Letter to Edmund Halley on work on ellipses and the descent of falling bodies

Author: Isaac Newton

Source: EL/N1/56, Royal Society Library, London, UK

Published online: June 2014

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  - 7 February 2014
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<56r>

July 14. 16{illeg}|8|6.

S^r

I have considered yo^r proposal about wooden cuts & beleive it will be much convenienter for y^e Reader & may be sufficiently handsome but I leave it to your determination. If you go this way, then I desire you would divide y^e first figure into these two. I crouded y^m into one to save y^e trouble of altering y^e numbers in y^e schemes you have. I am very sensible of y^e great kindness of y^e Gentlemen of your Society to me, far beyond w^t I could ever expect or deserve & know how to distinguish between their favour & anothers humour. Now I understand he was in some respects misrepresented to me I wish I had spared y^e Postscript in my last. This is true, that his Letters occasioned my finding the method of determining Figures, w^ch when I had tried in y^e Ellipsis, I threw the calculation by being upon other studies & so it rested for about 5 yeares till upon your request I sought for y^t paper, & not finding it did it again & reduced it into y^e Propositions shewed you by M^r Paget: but for y^e duplicate proportion I can affirm y^t I gathered it from Keplers Theorem about 20 yeares ago. And so S^r Christopher Wren's examining y^e Ellipsis over ag^t y^e Focus shews y^t he knew it many yeares ago before he left of his enquiry after y^e figure by an imprest motion & a descent compounded together. There was another thing in M^r Hooks letters w^ch he will think I had from him. He told me y^t my proposed exp^t about y^e descent of falling bodies was not y^e only way to prove y^e motion ofy^e earth & so added y^e exp^t of yo^r Pendulum Clock at S^t Helle{na} as an argum^t of gravities being lessened at y^e equator by y^e diurnal moti{on.} The exp^t was new to me but not y^e notion. For in y^t very paper w^ch I told you was writ some time above 15 yeares ago & to y^e best of my memory was writ 18 or 19 years ago, I calculated y^e force of ascent at y^e Equator arising from y^e earth's diurnal motion in order to know what would be y^e diminution \of gravity/ thereby. But yet to do this business right is a thing of far greater difficulty then I was aware of. A third thing there was in his letters, w^ch was new to me & I shall acknowledge it if I make use of it. 'Twas y^e deflexion of falling f|b|odies to y^e south east in o^r Latitude. And now having sincerely told you y^e case between M^r Hook & me I hope I shall be free for y^e future from y^e prejudice of his Letters. I have considered how best to compose y^e present dispute & I think it may be done by y^e inclosed Scholium to y^e fourth Proposition. In {illeg} turning over some old papers I met with another demonstration of that Proposition, w^ch I have added at y^e end of this Scholium. Which is all at present from

Yo^r affectionate Friend & humble Servant

Is. Newton.

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M^r Newton
July. 14 1686

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Lres from M^r Newton
Aug. 20. July. 14. Octob. 18

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