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                                   A
                                ~VIEW~
                                 ~OF~
                        Sir ~_ISAAC NEWTON_~’s
                              PHILOSOPHY.

[Illustration]

                             ~_LONDON_~:

                     Printed by _S. PALMER_, 1728.

[Illustration]

  To the Noble and Right Honourable
  SIR _ROBERT WALPOLE._

_SIR,_

I Take the liberty to send you this view of Sir ~ISAAC NEWTON’S~
philosophy, which, if it were performed suitable to the dignity of the
subject, might not be a present unworthy the acceptance of the greatest
person. For his philosophy operations of nature, which for so many
ages had imployed the curiosity of mankind; though no one before him
was furnished with the strength of mind necessary to go any depth in
this difficult search. However, I am encouraged to hope, that this
attempt, imperfect as it is, to give our countrymen in general some
conception of the labours of a person, who shall always be the boast
of this nation, may be received with indulgence by one, under whose
influence these kingdoms enjoy so much happiness. Indeed my admiration
at the surprizing inventions of this great man, carries me to conceive
of him as a person, who not only must raise the glory of the country,
which gave him birth; but that he has even done honour to human nature,
by having extended the greatest and most noble of our faculties,
reason, to subjects, which, till he attempted them, appeared to be
wholly beyond the reach of our limited capacities. And what can give us
a more pleasing prospect of our own condition, than to see so exalted
a proof of the strength of that faculty, whereon the conduct of our
lives, and our happiness depends; our passions and all our motives to
action being in such manner guided by our opinions, that where these
are just, our whole behaviour will be praise-worthy? But why do I
presume to detain you, SIR, with such reflections as these, who must
have the fullest experience within your own mind, of the effects of
right reason? For to what other source can be ascribed that amiable
frankness and unreserved condescension among your friends, or that
masculine perspicuity and strength of argument, whereby you draw the
admiration of the publick, while you are engaged in the most important
of all causes, the liberties of mankind?

       *       *       *       *       *

I humbly crave leave to make the only acknowledgement within my power,
for the benefits, which I receive in common with the rest of my
countrymen from these high talents, by subscribing my self

  ~_SIR_~,
  _Your most faithful_,
  _and_
  _Most humble Servant_,

  ~HENRY PEMBERTON~.




~PREFACE~.


I _Drew up the following papers many years ago at the desire of some
friends, who, upon my taking care of the late edition of Sir_ ~ISAAC
NEWTON’S~ _Principia, perswaded me to make them publick. I laid hold
of that opportunity, when my thoughts were afresh employed on this
subject, to revise what I had formerly written. And I now send it
abroad not without some hopes of answering these two ends. My first
intention was to convey to such, as are not used to mathematical
reasoning, some idea of the philosophy of a person, who has acquired
an universal reputation, and rendered our nation famous for these
speculations in the learned world. To which purpose I have avoided
using terms of art as much as possible, and taken care to define such
as I was obliged to use. Though this caution was the less necessary at
present, since many of them are become familiar words to our language,
from the great number of books wrote in it upon philosophical subjects,
and the courses of experiments, that have of late years been given by
several ingenious men. The other view I had, was to encourage such
young gentlemen as have a turn for the mathematical sciences, to pursue
those studies the more chearfully, in order to understand in our
author himself the demonstrations of the things I here declare. And to
facilitate their progress herein, I intend to proceed still farther in
the explanation of Sir_ ~ISAAC NEWTON’S~ _philosophy. For as I have
received very much pleasure from perusing his writings, I hope it is
no illaudable ambition to endeavour the rendering them more easily
understood, that greater numbers may enjoy the same satisfaction._

_It will perhaps be expected, that I should say something particular
of a person, to whom I must always acknowledge my self to be much
obliged. What I have to declare on this head will be but short; for
it was in the very last years of Sir_ ~ISAAC~_’s life, that I had the
honour of his acquaintance. This happened on the following occasion.
Mr._ Polenus, _a Professor in the University of_ Padua, _from a
new experiment of his, thought the common opinion about the force
of moving bodies was overturned, and the truth of Mr._ Libnitz_’s
notion in that matter fully proved. The contrary of what Polenus had
asserted I demonstrated in a paper, which Dr._ ~MEAD~, _who takes all
opportunities of obliging his friends, was pleased to shew Sir_ ~ISAAC
NEWTON~ _This was so well approved of by him, that he did me the honour
to become a fellow-writer with me, by annexing to what I had written,
a demonstration of his own drawn from another consideration. When I
printed my discourse in the philosophical transactions, I put what Sir_
~ISAAC~ _had written in a scholium by it self, that I might not seem to
usurp what did not belong to me. But I concealed his name, not being
then sufficiently acquainted with him to ask whether he was willing
I might make use of it or not. In a little time after he engaged me
to take care of the new edition he was about making if his Principia.
This obliged me to be very frequently with him, and as he lived at some
distance from me, a great number of letters passed between us on this
account. When I had the honour of his conversation, I endeavoured to
learn his thoughts upon mathematical subjects, and something historical
concerning his inventions, that I had not been before acquainted
with. I found, he had read fewer of the modern mathematicians, than
one could have expected; but his own prodigious invention readily
supplied him with what he might have an occasion for in the pursuit of
any subject he undertook. I have often heard him censure the handling
geometrical subjects by algebraic calculations; and his book of Algebra
he called by the name of Universal Arithmetic, in opposition to the
injudicious title of Geometry, which_ Des Cartes _had given to the
treatise, wherein he shews, how the geometer may assist his invention
by such kind of computations. He frequently praised_ Slusius, Barrow
_and_ Huygens _for not being influenced by the false taste, which then
began to prevail. He used to commend the laudable attempt of_ Hugo
de Omerique _to restore the ancient analysis, and very much esteemed
Apollonius’s book De sectione rationis for giving us a clearer notion
of that analysis than we had before. Dr._ Barrow _may be esteemed as
having shewn a compass of invention equal, if not superior to any of
the moderns, our author only excepted; but Sir_ ~ISAAC NEWTON~ _has
several times particularly recommended to me_ Huygens_’s stile and
manner. He thought him the most elegant of any mathematical writer of
modern times, and the most just imitator of the antients. 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 beginning of his mathematical studies,
in applying himself to the works of_ Des Cartes _and other algebraic
writers, before he had considered the elements of_ Euclide _with that
attention, which so excellent a writer deserves. As to the history
of his inventions, what relates to his discoveries of the methods of
series and fluxions, and of his theory of light and colours, the world
has been sufficiently informed of already. The first thoughts, which
gave rise to his Principia, he had, when he retired from_ Cambridge
_in 1666 on account of the plague. As he sat alone in a garden, he
fell into a speculation on the power of gravity: that as this power
is not found sensibly diminished at the remotest distance from the
center of the earth, to which we can rise, neither at the tops of the
loftiest buildings, nor even on the summits of the highest mountains;
it appeared to him reasonable to conclude, that this power must extend
much farther than was usually thought; why not as high as the moon,
said he to himself? and if so, her motion must be influenced by it;
perhaps she is retained in her orbit thereby. However, though the power
of gravity is not sensibly weakened in the little change of distance,
at which we can place our selves from the center of the earth; yet it
is very possible, that so high as the moon this power may differ much
in strength from what it is here. To make an estimate, what might be
the degree of this diminution, he considered with himself, that if the
moon be retained in her orbit by the force of gravity, no doubt the
primary planets are carried round the sun by the like power. And by
comparing the periods of the several planets with their distances from
the sun, he found, that if any power like gravity held them in their
courses, its strength must decrease in the duplicate proportion of the
increase of distance. This be concluded by supposing them to move in
perfect circles concentrical to the sun, from which the orbits of the
greatest part of them do not much differ. Supposing therefore the power
of gravity, when extended to the moon, to decrease in the same manner,
he computed whether that force would be sufficient to keep the moon
in her orbit. In this computation, being absent from books, he took
the common estimate in use among geographers and our seamen, before_
Norwood _had measured the earth, that 60 English miles were contained
in one degree of latitude on the surface of the earth. But as this is
a very faulty supposition, each degree containing about 69½ of our
miles, his computation did not answer expectation; whence he concluded,
that some other cause must at least join with the action of the power
of gravity on the moon. On this account he laid aside for that time
any farther thoughts upon this matter. But some years after, a letter
which he received from Dr._ Hook, _put him on inquiring what was the
real figure, in which a body let fall from any high place descends,
taking the motion of the earth round its axis into consideration.
Such a body, having the same motion, which by the revolution of the
earth the place has whence it falls, is to be considered as projected
forward and at the same time drawn down to the center of the earth.
This gave occasion to his resuming his former thoughts concerning the
moon; and_ Picart _in_ France _having lately measured the earth, by
using his measures the moon appeared to be kept in her orbit purely by
the power of gravity; and consequently, that this power decreases as
you recede from the center of the earth in the manner our author had
formerly conjectured. Upon this principle he found the line described
by a falling body to be an ellipsis, the center of the earth being one
focus. And the primary planets moving in such orbits round the sun, he
had the satisfaction to see, that this inquiry, which he had undertaken
merely out of curiosity, could be applied to the greatest purposes.
Hereupon he composed near a dozen propositions relating to the motion
of the primary planets about the sun. Several years after this, some
discourse he had with Dr._ Halley, _who at Cambridge made him a
visit, engaged Sir_ ~ISAAC NEWTON~ _to resume again the consideration
of this subject; and gave occasion to his writing the treatise
which he published under the title of mathematical principles of
natural philosophy. This treatise, full of such a variety of profound
inventions, was composed by him from scarce any other materials than
the few propositions before mentioned, in the space of one year and an
half._

_Though his memory was much decayed, I found he perfectly understood
his own writings, contrary to what I had frequently heard in discourse
from many persons. This opinion of theirs might arise perhaps from his
not being always ready at speaking on these subjects, when it might
be expected he should. But as to this, it may be observed, that great
genius’s are frequently liable to be absent, not only in relation to
common life, but with regard to some of the parts of science they are
the best informed of. Inventors seem to treasure up in their minds,
what they have found out, after another manner than those do the same
things, who have not this inventive faculty. The former, when they
have occasion to produce their knowledge, are in some measure obliged
immediately to investigate part of what they want. For this they are
not equally fit at all times: so it has often happened, that such as
retain things chiefly by means of a very strong memory, have appeared
off hand more expert than the discoverers themselves._

_As to the moral endowments of his mind, they were as much to be
admired as his other talents. But this is a field I leave others to
exspatiate in. I only touch upon what I experienced myself during
the few years I was happy in his friendship. But this I immediately
discovered in him, which at once both surprized and charmed me: Neither
his extreme great age, nor his universal reputation had rendred 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 publick testimony of his good opinion.
He also approved of the following treatise, a great part of which we
read together. As many alterations were made in the late edition of
his Principia, so there would have been many more if there had been
a sufficient time. But whatever of this kind may be thought wanting,
I shall endeavour to supply in my comment on that book. I had reason
to believe he expected such a thing from me, and I intended to have
published it in his life time, after I had printed the following
discourse, and a mathematical treatise Sir_ ~ISAAC NEWTON~ _had written
a long while ago, containing the first principles of fluxions, for I
had prevailed on him to let that piece go abroad. I had examined all
the calculations, and prepared part of the figures; but as the latter
part of the treatise had never been finished, he was about letting me
have other papers, in order to supply what was wanting. But his death
put a stop to that design. As to my comment on the Principia, I intend
there to demonstrate whatever Sir_ ~ISAAC NEWTON~ _has set down without
express proof, and to explain all such expressions in his book, as
I shall judge necessary. This comment I shall forthwith put to the
press, joined to an english translation of his Principia, which I have
had some time by me. A more particular account of my whole design has
already been published in the new memoirs of literature for the month
of march 1727._

_I have presented my readers with a copy of verses on Sir_ ~ISAAC
NEWTON~, _which I have just received from a young Gentleman, whom I am
proud to reckon among the number of my dearest friends. If I had any
apprehension that this piece of poetry stood in need of an apology,
I should be desirous the reader might know, that the author is but
sixteen years old, and was obliged to finish his composition in a very
short space of time. But I shall only take the liberty to observe, that
the boldness of the digressions will be best judged of by those who are
acquainted with_ ~PINDAR~.




                                   A
                                ~POEM~
                                  ON
                         Sir ~_ISAAC NEWTON_~.


  TO ~NEWTON~’s genius, and immortal fame
  Th’ advent’rous muse with trembling pinion soars.
  Thou, heav’nly truth, from thy seraphick throne
  Look favourable down, do thou assist
  My lab’ring thought, do thou inspire my song.
  NEWTON, who first th’ almighty’s works display’d,
  And smooth’d that mirror, in whose polish’d face
  The great creator now conspicuous shines;
  Who open’d nature’s adamantine gates,
  And to our minds her secret powers expos’d;
  NEWTON demands the muse; his sacred hand
  Shall guide her infant steps; his sacred hand
  Shall raise her to the Heliconian height,
  Where, on its lofty top inthron’d, her head
  Shall mingle with the Stars. Hail nature, hail,
  O Goddess, handmaid of th’ ethereal power,
  Now lift thy head, and to th’ admiring world
  Shew thy long hidden beauty. Thee the wise
  Of ancient fame, immortal ~PLATO~’s self,
  The Stagyrite, and Syracusian sage,
  From black obscurity’s abyss to raise,
  (Drooping and mourning o’er thy wondrous works)
  With vain inquiry sought. Like meteors these
  In their dark age bright sons of wisdom shone:
  But at thy ~NEWTON~ all their laurels fade,
  They shrink from all the honours of their names.
  So glimm’ring stars contract their feeble rays,
  When the swift lustre of ~AURORA~’s face
  Flows o’er the skies, and wraps the heav’ns in light.

  THE Deity’s omnipotence, the cause,
  Th’ original of things long lay unknown.
  Alone the beauties prominent to sight
  (Of the celestial power the outward form)
  Drew praise and wonder from the gazing world.
  As when the deluge overspread the earth,
  Whilst yet the mountains only rear’d their heads
  Above the surface of the wild expanse,
  Whelm’d deep below the great foundations lay,
  Till some kind angel at heav’n’s high command
  Roul’d back the rising tides, and haughty floods,
  And to the ocean thunder’d out his voice:
  Quick all the swelling and imperious waves,
  The foaming billows and obscuring surge,
  Back to their channels and their ancient seats
  Recoil affrighted: from the darksome main
  Earth raises smiling, as new-born, her head,
  And with fresh charms her lovely face arrays.
  So his extensive thought accomplish’d first
  The mighty task to drive th’ obstructing mists
  Of ignorance away, beneath whose gloom
  Th’ inshrouded majesty of Nature lay.
  He drew the veil and swell’d the spreading scene.
  How had the moon around th’ eth