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<title>Letter to Edmund Halley on the doctrine of projectiles and motions of the heavens</title>
<author xml:id="in"><persName key="nameid_1" sort="Newton, Isaac" ref="nameid_1" xml:base="http://www.newtonproject.sussex.ac.uk/catalogue/xml/persNames.xml">Isaac Newton</persName></author>

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<extent><hi rend="italic">c.</hi> <num n="word_count" value="2719">2,719</num> words</extent>

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<authority>The Newton Project</authority>
<pubPlace>Falmer</pubPlace>
<date>2014</date>
<publisher>Newton Project, University of Sussex</publisher>
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<note type="metadataLine">20 June 1686, in English with a little Latin, <hi rend="italic">c.</hi> 2,729 words, 4 pp.</note>
<note n="pages">4 pp.</note>
<note n="language">
<p>in English with a little Latin</p>
</note>
<note n="related_texts">
<p>Published in H.W. Turnbull (ed), <hi rend="italic">The Correspondence of Isaac Newton</hi>, vol. 2 (Cambridge: 1960), p. 435</p>
</note>
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<origDate when="1686-06-20">20 June 1686</origDate>
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<language ident="lat">Latin</language>
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<handNote sameAs="#in">Holograph</handNote>
<handNote xml:id="eh">Edmund Halley</handNote>
<handNote xml:id="unknown1">Unknown Cataloguer (1)</handNote>
<handNote xml:id="unknown2">Unknown Cataloguer (2)</handNote>
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<change when="2014-02-05">Transcription by <name>Daniele Cassisa</name></change>
<change when="2014-06-16" status="released">Code audited by <name xml:id="mjh">Michael Hawkins</name></change>
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<pb xml:id="p055r" n="55r" facs="#i55"/><fw type="shelfmark" place="topLeft" hand="#unknown2"><hi rend="large"><hi rend="bold">55</hi></hi></fw><fw type="shelfmark" place="topLeft" hand="#unknown1">Newton 14</fw><fw type="shelfmark" place="topCenter" hand="#unknown1">55</fw>
<p rend="indent0" xml:id="par1"><choice><abbr>S<hi rend="superscript">r</hi></abbr><expan>Sir</expan></choice></p>
<p xml:id="par2">In order to let you know <choice><abbr>y<hi rend="superscript">e</hi></abbr><expan>the</expan></choice> case between M<hi rend="superscript">r</hi> Hook &amp; me I gave you an <lb xml:id="l1"/>account of <choice><abbr>w<hi rend="superscript">t</hi></abbr><expan>what</expan></choice> past between us in <choice><abbr>o<hi rend="superscript">r</hi></abbr><expan>our</expan></choice> Letters so far as I could remember. For tis long <lb xml:id="l2"/>since they were writ &amp; I do not know that I have seen <choice><abbr>y<hi rend="superscript">m</hi></abbr><expan>them</expan></choice> since. I am almost con<lb xml:id="l3"/>fident by circumstances that <choice><abbr>S<hi rend="superscript">r</hi></abbr><expan>Sir</expan></choice> Chr. Wren knew <choice><abbr>y<hi rend="superscript">e</hi></abbr><expan>the</expan></choice> duplicate proportion <choice><abbr>w<hi rend="superscript">n</hi></abbr><expan>when</expan></choice> I gave him <lb xml:id="l4"/>a visit, &amp; then M<hi rend="superscript">r</hi> Hook (by his book Cometa written afterward) will prove <choice><abbr>y<hi rend="superscript">e</hi></abbr><expan>the</expan></choice> last <lb xml:id="l5"/>of us three <choice><abbr>y<hi rend="superscript">t</hi></abbr><expan>that</expan></choice> knew it. I intended in this Letter to let you understand <choice><abbr>y<hi rend="superscript">e</hi></abbr><expan>the</expan></choice> case fully <lb xml:id="l6"/>but it being a frivolous business, I shal content my self to give you <choice><abbr>y<hi rend="superscript">e</hi></abbr><expan>the</expan></choice> heads of it <lb xml:id="l7"/>in short: viz<hi rend="superscript">t</hi> <choice><abbr>y<hi rend="superscript">t</hi></abbr><expan>that</expan></choice> I never extended <choice><abbr>y<hi rend="superscript">e</hi></abbr><expan>the</expan></choice> duplicate proportion lower then to <choice><abbr>y<hi rend="superscript">e</hi></abbr><expan>the</expan></choice> superficies <lb xml:id="l8"/>of <choice><abbr>y<hi rend="superscript">e</hi></abbr><expan>the</expan></choice> earth &amp; before a certain demonstration I found <choice><abbr>y<hi rend="superscript">e</hi></abbr><expan>the</expan></choice> last year have suspected <lb xml:id="l9"/>it did not reach accurately enough down so low: &amp; therefore in <choice><abbr>y<hi rend="superscript">e</hi></abbr><expan>the</expan></choice> doctrine of <lb xml:id="l10"/>projectiles never used it nor considered <choice><abbr>y<hi rend="superscript">e</hi></abbr><expan>the</expan></choice> motions of <choice><abbr>y<hi rend="superscript">e</hi></abbr><expan>the</expan></choice> heavens: &amp; consequently <lb xml:id="l11"/>M<hi rend="superscript">r</hi> Hook could not from my Letters <choice><abbr>w<hi rend="superscript">ch</hi></abbr><expan>which</expan></choice> were about Projectiles &amp; <choice><abbr>y<hi rend="superscript">e</hi></abbr><expan>the</expan></choice> regions de<lb type="hyphenated" xml:id="l12"/>scending hence to <choice><abbr>y<hi rend="superscript">e</hi></abbr><expan>the</expan></choice> center conclude me ignorant of <choice><abbr>y<hi rend="superscript">e</hi></abbr><expan>the</expan></choice> Theory of <choice><abbr>y<hi rend="superscript">e</hi></abbr><expan>the</expan></choice> Heavens. <lb xml:id="l13"/>That what he told me of <choice><abbr>y<hi rend="superscript">e</hi></abbr><expan>the</expan></choice> duplicate proportion was erroneous, namely that it <lb xml:id="l14"/>reacht down from hence to <choice><abbr>y<hi rend="superscript">e</hi></abbr><expan>the</expan></choice> center of <choice><abbr>y<hi rend="superscript">e</hi></abbr><expan>the</expan></choice> earth. That it is not candid <del type="over"><gap reason="illgblDel" unit="chars" extent="3"/></del><add place="over" indicator="no">to</add> <lb xml:id="l15"/>require me now to confess my self in print <del type="over"><gap reason="illgblDel" unit="chars" extent="2"/></del><add place="over" indicator="no">th</add>en ignorant of <choice><abbr>y<hi rend="superscript">e</hi></abbr><expan>the</expan></choice> duplicate pro<lb xml:id="l16"/>portion in <choice><abbr>y<hi rend="superscript">e</hi></abbr><expan>the</expan></choice> heavens for no other reason but because he had told it me in <lb xml:id="l17"/>the case of projectiles &amp; so upon mistaken grounds accused me of that ignorance. <lb xml:id="l18"/>That in my answer to his first letter I refused his correspondence, told him I had <lb xml:id="l19"/>laid Philosophy aside, sent him only <choice><abbr>y<hi rend="superscript">e</hi></abbr><expan>the</expan></choice> <choice><abbr>experim<hi rend="superscript">t</hi></abbr><expan>experiment</expan></choice> of Projectiles (rather shortly <lb xml:id="l20"/>hinted then carefully described) in <choice><abbr>complem<hi rend="superscript">t</hi></abbr><expan>complement</expan></choice> to sw<del type="over">i</del><add place="over" indicator="no">e</add>eten my Answer, expected <lb xml:id="l21"/>to heare no further from him, could scarce perswade my self to answer his <lb xml:id="l22"/>second letter, did not answer his third, was upon other things, thought no <lb xml:id="l23"/>further of philosophical matters then his letters put me upon it, &amp; therefore <lb xml:id="l24"/>may be allowed not to have had my thoughts of that kind about me so well <lb xml:id="l25"/>at that time. That by the same reason he conclude<del type="over"><gap reason="illgblDel" unit="chars" extent="1"/></del><add place="over" indicator="no">s</add> me then ignorant of <lb xml:id="l26"/><choice><abbr>y<hi rend="superscript">e</hi></abbr><expan>the</expan></choice> duplicate proportion he may as well conclude me ignorant of <choice><abbr>y<hi rend="superscript">e</hi></abbr><expan>the</expan></choice> rest of <lb xml:id="l27"/>that Theory I had read before in his books. That in one <del type="over"><gap reason="illgblDel" unit="chars" extent="1"/></del><add place="over" indicator="no">o</add>f my papers writ <lb xml:id="l28"/>(I cannot say in what year but I am sure some time before I had any <lb xml:id="l29"/>correspondence <choice><abbr>w<hi rend="superscript">th</hi></abbr><expan>with</expan></choice> M<hi rend="superscript">r</hi> Oldenburg &amp; that's) above fifteen years ago, the proportion <lb xml:id="l30"/>of <choice><abbr>y<hi rend="superscript">e</hi></abbr><expan>the</expan></choice> forces of <choice><abbr>y<hi rend="superscript">e</hi></abbr><expan>the</expan></choice> Planets from <choice><abbr>y<hi rend="superscript">e</hi></abbr><expan>the</expan></choice> Sun reciprocally duplicate to their distan<lb xml:id="l31"/>ces from him is exprest &amp; <choice><abbr>y<hi rend="superscript">e</hi></abbr><expan>the</expan></choice> proportion of <choice><abbr>o<hi rend="superscript">r</hi></abbr><expan>our</expan></choice> gravity to <choice><abbr>y<hi rend="superscript">e</hi></abbr><expan>the</expan></choice> Moon's <foreign xml:lang="lat">conatus <lb xml:id="l32"/>recedendi a centro Terræ</foreign> is calculated thô not accurately enough. That <choice><abbr>w<hi rend="superscript">n</hi></abbr><expan>when</expan></choice> <lb xml:id="l33"/>Hugenius put out his <choice><abbr><foreign xml:lang="lat">Horol. Oscil.</foreign></abbr><expan><foreign xml:lang="lat">Horologium Oscillatorium</foreign></expan></choice> a copy being presented to me; in my letter of <lb xml:id="l34"/>thanks to him I gave those rules in <choice><abbr>y<hi rend="superscript">e</hi></abbr><expan>the</expan></choice> end thereof a particular commendation <lb xml:id="l35"/>for their usefulness in Philosophy, &amp; added out of my aforesaid paper an in<lb type="hyphenated" xml:id="l36"/>stance of their usefulness in comparing <choice><abbr>y<hi rend="superscript">e</hi></abbr><expan>the</expan></choice> forces of <choice><abbr>y<hi rend="superscript">e</hi></abbr><expan>the</expan></choice> Moon from <choice><abbr>y<hi rend="superscript">e</hi></abbr><expan>the</expan></choice> earth <lb xml:id="l37"/>&amp; earth from <choice><abbr>y<hi rend="superscript">e</hi></abbr><expan>the</expan></choice> Sun in determining a Probleme about <choice><abbr>y<hi rend="superscript">e</hi></abbr><expan>the</expan></choice> Moons phase &amp; putting <lb xml:id="l38"/>a limit to <choice><abbr>y<hi rend="superscript">e</hi></abbr><expan>the</expan></choice> Sun's parallax. Which shews that I had then my eye upon com<lb xml:id="l39"/>paring <choice><abbr>y<hi rend="superscript">e</hi></abbr><expan>the</expan></choice> forces of <choice><abbr>y<hi rend="superscript">e</hi></abbr><expan>the</expan></choice> Planets arising from their circular motion &amp; understoo<supplied reason="faded">d</supplied> <lb xml:id="l40"/>it: so that a while after <choice><abbr>w<hi rend="superscript">n</hi></abbr><expan>when</expan></choice> M<hi rend="superscript">r</hi> Hook propounded <choice><abbr>y<hi rend="superscript">e</hi></abbr><expan>the</expan></choice> Probleme solemnly in <lb xml:id="l41"/><choice><abbr>y<hi rend="superscript">e</hi></abbr><expan>the</expan></choice> end of his <hi rend="underline">Attempt to prove <choice><abbr>y<hi rend="superscript">e</hi></abbr><expan>the</expan></choice> motion of <choice><abbr>y<hi rend="superscript">e</hi></abbr><expan>the</expan></choice> earth</hi>, if I had not known <choice><abbr>y<hi rend="superscript">e</hi></abbr><expan>the</expan></choice> <lb xml:id="l42"/>duplicate proportion before I could not but have found it now. Between 10 &amp; <lb xml:id="l43"/>11 years ago there was an Hypothesis <add place="supralinear" indicator="yes">of mine</add> registred in <choice><abbr>yo<hi rend="superscript">r</hi></abbr><expan>your</expan></choice> <del type="over"><gap reason="illgblDel" unit="chars" extent="1"/></del><add place="over" indicator="no">b</add>ooks, wherein I hinted a <lb xml:id="l44"/>cause of gravity towards <choice><abbr>y<hi rend="superscript">e</hi></abbr><expan>the</expan></choice> earth Sun &amp; Planets <choice><abbr>w<hi rend="superscript">th</hi></abbr><expan>with</expan></choice> <choice><abbr>y<hi rend="superscript">e</hi></abbr><expan>the</expan></choice> dependance of <choice><abbr>y<hi rend="superscript">e</hi></abbr><expan>the</expan></choice> celestial <lb xml:id="l45"/>motions thereon: in <choice><abbr>w<hi rend="superscript">ch</hi></abbr><expan>which</expan></choice> <choice><abbr>y<hi rend="superscript">e</hi></abbr><expan>the</expan></choice> proportion of <choice><abbr>y<hi rend="superscript">e</hi></abbr><expan>the</expan></choice> decrease of gravity from <choice><abbr>y<hi rend="superscript">e</hi></abbr><expan>the</expan></choice> superficies <lb xml:id="l46"/>of <choice><abbr>y<hi rend="superscript">e</hi></abbr><expan>the</expan></choice> Planet (thô for brevities sake not there exprest) can be no other then re<lb type="hyphenated" xml:id="l47"/>ciprocally duplicate of <choice><abbr>y<hi rend="superscript">e</hi></abbr><expan>the</expan></choice> distance from <choice><abbr>y<hi rend="superscript">e</hi></abbr><expan>the</expan></choice> center. And I hope I shall not be urge<supplied reason="faded">d</supplied> <lb xml:id="l48"/>to declare in print <add place="supralinear" indicator="yes">that I understood not</add> <choice><abbr>y<hi rend="superscript">e</hi></abbr><expan>the</expan></choice> obvious mathematical conditions of my own Hypothesis. But <lb xml:id="l49"/>grant I received it afterwards from M<hi rend="superscript">r</hi> Hook, yet have I as great a right to it <lb xml:id="l50"/>as to <choice><abbr>y<hi rend="superscript">e</hi></abbr><expan>the</expan></choice> Ellipsis. For as Kepler knew <choice><abbr>y<hi rend="superscript">e</hi></abbr><expan>the</expan></choice> Orb to be not circular but oval &amp; guest <lb xml:id="l51"/>it to be Elliptical, so M<hi rend="superscript">r</hi> Hook without knowing what I have found out since his <lb xml:id="l52"/>letters to me, can know no more but that <choice><abbr>y<hi rend="superscript">e</hi></abbr><expan>the</expan></choice> proportion was duplicate <foreign xml:lang="lat">quam proximè</foreign> <lb xml:id="l53"/>at great distances from <choice><abbr>y<hi rend="superscript">e</hi></abbr><expan>the</expan></choice> center, &amp; only guest it to be so accurately &amp; guest amiss <pb xml:id="p055v" n="55v" facs="#i56"/> in extending <choice><abbr>y<hi rend="superscript">t</hi></abbr><expan>that</expan></choice> proportion down to <choice><abbr>y<hi rend="superscript">e</hi></abbr><expan>the</expan></choice> very center, whereas Kepler guest right at <lb xml:id="l54"/><choice><abbr>y<hi rend="superscript">e</hi></abbr><expan>the</expan></choice> Ellipsis. And so M<hi rend="superscript">r</hi> Hook found less of <choice><abbr>y<hi rend="superscript">e</hi></abbr><expan>the</expan></choice> Proportion then Kepler of <choice><abbr>y<hi rend="superscript">e</hi></abbr><expan>the</expan></choice> Ellipsis. <lb xml:id="l55"/>There is so strong an objection against <choice><abbr>y<hi rend="superscript">e</hi></abbr><expan>the</expan></choice> accurateness of this proportion, <choice><abbr>y<hi rend="superscript">t</hi></abbr><expan>that</expan></choice> without <lb xml:id="l56"/>my Demonstrations, to <choice><abbr>w<hi rend="superscript">ch</hi></abbr><expan>which</expan></choice> M<hi rend="superscript">r</hi> Hook is yet a stranger, it cannot be beleived by a <lb xml:id="l57"/>judicious Philosopher to be any where accurate. And so in stating this business I <lb xml:id="l58"/>do pretend to have done as much for <choice><abbr>y<hi rend="superscript">e</hi></abbr><expan>the</expan></choice> proportion as for <choice><abbr>y<hi rend="superscript">e</hi></abbr><expan>the</expan></choice> Ellipsis &amp; to have <lb xml:id="l59"/>as much right to <choice><abbr>y<hi rend="superscript">e</hi></abbr><expan>the</expan></choice> one from M<hi rend="superscript">r</hi> Hook &amp; all men as to <choice><abbr>y<hi rend="superscript">e</hi></abbr><expan>the</expan></choice> other from Kepler. <lb xml:id="l60"/>And therefor<del type="over"><gap reason="blotDel" unit="chars" extent="1"/></del><add place="over" indicator="no">e</add> on this account also he must at least moderate his pretenses.</p>
<space dim="vertical" unit="lines" extent="1"/>
<p xml:id="par3">The Proof you sent me I like very well. I designed <choice><abbr>y<hi rend="superscript">e</hi></abbr><expan>the</expan></choice> whole to consist of <lb xml:id="l61"/>three books, the second was finished last summer being short &amp; only wants transcri<lb xml:id="l62"/>bing &amp; drawing the cuts fairly. Some new Propositions I have since thought on <lb xml:id="l63"/><choice><abbr>w<hi rend="superscript">ch</hi></abbr><expan>which</expan></choice> I can as well let alone. The third wants <choice><abbr>y<hi rend="superscript">e</hi></abbr><expan>the</expan></choice> Theory of Comets. In Autumn <lb xml:id="l64"/>last I spent two months in calculations to no purpose for want of a good method, <lb xml:id="l65"/><choice><abbr>w<hi rend="superscript">ch</hi></abbr><expan>which</expan></choice> made me afterwards return to <choice><abbr>y<hi rend="superscript">e</hi></abbr><expan>the</expan></choice> first Book &amp; enlarge it <choice><abbr>w<hi rend="superscript">th</hi></abbr><expan>with</expan></choice> divers Propo<lb xml:id="l66"/>sitions some relating to Comets others to other things found out last Winter. The <lb xml:id="l67"/>third I now designe to suppress. Philosophy is such an impertinently litigious <lb xml:id="l68"/>Lady that a man had as good be engaged in Law suits <del type="strikethrough">as come neare</del> <add place="supralinear" indicator="yes">as have to do with</add> her<supplied reason="omitted">.</supplied> I found it so formerly &amp; now I no sooner come near her again but she <lb xml:id="l69"/>gives me warning. The two first books without the third will not so well <lb xml:id="l70"/>beare <choice><abbr>y<hi rend="superscript">e</hi></abbr><expan>the</expan></choice> title of <foreign xml:lang="lat">Philosophiæ naturalis Principia Mathematica</foreign> &amp; therefore I <lb xml:id="l71"/>had altered it to this <foreign xml:lang="lat">De motu corporum libri duo</foreign>: but upon second thoughts I <lb xml:id="l72"/>retain <choice><abbr>y<hi rend="superscript">e</hi></abbr><expan>the</expan></choice> former title. Twill help <choice><abbr>y<hi rend="superscript">e</hi></abbr><expan>the</expan></choice> sale of <choice><abbr>y<hi rend="superscript">e</hi></abbr><expan>the</expan></choice> book <choice><abbr>w<hi rend="superscript">ch</hi></abbr><expan>which</expan></choice> I ought not to diminish <lb xml:id="l73"/>now tis <choice><abbr>yo<hi rend="superscript">rs</hi></abbr><expan>yours</expan></choice>. The Articles are <choice><abbr>w<hi rend="superscript">th</hi></abbr><expan>with</expan></choice> <choice><abbr>y<hi rend="superscript">e</hi></abbr><expan>the</expan></choice> largest to be called by that name. If you <lb xml:id="l74"/>please you may change <choice><abbr>y<hi rend="superscript">e</hi></abbr><expan>the</expan></choice> word to <hi rend="underline">sections</hi>, th<del type="over"><gap reason="illgblDel" unit="chars" extent="1"/></del><add place="over" indicator="no">ô</add> it be not material. In <choice><abbr>y<hi rend="superscript">e</hi></abbr><expan>the</expan></choice> first <lb xml:id="l75"/>page I have struck out <choice><abbr>y<hi rend="superscript">e</hi></abbr><expan>the</expan></choice> words <foreign xml:lang="lat"><hi rend="underline">uti posthac</hi> <hi rend="underline">docebitur</hi></foreign> as referring to <choice><abbr>y<hi rend="superscript">e</hi></abbr><expan>the</expan></choice> third book. <lb xml:id="l76"/>Which is all at present from</p>
<p rend="indent25" xml:id="par4"><choice><abbr>Yo<hi rend="superscript">r</hi></abbr><expan>Your</expan></choice> affectionate friend &amp;</p>
<p rend="indent30" xml:id="par5">humble Servant</p>
<p rend="indent35" xml:id="par6">Is: Newton.</p>
<p rend="indent0" xml:id="par7">Cambridge <lb type="intentional" xml:id="l77"/>June 20. 1686.</p>
<space dim="vertical" unit="lines" extent="7"/>
<p xml:id="par8">Since my writing this letter I am told by one who had it from another <lb xml:id="l78"/>lately present at one of <choice><abbr>yo<hi rend="superscript">r</hi></abbr><expan>your</expan></choice> meetings, how that M<hi rend="superscript">r</hi> Hook should there make a great <lb xml:id="l79"/>stir pretending I had all from him &amp; desiring they would see that he had justice <lb xml:id="l80"/>done him. This carriage towards me is very strange &amp; undeserved, so that I <lb xml:id="l81"/>cannot forbeare <add place="supralinear" indicator="yes">in stating <choice><abbr>y<hi rend="superscript">t</hi></abbr><expan>that</expan></choice> point of justice</add> to tell you further, that he has published Borell's Hypothesis in <lb xml:id="l82"/>his own name &amp; the asserting of this to himself &amp; completing it as his own, seems <lb xml:id="l83"/>to me the ground of all <choice><abbr>y<hi rend="superscript">e</hi></abbr><expan>the</expan></choice> stir he makes. Borel did something in it &amp; wrote <lb xml:id="l84"/>modestly, he has <del type="strikethrough">such a way</del> done nothing &amp; yet written in such a way as if <lb xml:id="l85"/>he knew &amp; had sufficiently hinted all but what remained to be determined by <choice><abbr>y<hi rend="superscript">e</hi></abbr><expan>the</expan></choice> <lb xml:id="l86"/>drudgery of calculations &amp; observations, excusing himself from that labour by reason <lb xml:id="l87"/>of his other business: whereas he should rather have excused himself by reason of <lb xml:id="l88"/>his inability. For tis plain by his words he knew not how to go about it. Now <lb xml:id="l89"/>is not this very fine? Mathematicians that find out, settle &amp; do all the business <lb xml:id="l90"/>must content themselves with being nothing but dry calculators &amp; drudges &amp; another <lb xml:id="l91"/><supplied reason="faded" cert="high">that</supplied> does nothing but pretend &amp; grasp at all things must carry away all the invention <fw type="catch" place="bottomRight"><del type="cancelled"><gap reason="illgblDel" unit="chars" extent="1"/></del> as</fw><pb xml:id="p055ar" n="55ar" facs="#i57"/><fw type="shelfmark" place="topLeft" hand="#unknown2"><hi rend="large"><hi rend="bold"><supplied reason="damage" cert="high">5</supplied>5–</hi></hi></fw> as well of those that were to follow him as of those that went before. Much after <lb xml:id="l92"/>the same manner were his letters writ to me, telling me that gravity in descent <lb xml:id="l93"/>from hence to <choice><abbr>y<hi rend="superscript">e</hi></abbr><expan>the</expan></choice> center of <choice><abbr>y<hi rend="superscript">e</hi></abbr><expan>the</expan></choice> earth was reciprocally in a duplicate ratio of <choice><abbr>y<hi rend="superscript">e</hi></abbr><expan>the</expan></choice> <lb xml:id="l94"/>altitude, that <choice><abbr>y<hi rend="superscript">e</hi></abbr><expan>the</expan></choice> figure described by projectiles in this region would be an Ellipsis <lb xml:id="l95"/>&amp; that all <choice><abbr>y<hi rend="superscript">e</hi></abbr><expan>the</expan></choice> motions of <choice><abbr>y<hi rend="superscript">e</hi></abbr><expan>the</expan></choice> heavens were t<del type="over"><gap reason="illgblDel" unit="chars" extent="1"/></del><add place="over" indicator="no">h</add>us to be accounted for: &amp; this he did <lb xml:id="l96"/>in such a way as if he had found out all &amp; knew it most certainly. And <lb xml:id="l97"/>upon this information I must now acknowledge in print I had all from him &amp; so <lb xml:id="l98"/>did nothing my self but drudge <del type="cancelled"><gap reason="illgblDel" unit="chars" extent="1"/></del> in calculating demonstrating &amp; writing upon <lb xml:id="l99"/><choice><abbr>y<hi rend="superscript">e</hi></abbr><expan>the</expan></choice> inventions of this great man. And yet after all, the first of those three <lb xml:id="l100"/>things he told me is fals &amp; very unphilosophical, the second is as fals &amp; <choice><abbr>y<hi rend="superscript">e</hi></abbr><expan>the</expan></choice> <lb xml:id="l101"/>third was more then he knew or could affirm me ignorant of by any <lb xml:id="l102"/>thing that past between us in <choice><abbr>o<hi rend="superscript">r</hi></abbr><expan>our</expan></choice> letters. Nor do I understand by <add place="supralinear" indicator="yes"><choice><abbr>w<hi rend="superscript">t</hi></abbr><expan>what</expan></choice></add> right he <lb xml:id="l103"/>claims it as his own. For as Borell wrote long before him that by <lb xml:id="l104"/>a tendency of <choice><abbr>y<hi rend="superscript">e</hi></abbr><expan>the</expan></choice> Planets towards <choice><abbr>y<hi rend="superscript">e</hi></abbr><expan>the</expan></choice> sun like that of gravity or magnetism <lb xml:id="l105"/>the Planets would move in Ellipses, so Bullialdus wrote that all force re<lb type="hyphenated" xml:id="l106"/>specting <choice><abbr>y<hi rend="superscript">e</hi></abbr><expan>the</expan></choice> Sun as its center &amp; depending on matter must be reciprocally <lb xml:id="l107"/>in a duplicate ratio of <choice><abbr>y<hi rend="superscript">e</hi></abbr><expan>the</expan></choice> distance from <choice><abbr>y<hi rend="superscript">e</hi></abbr><expan>the</expan></choice> center, &amp; used that very <lb xml:id="l108"/>argument for it by <choice><abbr>w<hi rend="superscript">ch</hi></abbr><expan>which</expan></choice> you, <choice><abbr>S<hi rend="superscript">r</hi></abbr><expan>Sir</expan></choice>, in the last Transactions have proved <lb xml:id="l109"/>this ratio in gravity. Now if M<hi rend="superscript">r</hi> Hook from this general Proposition in Bul<lb type="hyphenated" xml:id="l110"/>lialdus might learn <choice><abbr>y<hi rend="superscript">e</hi></abbr><expan>the</expan></choice> proportion in gravity, why must this proportion here <lb xml:id="l111"/>go for his invention? My letter to Hugenius <add place="supralinear" indicator="yes"><choice><abbr>w<hi rend="superscript">ch</hi></abbr><expan>which</expan></choice> I mentioned above</add> was directed to M<hi rend="superscript">r</hi> Oldenburg <lb xml:id="l112"/>who used to keep <choice><abbr>y<hi rend="superscript">e</hi></abbr><expan>the</expan></choice> Originals. His papers came into M<hi rend="superscript">r</hi> Hooks possession. M<hi rend="superscript">r</hi> <lb xml:id="l113"/>Hook knowing my hand might have <choice><abbr>y<hi rend="superscript">e</hi></abbr><expan>the</expan></choice> curiosity to look into that letter &amp; thence <lb xml:id="l114"/>take <choice><abbr>y<hi rend="superscript">e</hi></abbr><expan>the</expan></choice> notion of comparing <choice><abbr>y<hi rend="superscript">e</hi></abbr><expan>the</expan></choice> forces of <choice><abbr>y<hi rend="superscript">e</hi></abbr><expan>the</expan></choice> Planets arising from their circular <lb xml:id="l115"/>motion &amp; so what he wrote to me afterwards about <choice><abbr>y<hi rend="superscript">e</hi></abbr><expan>the</expan></choice> rate of gravity, might <lb xml:id="l116"/>be nothing but <choice><abbr>y<hi rend="superscript">e</hi></abbr><expan>the</expan></choice> fruit of my own Garden. And its more then I can affirm <choice><abbr>y<hi rend="superscript">t</hi></abbr><expan>that</expan></choice> <choice><abbr>y<hi rend="superscript">e</hi></abbr><expan>the</expan></choice> <lb xml:id="l117"/>duplicate proportion was not <add place="supralinear" indicator="yes">exprest</add> in that letter. However he knew it not (<del type="over">i</del><add place="over" indicator="no">a</add>s I gather from <lb xml:id="l118"/>his books) till five years after any Mathematician could have told it him. For when <lb xml:id="l119"/>Hugenius had told how to find <choice><abbr>y<hi rend="superscript">e</hi></abbr><expan>the</expan></choice> force in all cases of circular motion, he <lb xml:id="l120"/>had told <choice><abbr>'em</abbr><expan>them</expan></choice> how to do it in this as w<del type="over"><gap reason="illgblDel" unit="chars" extent="1"/></del><add place="over" indicator="no">e</add>ll as all others. And so <choice><abbr>y<hi rend="superscript">e</hi></abbr><expan>the</expan></choice> honour of doing <lb xml:id="l121"/>it <add place="inline" indicator="no">in</add> this <del type="cancelled">way</del> is due to Hugenius. For another five <add place="supralinear" indicator="yes">years</add> after to claim it as his own <lb xml:id="l122"/>invention, is as if some Mechanick who had learnt <choice><abbr>y<hi rend="superscript">e</hi></abbr><expan>the</expan></choice> Art of surveying from a <lb xml:id="l123"/>Master should afterwards claim the surveying of this or that piece of ground <lb xml:id="l124"/>for his own invention &amp; keep a heavy quarter to be in print for <choice><abbr>'t</abbr><expan>it</expan></choice>. But wh<del type="over"><gap reason="illgblDel" unit="chars" extent="2"/></del><add place="over" indicator="no">at</add> if <lb xml:id="l125"/>this surveyor be a bungler &amp; give in an erroneous survey? M<del type="cancelled"><gap reason="illgblDel" unit="chars" extent="1"/></del><hi rend="superscript">r</hi> Hook has erred <lb xml:id="l126"/>in the invention he pretends to &amp; his error is <choice><abbr>y<hi rend="superscript">e</hi></abbr><expan>the</expan></choice> cause of all the stirr he makes. <lb xml:id="l127"/>For his extending <choice><abbr>y<hi rend="superscript">e</hi></abbr><expan>the</expan></choice> duplicate proportion down to <choice><abbr>y<hi rend="superscript">e</hi></abbr><expan>the</expan></choice> center (which I do not) <lb xml:id="l128"/>made him correct me &amp; tell me <choice><abbr>y<hi rend="superscript">e</hi></abbr><expan>the</expan></choice> rest of his Theory as a new thing to me <lb xml:id="l129"/>&amp; now stand upon it that I had all from that his letter: notwithstanding that <lb xml:id="l130"/>he had told it to all <choice><abbr>y<hi rend="superscript">e</hi></abbr><expan>the</expan></choice> world before &amp; I had seen it in his printed books <lb xml:id="l131"/>all but <choice><abbr>y<hi rend="superscript">e</hi></abbr><expan>the</expan></choice> proportion. And why should I record a man for an Invention who <lb xml:id="l132"/>founds his claim upon an error therein &amp; on that score gives me trouble? He <lb xml:id="l133"/>imagins he obliged me by telling me his Theory, but I thought my self disobli<lb xml:id="l134"/>ged by being upon his own mistake corrected magisterially &amp; taught a Theory <lb xml:id="l135"/><choice><abbr>w<hi rend="superscript">ch</hi></abbr><expan>which</expan></choice> every body knew &amp; I had a truer notion of then himself. Should a man <lb xml:id="l136"/>who thinks himself knowing, &amp; loves to shew it in correcting &amp; instructing others, <lb xml:id="l137"/>come to you when you are busy, &amp; notwithstanding your excuse, press discourses <lb xml:id="l138"/>upon you &amp; through his own mistakes <del type="cancelled">pr<gap reason="illgblDel" unit="chars" extent="2"/></del> correct you &amp; multiply discourses &amp; <lb xml:id="l139"/>then make this use of it, to boast that he taught you all he spake &amp; oblige <lb xml:id="l140"/>you to acknowledge it &amp; cry out injury &amp; injustice if you do not, I beleive <lb xml:id="l141"/>you would think him a man of a strange unsociable temper. M<hi rend="superscript">r</hi> Hooks letters <lb xml:id="l142"/>in several respects abounded too much <choice><abbr>w<hi rend="superscript">th</hi></abbr><expan>with</expan></choice> that humour <choice><abbr>w<hi rend="superscript">ch</hi></abbr><expan>which</expan></choice> Hevelius &amp; others <lb xml:id="l143"/>complain of &amp; therefore he may do well <add place="supralinear" indicator="yes">in time</add> to consider whether after this new <supplied reason="damage">pro</supplied>vocation I be much more bound <del type="cancelled"><gap reason="illgblDel" unit="chars" extent="1"/></del> (in doing him that justice he claims) to make an hon<supplied reason="damage">ourable</supplied> <pb xml:id="p055av" n="55av" facs="#i58"/> mention of him in <del type="over"><gap reason="illgblDel" unit="chars" extent="1"/></del><add place="over" indicator="no">p</add>rint, especially since this is <choice><abbr>y<hi rend="superscript">e</hi></abbr><expan>the</expan></choice> third time that he has given <lb xml:id="l144"/>me trouble in this kind.</p>
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<p xml:id="par9">For your further satisfaction in this business, I beg <choice><abbr>y<hi rend="superscript">e</hi></abbr><expan>the</expan></choice> favour you would con<lb type="hyphenated" xml:id="l145"/>sult <choice><abbr>yo<hi rend="superscript">r</hi></abbr><expan>your</expan></choice> books for a paper of mine entitled, <hi rend="underline">An Hypothesis explaining <choice><abbr>y<hi rend="superscript">e</hi></abbr><expan>the</expan></choice> properties of light</hi>. <choice><abbr>Twas</abbr><expan>It was</expan></choice> dated Decemb. 7<hi rend="superscript">th</hi> 1675 &amp; registred in your Book about <lb xml:id="l146"/>Ian or Feb following. Not far from <choice><abbr>y<hi rend="superscript">e</hi></abbr><expan>the</expan></choice> beginning there is a Paragraph ending <lb xml:id="l147"/><choice><abbr>w<hi rend="superscript">th</hi></abbr><expan>with</expan></choice> these words. <hi rend="underline">And as <choice><abbr>y<hi rend="superscript">e</hi></abbr><expan>the</expan></choice> Earth so perhaps may the Sun imbibe this spirit copi<lb xml:id="l148"/>ously to conserve his shining &amp; keep <choice><abbr>y<hi rend="superscript">e</hi></abbr><expan>the</expan></choice> Planets from receding further from him <lb xml:id="l149"/>&amp; they that will may also suppose that this spirit affords or carries thither the solary <lb xml:id="l150"/>fewel &amp; materiall principle if light: And that <choice><abbr>y<hi rend="superscript">e</hi></abbr><expan>the</expan></choice> vast ethereal spaces between <lb xml:id="l151"/>us &amp; <choice><abbr>y<hi rend="superscript">e</hi></abbr><expan>the</expan></choice> stars are for a sufficient repository for this food if <choice><abbr>y<hi rend="superscript">e</hi></abbr><expan>the</expan></choice> Sun &amp; Planets. <lb xml:id="l152"/>But this if <choice><abbr>y<hi rend="superscript">e</hi></abbr><expan>the</expan></choice> constitution if ethereal natures by <choice><abbr>y<hi rend="superscript">e</hi></abbr><expan>the</expan></choice> by</hi>. In these &amp; <choice><abbr>y<hi rend="superscript">e</hi></abbr><expan>the</expan></choice> foregoing <lb xml:id="l153"/>words you have <choice><abbr>y<hi rend="superscript">e</hi></abbr><expan>the</expan></choice> common cause of gravity towards <choice><abbr>y<hi rend="superscript">e</hi></abbr><expan>the</expan></choice> earth Sun &amp; all the <lb xml:id="l154"/>Planets, &amp; that by this cause <choice><abbr>y<hi rend="superscript">e</hi></abbr><expan>the</expan></choice> Planets are kept in their Orbs about <choice><abbr>y<hi rend="superscript">e</hi></abbr><expan>the</expan></choice> Sun. <lb xml:id="l155"/>And this is all <choice><abbr>y<hi rend="superscript">e</hi></abbr><expan>the</expan></choice> Philosophy M<hi rend="superscript">r</hi> Hook pretends I had from his letters some <lb xml:id="l156"/>years after, the duplicate proportion only excepted. The preceding words contein <lb xml:id="l157"/><choice><abbr>y<hi rend="superscript">e</hi></abbr><expan>the</expan></choice> cause of <choice><abbr>y<hi rend="superscript">e</hi></abbr><expan>the</expan></choice> phænomena of gravity as we find it on <choice><abbr>y<hi rend="superscript">e</hi></abbr><expan>the</expan></choice> surf<del type="over"><gap reason="illgblDel" unit="chars" extent="1"/></del><add place="over" indicator="no">a</add>ce of the earth <lb xml:id="l158"/>without any regard to <choice><abbr>y<hi rend="superscript">e</hi></abbr><expan>the</expan></choice> various distances from <choice><abbr>y<hi rend="superscript">e</hi></abbr><expan>the</expan></choice> center: For at first I designed <lb xml:id="l159"/>to write of nothing more. Afterwards, as my manuscript shews, I interlined <choice><abbr>y<hi rend="superscript">e</hi></abbr><expan>the</expan></choice> <lb xml:id="l160"/>words above cited relating to <choice><abbr>y<hi rend="superscript">e</hi></abbr><expan>the</expan></choice> heavens, &amp; in so short &amp; transitory an inter<lb xml:id="l161"/>lined hint of things, the expression of <choice><abbr>y<hi rend="superscript">e</hi></abbr><expan>the</expan></choice> proportion may well be excused. <lb xml:id="l162"/>But if you consider <choice><abbr>y<hi rend="superscript">e</hi></abbr><expan>the</expan></choice> nature of <choice><abbr>y<hi rend="superscript">e</hi></abbr><expan>the</expan></choice> Hypothesis you'l find that <add place="supralinear" indicator="yes">gravity decreases upward &amp;</add> can be no other <lb xml:id="l163"/>from <choice><abbr>y<hi rend="superscript">e</hi></abbr><expan>the</expan></choice> superficies of <choice><abbr>y<hi rend="superscript">e</hi></abbr><expan>the</expan></choice> Planet then reciprocally duplicate of <choice><abbr>y<hi rend="superscript">e</hi></abbr><expan>the</expan></choice> distance from <lb xml:id="l164"/>the center, but downwards that proportion does not hold. This was but an <lb xml:id="l165"/>Hypothesis &amp; so to be looked upon only as one of my guesses which I did not <lb xml:id="l166"/>rely on: but it sufficiently explains to you why in considering <choice><abbr>y<hi rend="superscript">e</hi></abbr><expan>the</expan></choice> descent of a <lb xml:id="l167"/>body down to <choice><abbr>y<hi rend="superscript">e</hi></abbr><expan>the</expan></choice> center I used not <choice><abbr>y<hi rend="superscript">e</hi></abbr><expan>the</expan></choice> duplicate proportion. In <choice><abbr>y<hi rend="superscript">e</hi></abbr><expan>the</expan></choice> small <lb xml:id="l168"/>ascent &amp; descent of projectiles above <choice><abbr>y<hi rend="superscript">e</hi></abbr><expan>the</expan></choice> earth <choice><abbr>y<hi rend="superscript">e</hi></abbr><expan>the</expan></choice> variation of gravity is so <lb xml:id="l169"/>inconsiderable <choice><abbr>y<hi rend="superscript">t</hi></abbr><expan>that</expan></choice> Mathematicians neglect it. Hence <choice><abbr>y<hi rend="superscript">e</hi></abbr><expan>the</expan></choice> vulgar Hypothesis with <lb xml:id="l170"/>them is uniform gravity. And why might not I as a Mathematician use it fre<lb type="hyphenated" xml:id="l171"/>quently without thinking on <choice><abbr>y<hi rend="superscript">e</hi></abbr><expan>the</expan></choice> philosophy of <choice><abbr>y<hi rend="superscript">e</hi></abbr><expan>the</expan></choice> heavens or beleiving it to be <lb xml:id="l172"/>philosophically true?</p>
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<p rend="indent0" xml:id="par10"><hi rend="large">For M<hi rend="superscript">r</hi> Edmund Halley.</hi></p>
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<p xml:id="par11">M<hi rend="superscript">r</hi> Newton of <lb type="intentional" xml:id="l173"/><space dim="horizontal" unit="chars" extent="5"/> June <hi rend="overline">20</hi><hi rend="superscript">o</hi> 1686</p>
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