Table Of ContentINTRODUCTION TO
NEWTON’S
‘P R I N G I P I A ’
I. BERNARD COHEN
CAM BRIDGE
AT TH E U N IV E R SIT Y PRESS
1971
Published by
The Syndics of the Cambridge University Press
Bentley House, 200 Euston Road, London N.W.l
Published in the United States by
Harvard University Press
Copyright © 1971 by the President
and Fellows of Harvard College
All rights reserved
Library of Congress Catalogue Card Number 76-75429
SBN 521 07648 X
Printed in Great Britain
at the University Printing House, Cambridge
(Brooke Crutchley, University Printer)
This Introduction is dedicated to
H ERBERT BU TTER FIELD
with great respect and warmth
LB. a
PREFACE
Isaac Newton published his great treatise, Philosophiae Naturalis Principia Mathema
tical in three editions (London, 1687; Cambridge, 1713 [reprinted Amsterdam,
1714, 1723]; and London, 1726), differing from one another in choice of language,
in technical content, and in expressed philosophical position. But there has never
been till now, some two and a half centuries later, an edition with variant readings
(or ‘variorum’^ edition) enabling the reader to see at a glance the successive altera
tions made by Newton during the span of about four decades from the completion
(in 1686) of the manuscript for the first edition up to the printing of the third and
ultimate authorized edition in 1726.
The present edition—to which this volume constitutes the Introduction—
primarily displays for comparison the variants uncovered by a verbatim et litteratim
collation of the three authorized editions and the manuscript from which the first
edition was printed—thus presenting Newton’s concepts, biases, tastes, knowledge,
and mastery of the subject, at three successive times: 1685-7, 1713, 1726. At the
same time there are made readily accessible to the reader the corrections, improve
ments, and additions entered by Newton himself into one or both of a pair of
copies of the first and of the second edition in his own library, thus giving some clue
to the stages of development during the intervening period.
This edition of the Principia with variant readings was conceived by the late
Professor Alexandre Koyre and me in 1956. The textual part was completed and
delivered to Harvard University Press just one decade later, followed by the Intro
duction within the next year. The edition as a whole will consist of a number of
parts, of which these first two comprise (i) the one-volume Introduction with its
Supplements and (ii) the Latin text together with the Apparatus Criticus and
Appendices, in two volumes. (Information concerning the further parts of this
edition is given below.)
The heart of our edition is, of course, the text: here we display in facsimile—
page by page—the third and ultimate approved version of the Principia (London,
1726), ultimate in the sense of representing the final revised authorized edition,
completed and seen through the press just before the aged Newton’s death (in
March 1726/7).^ To this facsimile there has been joined an Apparatus Criticus,
giving—line by line—the prior versions from the first two authorized editions
and the manuscript of the first edition, plus all textual modifications entered by
Newton himself in the above-mentioned personal copies of the first and second
^ On the pure or original sense of ‘variorum’, as contrasted with current usage today, see Chapter I, §1,
note 1.
2 A bibliography of all the editions of the Principia is given in Appendix VIII.
[vii]
Vlll Preface
editions.^ Because the Apparatus Criticus contains all textual differences found by
collating the editio princeps of 1687 and the manuscript from which it was printed,
the reader may see for himself the final alterations made just as the book was going
to press and even while it was being printed. The printer’s manuscript is written
in the hand of an amanuensis, Humphrey Newton; Edmond Halley saw the book
through the press (see Chapter HI, §§1, 7; Chapter IV; Chapter V, §3; Supple
ments II and VII). To make the record complete, all textual changes that may be
positively identified as in Newton’s hand or in Halley’s hand are so indicated in the
Apparatus Criticus.
During the course of our labours in preparing this edition. Professor Koyre and
I often asked ourselves how it could have happened that no one before us had
undertaken this task. Certain obvious answers suggested themselves at once: the
difficulty and magnitude of the undertaking, and the fact that editions with variant
readings have not generally been made of modern scientific works. Furthermore,
the history of science is a newcomer to the scholarly specialties, and hence the
demand for detailed information on the textual growth of the Principia has not
been appreciable until very recently (Chapter I, §9; Chapter II, §§1, 2). We
found, once our own edition with variant readings was under way, that at least
three suggestions had been made in the past that the Principia be edited so as to
show some (if not all) of the changes made in successive editions: the first, seven
decades ago by W. W. Rouse Ball (Chapter I, §§6- 8). No doubt one of the reasons
why scholars did not carefully study the variations among the three authorized
editions was simply that they were unaware of how illuminating or significant the
changes made by Newton actually are. Indeed, both Professor Koyre and I became
interested in undertaking to produce an edition with variant readings only when,
independently and wholly by chance, we had encountered a striking difference
between the first and the later two authorized editions in the Regulae Philosophandi
and Phaenomena which occur at the beginning of Book HI (see the Introduction,
Chapter I, §§1, 9; Chapter II, §§1, 2). Not only were the actual sense and content
modified from edition to edition, but in the first presentation a single rubric of
Hypotheses embraces the statements later presented separately as Regulae Philoso
phandi and Phaenomena.^ We were thus made aware that in the case of the
Principia any conceptual analysis would be inadequate if it did not take account of
the changes introduced by Newton in successive editions.
The fourth Regula Philosophandi occurs only in the third edition, while the
third Regula occurs in the second and the third editions. The concluding Scholium
Generale does not appear in the first edition, but in the second and—with some
® These four copies from Newton’s personal library are described below in Chapter I, §4, and in the Guide
to the Apparatus Criticus, §1. The onetime existence of other copies of the first edition with annotations by
Newton is discussed in Chapter VIII, §§4, 5.
^ Actually, the transformation of the original set of Hypotheses is even more complex than this. One of the
original Hypotheses remained a Hypothesis in all editions, and a Lemma of the first edition became Hypo
thesis II in the later editions. For details, see the Apparatus Criticus, {387-394}, (408.1-5}, {476.1-7}.
Preface IX
revisions^—in the third edition. Not only is it anachronous to lump together the
Preface (1687), the first two Regulae (1687), the third Regula (1713), the Scholium
Generale (1713, revised 1726), and the fourth Regula (1726), as if they all repre
sented Newton’s state of mind at one and the same time: to do so is also to deny
the dynamic quality of a creative mind by assuming that there were no changes on
fundamental questions during a span of some forty years (Chapter II).
Not all textual modifications from edition to edition represent a shift in Newton’s
avowed philosophic position; some are of a technical (i.e. purely scientific or
mathematical) character. Thus, Newton was always on the look-out for new data
of observation and experiment, to be introduced in both of the revised editions.
In the second edition, the Corollaries to Prop. I, Book I, were (with alterations)
shifted to Prop. II, and a wholly different set of Corollaries was added to Prop. I;
this change enabled Newton to present a completely fresh and streamlined proof
of Prop. IV, on the magnitude of the centripetal force in uniform circular motion.
Almost all of Sec. VII of Book II, on the resistance of fluids, is new in the second
edition. The proof of Prop. X, Book II, completely redone in the second edition, is
of special interest because of the criticism by Johann Bernoulli, brought to Newton’s
attention by Johann’s nephew, Nicolaus (Chapter IX, §4). The alterations in the
so-called Leibniz Scholium (following Lemma II in Book II) are similarly attractive
to study in the light of the great controversy between Newton and Leibniz concern
ing the first invention of the calculus.
The many textual alterations do not equally excite the reader’s attention.
Nevertheless, we have presented in the Apparatus Criticus every proper textual
variant, including each alteration and addition found by collating the three
printed editions, the printer’s manuscript, and the two annotated copies of the
first and of the second editions from Newton’s library, mentioned above. The
reasons for giving all proper textual variants,® and not trying to eliminate any
supposedly ‘insignificant’ ones, are spelled out at length in Chapter II. Suffice it
to say here that the exact borderline between the ‘significant’ and the ‘insignificant’
would not only differ from one scholar to another, but also from one age to the
next. Because it was our intention that students of the Principia^ now and in future,
should not have to wonder what ‘significant’ variant readings had been omitted
by us as supposedly ‘insignificant’, we did not pick and choose. The end we had
5 For instance, in the second edition Newton says that to discourse about God on the basis of phenomena
belongs to ‘experimental philosophy’, whereas in the third edition such discourse is said to belong to ‘natural
philosophy’.
® By proper textual variants I mean any difference in the actual words or mathematical expressions. We
have not included printing or spelling variants, such as capitalization or non-capitalization of the same word,
or the abbreviation or non-abbreviation of a given word (as ‘Corol.’ for ‘Corollarium’), or the use of italic
or roman type, or the change from roman to arabic numerals, or the change of spelling (as from ‘caelo’ to
‘coelo’). Similarly, we have not included printer’s misprints unless the misprint is a different word, or another
and distinct form of accidence from the one intended; but we have given all printer’s misprints considered to
have been of sufficient importance to warrant inclusion in the printed Errata. (For further details see the Guide
to the Apparatus Criticus.)
X Preface
in mind was that scholars could readily find in the Apparatus Criticus every textual
variant and every manuscript annotation of the original texts on which this edition
with variant readings is based, and not be required to have constant recourse to
the originals, save on very special occasions. Professor Koyre and I hoped from
the very start that the textual part of our joint labours might stand the test of time,
that this editing would not soon have to be undertaken again in its entirety—
although the discovery of new manuscripts could of course require supplements.
Throughout this Introduction and its Supplements, superscript letters are printed
in small letters above the line (‘y*^’ rather than ‘ye’ or ‘the’, ‘y*^’ rather than ‘yn’,
‘then’, or ‘than’, and so on); abbreviations have not been spelled out, and no
attempt has been made to introduce a modern editorial consistency; punctuation,
capitalization, and italicization generally follow the style of the manuscript as
closely as possible. The major departures from the actual form of manuscripts and
printed sources are the following: (1) accents on Latin words have, for the most
part, been ignored; (2) the special abbreviation (sometimes represented by a semi
colon) for ‘ue’ in the enclitic ‘que’ has been consistently spelled out; (3) the ‘j’
frequently written and sometimes printed for the final ‘i’ in the combination ‘ii’
(for example, ‘ij’, ‘medij’, ‘medijs’, ‘distantijs’, ‘spatij’, ‘spatijs’) is printed
throughout as ‘i’; and (4) the ligatures ‘ae’ and ‘oe’ have always been rendered by
the pairs of separate letters ‘ae’ and ‘oe’. The omission of accents on Latin words
has made it unnecessary to introduce variant readings when manuscripts or the
several printed editions of the Principia are word-for-word identical in all respects
save for accents (in such cases, how could one choose which accents to print, when
their use varies among the several manuscripts and printed versions?). In quoting
any single passage, however, from a manuscript or printed text, we have for the
most part included the accents. The ‘ j ’ presents similar problems, since (although
Newton himself wrote ‘ij’) the same printed text may use both ‘ii’ and ‘ij’ for the
identical word: for instance, ‘spatii’ on pages 5, 6, 7 of but ‘spatij’ on pages 10,
11, or both ‘ ijsdem ’ and ‘ iisdem ’ on page 7. The ligatures ‘ ae ’ and ‘ oe ’ were avoided
because of the obvious additional burden on compositors; we had encountered
erroneous introductions of ligatures resulting from the difficulties of setting up
Latin in type and of proof-reading. Lynx-eyed readers may observe that many
printed documents are presented in the Introduction in new transcriptions from the
manuscripts. All extracts are printed wholly in roman type, even though portions
of the original may be in italics.’^
The occurrence of even the most minor textual alterations may be not wholly
devoid of scholarly interest. One very important function of any textual modifica-
All titles—whether of books, of articles in journals, of names of chapters, or of statements of propositions—
have generally been given in lower-case letters, without regard to whether individual words (other than initial
words, proper names, and German nouns) are capitalized in the original. This statement applies equally to
text references, footnotes, and the bibliography. But in actual quoted extracts from manuscripts and printed
sources I have, as mentioned above, attempted to follow the style of the original as closely as possible with
regard to capital letters, spelling, and punctuation, with the exceptions noted.
Preface XI
tion is to enable us to prove that Newton actually re-read (since he later worked
over) a particular passage, proof, or section of the Principia. At first glance the
many changes in ‘pure’ terminology may not seem to be very significant, but it
must be kept in mind that the whole subject of scientific and methodologic or
philosophic terminology is only just beginning to be studied seriously. In this new
area of inquiry, the changes in terminology on Newton’s part are likely to
prove a most valuable component of our understanding of a significant aspect of
the history of thought.
In Chapter II (§§2-4) the reasons are given for including in the Apparatus
Criticus a certain number of Newton’s manuscript alterations and additions, so as
not merely to present the Principia at three discrete stages: 1685-7, 1713, 1726.
Once we had decided to extend the Apparatus Criticus beyond the results of a
verbatim et litteratim collation of the three printed editions and the printer’s
manuscript, and to include certain intermediate manuscript versions, the question
of how to set the limits on the latter proved most vexatious. Professor Koyre and
I devoted many long months of thought, and made a number of trials, before we
found the solution adopted here: of including in the Apparatus Criticus only
those manuscript annotations actually entered by Newton in his own copies of the
first and second editions of the Principia. (This topic is discussed further in Chap
ter II, §§5-7.) In a sense, having recognized the practical impossibility of printing
every known manuscript alteration, we decided that it would be better to have
Newton himself make the choice of what to include.
Another major problem that Professor Koyre and I had to face from the very start
was how to deal with the editorial and explanatory comments which we would
wish to make. Our first thought was that they would take the form of footnotes, as
a running commentary: explaining a difficult point; giving the significance of
each major topic; presenting the antecedent history or the subsequent effect of a
given concept or method or result; even expanding the mathematical proofs as
needed; explaining the cause, occasion, or significance of a given alteration
proposed or made by Newton; and even bringing in relevant material from New
ton’s manuscripts and published writings, and the writings of others.®
But we soon realized that it would be of most advantage to have our com
mentary appear separately from the text. It had been our experience as scholars
that commentaries become dated much sooner than well-edited texts. Again and
again, in the course of our separate and our joint researches, we had found
* In preparation for this task we began to assemble the various commentaries that had been written to aid
the reader or student of the Principia during the eighteenth and nineteenth centuries. We contemplated giving
the history of such commentaries, in some cases, problem by problem, as a means of providing an interesting
cross-section of the development of the philosophy of science. This plan was adumbrated in the report on our
progress which we wrote for the Yearbook of the American Philosophical Society (1960), pp. 516-20. Before long,
however, two great difficulties arose. First we saw that the sheer bulk of the commentary, so conceived, would
overwhelm the text and Apparatus Criticus: a rough estimate gave us some 1,500-2,400 pages of small type!
Clearly any such opus could not conveniently be published along with the text and Apparatus Criticus.
Preface
Xll
ourselves still using for our purposes a text edited a century or more ago—often when
the commentary to that same edition was no longer fully acceptable because of
the discovery of new sources, the changes that had occurred in scholarly perspective
or points of view, or even simply the normal march of scholarship. As I have said
earlier, we hoped that our text—within the limits of human frailty—might serve
all scholars for a long time and not be subject to doubt, disagreement, and re
placement (save in details); but we cherished no such illusion about our own
comments, happily recognizing the fact of progress in knowledge and understand
ing, even in historical studies. Furthermore, it seemed to us to be of decided
advantage to separate physically the presentation of what Newton wrote and our
own interpretations. For these reasons, both the Commentary and the Introduc
tion have been planned so as to appear as separate volumes.®
While the Apparatus Criticus was taking shape. Professor Koyre and I discussed
the Introduction to it at great length. The form adopted here evolved slowly.
Part I of the Introduction (Chapters I and II), a sort of extended preface, was
agreed on from the start: it was to be a presentation of the history of changes
made in the Principia in its several editions, and of those contemplated by Newton
between editions, so far as they would be of interest, together with an account of
earlier attempts or proposals to produce such an edition as ours. We also decided
that there should be a documentary ‘biography’ of the Principia, starting from
Halley’s famous visit in the summer of 1684, and recounting how Newton actually
wrote his magnum opus,’ then some presentation seemed required of the Principia^
critical reception, its subsequent revisions and editions, and the way in which each
of the two later authorized versions was received. Although Professor Koyre and
I had more than once discussed what kind of things should go into this Introduction,
we had not at the time of his death actually begun to write out any part of it,
nor had we even made a complete or detailed outline. Hence this Introduction,
written by me alone, could not profit from his elegant taste, his shrewd critical
perception, or his vast learning.
I have, in so far as possible, tried to follow the general plan that we had worked
out together, and—above all—to keep the Introduction a history of a book, and
not too much a critical interpretation or analytic history of Newton’s concepts,
reserving that task for the commentary volume to come. Of course, it is impossible
to write such a documentary ‘ biography ’ of the Principia as this without presenting
interpretations of concepts and their history. Anyone who knew Professor Koyre, or
who is at all familiar with his writings, will appreciate how much I missed his
collaboration during the writing of this Introduction, and in the research that I had
to undertake as the Introduction began to take form, as new and exciting docu
ments came to light, and as new problems arose and new interpretations were
® Similar considerations led to the decision to separate any English translation or paraphrase from the
Latin text and Apparatus Criticus and to combine it with the interpretative commentary and explanations.
This is explained further below.
