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自然哲学的数学原理

_6 伊萨克·牛顿(英国)
when it went frpm it
; that he could not say when this comet
would drop into the sun ;
it might perhaps have five or six revo
lutions more first, but whenever it did it would so much increase
the heat of the sun that this earth would be burned, and no ani
mals in it could live. That he took the three phenomena, seen
by Hipparchus, Tycho Brahe, and Kepler s disciples, to have been
of this kind, for he could not otherwise account for an extraor
dinary light, as those were, appearing, all at once, among the
the fixed stars (all which he took to be suns, enlightening other
planets, as our sun does ours), as big as Mercury or Venus seems
to us, and gradually diminishing, for sixteen months, and then
sinking into nothing. He seemed to doubt whether there were
not intelligent beings, superior to us, who superintended these
revolutions of the heavenly bodies, by the direction of the Supreme
Being. He appeared also to be very clearly of opinion that the
inhabitants of this world were of short date, and alledged, as one
reason for that opinion, that all arts, as letters, ships, printing,
needle, &c., were discovered within the memory of history, which
could not have happened if the world had been eternal
; and that
there were visible marks of ruin upon it which could not be
effected by flood only. When I asked him how this earth could
have been repeopled if ever it had undergone the same fate
it was threatened with hereafter, by the comet of 1680, he
answered, that required the power of a Creator. He said he
took all the planets to be composed of the same matter with this
earth, viz. : earth, water, stones, &c.3 but variously concocted. J

LIFE OP SIR ISAAC NEWTON. 55
asked him why he would not publish his conjectures, as conjec
tures, and instanced that Kepler had communicated his
; and
though he had not gone near so far as Kepler, yet Kepler s
guesses were so just and happy that they had been proved and
demonstrated by him. His answer was, " I do not deal in con
jectures." But, on my talking to him about the four observations
that had been made of the comet of 1680, at 574 years distance,
and asking him the particular times, he opened his Principia,
which laid on the table, and showed me the particular periods,
viz.: 1st. The Julium Sidus, in the time of Justinian, in 1106,
in 1680.
" And I, observing that he said there of that comet, incidet
in corpus solis, and in the next paragraph adds, stellae fixae
refici possunt, told him I thought he owned there what we had
been talking about, viz. : that the comet would drop into the sun,
and that fixed stars were recruited and replenished by comets
when they dropped into them ; and, consequently, that the sun
would be recruited too ; and asked him why he would not own as
fully what he thought of the sun as well as what he thought of
the fixed stars. He said, that concerned us more; and, laugh
ing, added, that he had said enough for people to know his
meaning."
In the summer of 1725, a French translation of the chronolo
gical MS., of which the Abbe Conti had been permitted, some
time previous, to have a copy, was published at Paris, in violation
of all good faith. The Punic Abbe had continued true to his
promise of secrecy while he remained in England ; but no sooner
did he reach Paris than he placed the manuscript into the hands
of M. Freret, a learned antiquarian, who translated the work, and
accompanied it with an attempted refutation of the leading points
of the system. In November, of the same year, Newton received
a presentation copy of this publication, which bore the title of
ABREGE DE CHRONOLOGIE DE M. LE CHEVALIER NEWTON, FAIT
PAR LUI-MEME, ET TRADUIT SUR LE MANUSCRIPT ANGLAIS. Soon
afterward a paper entitled, REMARKS ON TFE OBERVATIONS MADE
ON A CHRONOLOGICAL INDEX OF SIR ISAAC NE.WTON, TRANSLATED
INTO FRENCH BY THE OBSERVATOR, ANL PUBLISHED AT PARIS,

56 LIFE OF SIR ISAAC NEWTON,
was drawn up by our author, and printed in the Philosophical
Transactions for 1725. It contained a history of the whole
matter, and a triumphant reply to the objections of M. Freret.
This answer called into the field a fresh antagonist, Father Soueiet,
whose five dissertations on this subject were chiefly remarkable
for the want of knowledge and want of decorum, which they
displayed. In consequence of these discussions, Newton was in
duced to prepare his larger work for the press, and had nearly
completed it at the time of his death. It was published in 1728,
under the title of THE CHRONOLOGY OF THE ANCIENT KINGDOMS
AMENDED, TO WHICH is PREFIXED A SHORT CHRONICLE FROM THE
FIRST MEMORY OF THINGS IN EUROPE TO THE CONQUEST OF
PERSIA BY ALEXANDER THE GREAT. It consists of six chap
ters: 1. On the Chronology of the Greeks; according to Whiston,
our author wrote out eighteen copies of this chapter with his
own hand, differing little from one another. 2. Of the Empire
of Egypt; 3. Of the Assyrian Empire; 4. Of the two contempo
rary Empires of the Babylonians and Medes ;
5. A Description
of the Temple of Solomon ;
6. Of the Empire of the Persians ;
this chapter was not found copied with the other five, but as it
was discovered among his papers, arid appeared to be a continu
ation of the same work, the Editor thought proper to add it
thereto. Newton s LETTER TO A PERSON OF DISTINCTION WHO
HAD DESIRED HIS OPINION OF THE LEARNED BlSHO^ LLOYD S
HYPOTHESIS CONCERNING THE FORM OF THE MOST ANCIENT
^EAR, closes this enumeration of his Chronological Writings.
A ihird edition of the PRINCIPIA appeared in 1726, with many
changes and additions. About four years were consumed in its
preparation and publication, which were under the superintendance
of Dr. Henry Pemberton, an accomplished mathematician,
and the author of "A VIEW OF SIR ISAAC NEWTON S PHILO
SOPHY." 1728. This gentleman enjoyed numerous opportunities
of conversing with the aged and illustrious author. " I found,"
says Pemberton, " he had read fewer of the modern mathemati
cians than one could have expected; but his own prodigious
invention readily supplied him with what he might have an occa
sion for in the pursuit of any subject he undertook. I have often

LIFE OF SIR ISAAC NEWTON. 57
heard him censure the handling geometrical subjects ly algebraic
calculations ; and his book of Algebra he called by the name of
Universal Arithmetic, in opposition to the injudicious title of
Geometry, which Descartes had given to the treatise, wherein he
shows how the geometer may assist his invention by such kind
of computations. He thought Huygens the most elegant of any
mathematical writer of modern times, and the most just imitator
of the ancients. Of their taste and form of demonstration, Sir
Isaac always professed himself a great admirer. I have heard
him even censure himself for not following them yet more closely
than he did ; and speak with regret of his mistake at the begin
ning of his mathematical studies, in applying himself to the works
of Descartes and other algebraic writers, before he had considered
the elements of Euclid with that attention which so excellent a
writer deserves."
" Though his memory was much decayed," continues Dr. Pemberton,
"he perfectly understood his own writings." And even
this failure of memory, we would suggest, might have been more
apparent than real, or, in medical terms, more the result of func
tional weakness than organic decay. Newton seems never to
have confided largely to his memory : and as this faculty mani
fests the most susceptibility to cultivation ; so, in the neglect of
due exercise, it more readily and plainly shows a diminution of
its powers.
Equanimity and temperance had, indeed, preserved Newton
singularly free from all mental and bodily ailment. His hair was,
to the last, quite thick, though as white as silver. He never
made use of spectacles, and lost but one tooth to the day of his
death. He was of middle stature, well-knit, and, in the latter
part of his life, somewhat inclined to be corpulent. Mr. Conduit
says,
" he had a very lively and piercing eye, a comely and gra
cious aspect, with a fine head of hair, white as silver, without any
baldness, and when his peruke was off was a venerable sight."
According to Bishop Atterbury, "in the whole air of his face and
make there was nothing of that penetrating sagacity which
appears in his compositions. He had something rather languid
in his look and manner which did not raise any great expectation

58 LIFE OF SIR ISAAC NEWTON.
in those who did not know him." Hearne remarks, " Sir Isaac
was a man of no very promising aspect. He was a short, wellset
man. He was full of thought, and spoke very little in com
pany, so that his conversation was not agreeable. When he rode
in his coach, one arm would be out of his coach on one side and
the other on the other." These different accounts we deem
easily reconcilable. In the rooms of the Royal Society, in the
street, or in mixed assemblages, Newton s demeanour always
courteous, unassuming and kindly still had in it the overawings
of a profound repose and reticency, out of which the communica
tive spirit, and the "lively and piercing eye" would only gleam
in the quiet and unrestrained freedom of his own fire-side.
" But this I immediately discovered in him," adds Pemberton,
still further, "which at once both surprised and charmed me.
Neither his extreme great age, nor his universal reputation had
rendered him stiff in opinion, or in any degree elated. Of this I
had occasion to have almost daily experience. The remarks I
continually sent him by letters on his Principia, were received
with the utmost goodness. These were so far from being any
ways displeasing to him, that, on the contrary, it occasioned him
to speak many kind things of me to my friends, and to honour me
with a public testimony of his good opinion." A modesty, open
ness, and generosity, peculiar to the noble and comprehensive
spirit of Newton. " Full of wisdom and perfect in
beauty," yet
not lifted up by pride nor corrupted by ambition. None, how
ever, knew so well as himself the stupendousness of his discoveries
in comparison with all that had been previously achieved ; and
none realized so thoroughly as himself the littleness thereof in
comparison with the vast region still unexplored. A short time
before his death he uttered this memorable sentiment: " I do not
know what I may appear to the world ; but to myself I seem to
have been only like a boy playing on the sea-shore, and diverting
myself in now and then finding a smoother pebble or a prettier
shell than ordinary, while the great ocean of truth lay all undis
covered before me." How few ever reach the shore even, much
less find "a smoother pebble or a prettier shell!"
Newton had now resided about two years at Kensington ; and

LIFE OF SIR ISAAC NEWTON. 59
the air which he enjoyed there, and the state of absolute rest,
proved of great benefit to him. Nevertheless he would occasion
ally go to town. And on Tuesday, the 28th of February, 1727,
he proceeded to London, for the purpose of presiding at a meeting
of the Royal Society. At this time his health was considered,
by Mr. Conduit, better than it had been for many years. But
the unusual fatigue he was obliged to suffer, in attending the
meeting, and in paying and receiving visits, speedily produced a
violent return of the affection in the bladder. He returned to
Kensington on Saturday, the 4th of March. Dr. Mead and Dr.
Cheselden attended him ; they pronounced his disease to be the
stone, and held out no hopes of recovery. On Wednesday, the
15th of March, he seemed a little better; and slight, though
groundless, encouragement was felt that he might survive the
attack. From the very first of it, his sufferings had been intense.
Paroxysm followed paroxysm, in quick succession : large drops
)f sweat rolled down his face ; but not a groan, not a complaint,
not the least mark of peevishness or impatience escaped him :
and during the short intervals of relief, he even smiled and con
versed with his usual composure and cheerfulness. The flesh
quivered, but the heart quaked not ; the impenetrable gloom was
settling down : the Destroyer near ; the portals of the tomb
opening, still, arnid this utter wreck and dissolution of the mortal,
the immortal remained serene, unconquerable : the radiant light
broke through the gathering darkness ; and Death yielded up its
sting, and the grave its victory. On Saturday morning, 18th,
he read the newspapers, and carried on a pretty long conversation
with Dr. Mead. His senses and faculties were then strong and
vigorous ; but at six o clock, the same evening, he became insen
sible ; and in this state he continued during the whole of Sunday,
and till Monday, the 20th, when he expired, between one and
two o clock in the morning, in the eighty-fifth year of his age.
And these were the last days of Isaac Newton. Thus closed
the career of one of earth s greatest and best men. His mission
was fulfilled. Unto the Giver, in many-fold addition, the talents
were returned. While it was yet day he had worked ; and for
the night that quickly cometh he was not unprepared. Full of

60 LIFE OF SIR ISAAC NEWTON.
years, ind full of honours, the heaven-sent was recalled ; and, in
the confidence of a " certain hope," peacefully he passed awa}
into the silent depths of Eternity.
His body was placed in Westminster Abbey, with the state
and ceremonial that usually attended the interment of the most
distinguished. In 1731, his relatives, the inheritors of his personal
estate, erected a monument to his memory in the most conspicu
ous part of the Abbey, which had often been refused by the dean
and chapter to the greatest of England s nobility. During the
same year a medal was struck at the Tower in his honour ; arid,
in 1755, a full-length statue of him, in white marble, admirably
executed, by Roubiliac, at the expense of Dr. Robert Smith, was
erected in the ante-chamber of Trinity College, Cambridge.
There is a painting executed in the glass of one of the windows
of the same college, made pursuant to the will of Dr. Smith, who
left five hundred pounds for that purpose.
Newton left a personal estate of about thirty-two thousand
pounds. It was divided among his four nephews and four nieces
of the half blood, the grand-children of his mother, by the Reve
rend Mr. Smith. The family estates of Woolsthorpe arid Sustern
fell to John Newton, the heir-at-law, whose great grand-father
was Sir Isaac s uncle. Before his death he made an equitable
distribution of his two other estates : the one in Berkshire to the
sons and daughter of a brother of Mrs. Conduit ; and the other,
at Kensington, to Catharine, the only daughter of Mr. Conduit,
and who afterward became Viscountess Lymington. Mr. Con
duit succeeded to the offices of the Mint, the duties of which he
had discharged during the last two years of Sir Isaac s life.
Our author s works are found in the collection of Castilion,
Berlin, 1744, 4to. 8 torn.; in Bishop Horsley s Edition, London,
1779, 4to. 5 vol.; in the Biographia Brittannica, &c. Newton
also published Bern. Varcnii Geographia, &c., 1681, 8vo.
There are, however, numerous manuscripts, letters, and other
papers, which have never been given to the world: these are
preserved, in various collections, namely, in the library of Trinity
College, Cambridge ;
in the library of Corpus Christi College,
Oxford ;
in the library of Lord Macclesfield : and, lastly arid

LIFE OF SIR ISAAC NEWTON. 61
chiefly, in the possession of the family of the Earl of Portsmouth,
through the Viscountess Lymington.
Everything appertaining to Newton has been kept and che
rished with peculiar veneration. Different memorials of him are
preserved in Trinity College, Cambridge ;
in the rooms of the
Royal Society, of London : and in the Museum of the Royal
Society of Edinburgh.
The manor-house, at Woolsthorpe, was visited by Dr. Stuke
ley, in October, 1721, who, in a letter to Dr. Mead, written in
1727, gave the following description of it: " Tis built of stone,
as is the way of the country hereabouts, and a reasonably good
one. They led me up stairs and showed me Sir Isaac s stud}-,
where I supposed he studied, when in the country, in his younger
days, or perhaps when he visited his mother from the University.
I observed the shelves were of his own making, being pieces of
deal boxes, which probably he sent his books and clothes down
in on those occasions. There were, some years ago, two or threr
hundred books in it of his father-in-law, Mr. Smith, which Sir
Isaac gave to Dr. Newton, of our town." The celebrated appletree,
the fall of one of the apples of which is said to have turned
the attention of Newton to the subject of gravity, was destroyed
by the wind about twenty years ago ; but it has been preserved
in the form of a chair. The house itself has been protected with
religious care. It was repaired in 1798, and a tablet of white
marble put up in the room where our author was born, with the
follow, ng inscription :
" Sir Isaac Newton, son of John Newton, Lord of the Manor
of Woolsthorpe, was born in this room, on the 25th of December,
1642."
Nature and Nature s Laws wei-e hid in night,
God said, " Let NEWTON be," and all was light.

THE PEINCIPIA.

THE AUTHOR S PREFACE
SINCE the ancients (as we are told by Pappus), made great account oi
the science of mechanics in the investigation of natural things : and the
moderns, laying aside substantial forms and occult qualities, have endeav
oured to subject the phenomena of nature to the laws of mathematics, I
have in this treatise cultivated mathematics so far as it regards philosophy.
The ancients considered mechanics in a twofold respect ; as rational, which
proceeds accurately by demonstration ; and practical. To practical me
chanics all the manual arts belong, from which mechanics took its name.
Rut as artificers do not work with perfect accuracy, it comes to pass that
mechanics is so distinguished from geometry, that what is perfectly accu
rate is called geometrical , what is less so, is called mechanical. But the
errors are not in the art, but in the artificers. He that works with less
accuracy is an imperfect mechanic ; and if any could work with perfect
accuracy, he would be the most perfect mechanic of all
; for the description
if right lines and circles, upon which geometry is founded, belongs to me
chanics. Geometry does not teach us to draw these lines, but requires
them to be drawn ;
for it requires that the learner should t be taught
to describe these accurately, before he enters upon geometry ; then it shows
how by these operations problems may be solved. To describe right lines
and circles are problems, but not geometrical problems. The solution of
these problems is required from mechanics ; and by geometry the use of
them, when so solved, is shown ; and it is the glory of geometry that from
those few principles, brought from without, it is able to produce so many
things. Therefore geometry is founded in mechanical practice, and is
nothing but that part of universal mechanics which accurately proposes
and demonstrates the art of measuring. But since the manual arts are
chiefly conversant in the moving of bodies, it comes to pass that geometry
is commonly referred to their magnitudes, and mechanics to their motion.
In this sense rational mechanics will be the science of motions resulting
from any forces whatsoever, and of the forces required to produce any mo
tions, accurately proposed and demonstrated. This part of mechanics was

i:;vm THE AUTHOR & PREFACE.
cultivated by the ancients in the five powers which relate to manual arts,
who considered gravity (it not being a manual power), ho Otherwise than
as it moved weights by those powers. Our design not respecting arts, but
philosophy, and our subject not manual but natural powers, we consider
chiefly those things which relate to gravity, levity, elastic force, the resist
ance of fluids, and the like forces, whether attractive or impulsive ; and
therefore we offer this work as the mathematical principles :f philosophy ;
for
all the difficulty of philosophy seems to consist in this from the phenom
ena of motions to investigate the forces of nature, and then from these
forces to demonstrate the other phenomena ; and to this end the general
propositions in the first and second book are directed. In the third book
we give an example of this in the explication of the System of the World :
for by the propositions mathematically demonstrated in the former books,
we in the third derive from the celestial phenomena the forces of gravity
with which bodies tend to the sun and the several planets. Then from these
forces, by other propositions which are also mathematical, we deduce the mo
tions of the planets, the comets, the moon, and the sea. I wish we could dorive
the rest of the phenomena of nature by the same kind of reasoning from
mechanical principles; for I am induced by many reasons to suspect that
they may all depend upon certain forces by which the particles of bodies.
by some causes hitherto unknown, are either mutually impelled towards
each other, and cohere in regular figures, or are repelled and recede from
each other; which forces being unknown, philosophers have hitherto at
tempted the search of nature in vain ; but I hope the principles here laid
down will afford some light either to this or some truer method of philosophy.
In the publication of this work the most acute and universally learned
Mr. Edmund Halley not only assisted me with his pains in correcting the
press and taking care of the schemes, but it was to his solicitations that its
becoming public is owing ; for when he had obtained of me my demonstra
tions of the figure of the celestial orbits, he continually pressed me to com
municate the same to the Royal Societ//, who afterwards, by their kind en
couragement and entreaties, engaged me to think of publishing them. But
after I had begun to consider the inequalities of the lunar motions, and
had entered upon some other things relating to the laws and measures oi
gravity, and other forces : and the figures that would be described by bodies
attracted according to given laws ; and the motion of several bodies moving
among themselves; the motion of bodies in resisting mediums; the forces,
densities, and motions, of rn( Hums ; the orbits of the comets, and such like ;

Ixix
deferred that publication till I had made a searcli into those matters, and
could put forth the whole together. What relates to the lunar motions (be
ing imperfect), I have put all together in the corollaries of Prop. 66, to
avoid being obliged to propose and distinctly demonstrate the several things
there contained in a method more prolix than the subject deserved, and in
terrupt the series of the several propositions. Some things, found out after
the rest, I chose to insert in places less suitable, rather than change the
number of the propositions and the citations. I heartily beg that what 1
have here done may be read with candour; and that the defects in a
subject so difficult be not so much reprehended as kindly supplied, and in
vestigated by new endeavours of mv readers.
ISAAC NEWTON.
Cambridge, Trinity Coupge May 8, liHB.
In the second edition the second section of the first book was enlarged.
In the seventh section of the second book the theory of the resistances of fluids
was more accurately investigated, and confirmed by new experiments. In
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