<55r>

Sr

The Proof you sent me I like very well. I designed ye whole to consist of three books, the second was finished last summer being short & only wants transcribing & drawing the cuts fairly. Some new Propositions I have since thought on wch I can as well let alone. The third wants ye Theory of Comets. In Autumn last I spent two months in calculations to no purpose for want of a good method, wch made me afterwards return to ye first Book & enlarge it wth divers Propositions some relating to Comets others to other things found out last Winter. The third I now designe to suppress. Philosophy is such an impertinently litigious Lady that a man had as good be engaged in Law suits as come neare \as have to do with/ her{.} I found it so formerly & now I no sooner come near her again but she gives me warning. The two first books without the third will not so well beare ye title of Philosophiæ naturalis Principia Mathematica & therefore I had altered it to this De motu corporum libri duo: but upon second thoughts I retain ye former title. Twill help ye sale of ye book wch I ought not to diminish now tis yors. The Articles are wth ye largest to be called by that name. If you please you may change ye word to sections, th{illeg}|ô| it be not material. In ye first page I have struck out ye words uti posthac docebitur as referring to ye third book. Which is all at present from

Yor affectionate friend &

humble Servant

Is: Newton.

Cambridge
June 20. 1686.

For your further satisfaction in this business, I beg ye favour you would consult yor books for a paper of mine entitled, An Hypothesis explaining ye properties of light. Twas dated Decemb. 7th 1675 & registred in your Book about Ian or Feb following. Not far from ye beginning there is a Paragraph ending wth these words. And as ye Earth so perhaps may the Sun imbibe this spirit copiously to conserve his shining & keep ye Planets from receding further from him & they that will may also suppose that this spirit affords or carries thither the solary fewel & materiall principle if light: And that ye vast ethereal spaces between us & ye stars are for a sufficient repository for this food if ye Sun & Planets. But this if ye constitution if ethereal natures by ye by. In these & ye foregoing words you have ye common cause of gravity towards ye earth Sun & all the Planets, & that by this cause ye Planets are kept in their Orbs about ye Sun. And this is all ye Philosophy Mr Hook pretends I had from his letters some years after, the duplicate proportion only excepted. The preceding words contein ye cause of ye phænomena of gravity as we find it on ye surf{illeg}|a|ce of the earth without any regard to ye various distances from ye center: For at first I designed to write of nothing more. Afterwards, as my manuscript shews, I interlined ye words above cited relating to ye heavens, & in so short & transitory an interlined hint of things, the expression of ye proportion may well be excused. But if you consider ye nature of ye Hypothesis you'l find that \gravity decreases upward &/ can be no other from ye superficies of ye Planet then reciprocally duplicate of ye distance from the center, but downwards that proportion does not hold. This was but an Hypothesis & so to be looked upon only as one of my guesses which I did not rely on: but it sufficiently explains to you why in considering ye descent of a body down to ye center I used not ye duplicate proportion. In ye small ascent & descent of projectiles above ye earth ye variation of gravity is so inconsiderable yt Mathematicians neglect it. Hence ye vulgar Hypothesis with them is uniform gravity. And why might not I as a Mathematician use it frequently without thinking on ye philosophy of ye heavens or beleiving it to be philosophically true?

For Mr Edmund Halley.

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Mr Newton of
June 20o 1686

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