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in English
r
I agree with you that if matter eavenly diffused through a finite space
not spherical, should fall into a solid mass, this mass would affect e
of ee
solid from ee
it yeild to their pressure. Yet by earthquakes loosing ee
tuberances might sometimes sink alittle by their Weight, & thereby e
by degrees approach a spherical figure.
The reason why matter ee
ticle so accurately placed in e
sides & thereby continue without motion, seems to me a supposition fully as hard
as to make eeeeeee
will not be attracted equally on all sides
And much harder it is to suppose that all e
space should be so accurately poised one among another as to stand still in a
perfect equilibrium. ffor I reccon this as hard as to make not one needle only
but an infinite number of them (so many as there are particles in an infinite
space) stand accurately poised upon their points. Yet I grant it possible, at least
by a divine power; & if they were once so placed I agree with you that
they would continue in that posture without motion for ever, unless put into
new motion by the same power. When therefore I said that matter eavenly
spread through all spaces would convene by its gravity into one or more great
masses
But you argue in e
of matter in an infinite space has an infinite quantity of matter on all sides
& by consequence an infinite attraction every way & therefore must rest
equilibrio
this tee
Equal. The generality of mankind consider infinites no other ways then
definitely, & in this sense they say all infinites are equal, though they
speak more truly if they should say they are neither equal nor unequal nor
have any certain difference or proportion one to another. In this sense there
fore no conclusions can be drawn fre
differences of things, & they that attempt to do it, usually fall into parallogism.
So when men argue against e
that if an inch may be divided into an infinite number of parts, e
those parts will be an inch, & if a foot may be divided into an infinite number
of parts e
are equal those summs must be equal, that is an inch equal to a foot. The
falsness of eeee
position that all infinites are equal. There is therefore another way of con
sidering infinites used by Mathematicians, & that is under certain definite re
strictions & limitations whereby infinites are determined to have certain differen
ces or proportions to one another. Thus Dr Wallis considers
Infinitorumee
allowed by Mathematicians & yet would not be good were all infinites equall.
According to e
you that though there be an infinite number of infinitely little parts in an inch
yet there is twelve times that number of such parts in a foot; that is, e
finite number of those parts in a foot is not equall to, but twelve times big
ger then e
will tell you that if a body stood
contrary attracting infinite forces, & if to either of those forces you add any
new finite attracting force: that new force how little so ever will destreee
in this case two equal infinites by e
become unequal in our ways of recconning. And after these ways we must
reccon, if from e
sions.
To the last part of your letter I answer ee
moon) were placed any where with its center in e
there without any gravitation or projection & then at once were i infused into
it both a gravitating energy towards e
quantity moving it directly in a tangent to ee
this attraction & prp
revolution of eee
just quantity, for if it be too big or too little it will cause e
in some other line.
Secondly I do not know any power in nature ch
verse motion without e
book of Bombs that Plato affirms that ee
they had all of them been created by God in some region very remote from
our Systeme & let fall from thence towards e
their several orbs their motion of falling turned aside into a transverse one;
& this is true supposing ee
moment of time in cheeeee
attractive power of ee
but without e
motion as they have about e
I am compelled to ascribe e
You sometimes speak of gravity as essential & inherent to matter:
pray do not ascribe that notion to me, for e
do not pretend to know, & therefore would take more time to consider of it
I fear what I have said of infinites will seem obscure to you: but it is enough
if you understand that infinites when considered absolutely without any restric
tion or limitation, are neither equal nor unequal nor have any certain
proportion to one another, & therefore e
equal is a precarious one. r
r
Is. Newton
Trin. Coll. Ian. 17.
1692/3
For Mr Bently at the
Palace in
Worcester
d Letter from Mr Newton
in answer to some further
Queries