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Sr

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 ye figure of ye whole space, provided it were not soft like ye old Chaos, but so hard & solid from ye beginning, that ye weight of its protuberant parts could not make it yeild to their pressure. Yet by earthquakes loosing ye parts of this solid, ye protuberances might sometimes sink alittle by their Weight, & thereby ye mass might by degrees approach a spherical figure.

The reason why matter \eavenly/ scattered through a finite space would convene in ye midst you conceive ye same with me: but that there should be a Central particle so accurately placed in ye middle as to be always equally attracted on all sides & thereby continue without motion, seems to me a supposition fully as hard as to make ye sharpest needle stand upright on its point upon a lookingglass. {ffor} if ye very mathematical center of ye central particle be not accurately in ye very mathematical center of ye attractive power of ye whole mass, ye particle will not be attracted equally on all sides{.}

And much harder it is to suppose that all ye particles in an infinite 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{sic} I understand it of matter not resting in an accurate poise.

But you argue in ye next paragraph of your letter that every particle 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 in equilibrio because all infinites are equal. Yet you suspect a parallogism in this argumt, & I conceive ye parallogism lies in ye position that all infinites are Equal. The generality of mankind consider infinites no other ways then definitely, & in this sense they say all infinites are equal, though they {would} 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 therefore no conclusions can be drawn frō them about ye equality, proportions or differences of things, & they that attempt to do it, usually fall into parallogism. So when men argue against ye infinite divisibility of magnitude by saying that if an inch may be divided into an infinite number of parts, ye sum of those parts will be an inch, & if a foot may be divided into an infinite number of parts ye sum of those parts must be a foot, & therefore since all infinites are equal those summs must be equal, that is an inch equal to a foot. The falsness of ye conclusion shews an error in ye premisses, & ye error lies in ye position that all infinites are equal. There is therefore another way of considering infinites used by Mathematicians, & that is under certain definite restrictions & limitations whereby infinites are determined to have certain differences or proportions to one another. Thus Dr Wallis considers \them/ in his Arithmetica Infinitorum, where by ye various proportions of infinite summs he gathers ye <5v> various proportions of infinite magnitudes: which way of arguing is generally allowed by Mathematicians & yet would not be good were all infinites equall. According to ye same way of Considering infinites, a Mathematician would tell 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, ye infinite number of those parts in a foot is not equall to, but twelve times bigger then ye infinite number of them in an inch. And so a Mathematician will tell you that if a body stood in equilibrio between any two equal and 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 destr{oy} ye equilibrium & put ye body into ye same motion into which it would pu{t} it were those two contrary \equal/ forces but finite or even none at all: so tha{t} in this case two equal infinites by ye addition of a finite to either of them become unequal in our ways of recconning. And after these ways we must reccon, if from ye consideration of infinites we would always draw true conclusions.

To the last part of your letter I answer \first/ that if ye earth (without ye moon) were placed any where with its center in ye Orbis magnus & stood sti{ll} there without any gravitation or projection & then at once were i{n} infused into it both a gravitating energy towards ye sun & a transverse impulse of a just quantity moving it directly in a tangent to ye Orbis magnus: ye compound of this attraction & prp|o|jection would according to my notion cause a circular revolution of ye earth about ye Sun. But ye transverse impulse must be of a just quantity, for if it be too big or too little it will cause ye earth to move in some other line.

Secondly I do not know any power in nature wch could cause this transverse motion without ye divine arm. Blondel tells us some where in his book of Bombs that Plato affirms that ye motion of ye planets is such as if they had all of them been created by God in some region very remote from our Systeme & let fall from thence towards ye Sun, & so soon as they arrived at their several orbs their motion of falling turned aside into a transverse one; & this is true supposing ye gravitating power of ye Sun was doubled at that moment of time in wch they all arrive at their several orbs: but then ye divine {po}wer is here required in a double respect; namely to turn ye descending mo{tion} of ye falling planets into a side motion, & at ye same time to double ye attractive power of ye Sun. So then gravity may put ye planets into motion but without ye divine power it could never put them into such a Circulating motion as they have about ye Sun, & therefore for this as well as other reasons I am compelled to ascribe ye frame of this Systeme to an intelligent agent.

You sometimes speak of gravity as essential & inherent to matter: pray do not ascribe that notion to me, for ye cause of gravity is what I 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 restriction or limitation, are neither equal nor unequal nor have any certain proportion to one another, & therefore ye principle that all infinites are equal is a precarious one. Sr I am

Yor most humble Servant

Is. Newton

Trin. Coll. Ian. 17.

1692/3

<envelope>

For Mr Bently at the
Palace in

Worcester

A 2d Letter from Mr Newton in answer to some further Queries