectly understood Newton’s text and of having found the proper meaning of every proof and construction. We have ever been aware that a translation of a work as difficult as Newton’s Principia will certainly contain some serious blunders or errors of interpretation. We were not so vain that we were always sure that we fully understood every level of Newton’s meaning. We took comfort in noting that even Halley, who probably read the original Principia as carefully as anyone could, did not always fully understand the mathematical significance of Newton’s text. We therefore, in close paraphrase of Newton’s own preface to the first edition, earnestly ask that everything be read with an open mind and that the defects in a subject so difficult may be not so much reprehended as kindly corrected and improved by the endeavors of our readers.