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<title xml:id="main_title">Letter from John Collins to Newton, dated 9 September 1676</title>
<author xml:id="jcollins"><persName key="nameid_152" sort="Collins, John" ref="nameid_152" xml:base="http://www.newtonproject.sussex.ac.uk/catalogue/xml/persNames.xml">John Collins</persName></author>

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<extent><hi rend="italic">c.</hi> <num n="word_count" value="452">452</num> words</extent>

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<authority>The Newton Project</authority>
<pubPlace>Falmer</pubPlace>
<date>2012</date>
<publisher>Newton Project, University of Sussex</publisher>
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<note type="metadataLine">9 September 1676, in English with some Latin, <hi rend="italic">c.</hi> 459 words, 1 f.</note>
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<p>in English with some Latin</p>
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<origDate when="1676-09-09">9 September 1676</origDate>
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<pb xml:id="p001r" n="1r" facs="#MS-ADD-03977-012-00001.jpg"/><fw type="shelfmark" place="topRight" hand="#unknown1">(12)</fw><fw type="pag" place="topRight" hand="#unknown2">1</fw>
<p rend="center" xml:id="par1">9<hi rend="superscript">th</hi> September 1676</p>
<p xml:id="par2">M<hi rend="superscript">r</hi> Newton <lb type="intentional" xml:id="l1"/><choice><abbr>S<hi rend="superscript">r</hi></abbr><expan>Sir</expan></choice></p>
<p xml:id="par3">I received yours with the returne of the Papers inclosed, it is likely <lb xml:id="l2"/>being in hast I did not so warily word D<hi rend="superscript">r</hi> Pells sense of the infinite <lb xml:id="l3"/>Series, which whatsoever it be it matters not, for he is utterly a <lb xml:id="l4"/>Stranger to that kind of doctrine, he doth indeed affirme he can gett <lb xml:id="l5"/>the Sum of many Algebraick Nomes giving a roote in order to <choice><abbr>y<hi rend="superscript">e</hi></abbr><expan>the</expan></choice> <lb xml:id="l6"/>raising of a Resolvend, by ayd of tables of <choice><abbr>Logmes</abbr><expan>Logarithmes</expan></choice> or Sines, the <lb xml:id="l7"/>great promises in his Idea being attended with few or noe performances <lb xml:id="l8"/>or Communications suitable causeth his esteeme much to fall &amp;c M<hi rend="superscript">r</hi> <lb xml:id="l9"/>Oldenburgh is gone into the Country for 10 dayes however hath sent <lb xml:id="l10"/>you a Coppy of the Letters both of Leibnitz and Schurnhaus, who <lb xml:id="l11"/>are persons of great worth and Candour, and though they pretend or <lb xml:id="l12"/>assert that the doctrine of infinite Series may be enlarged or the Series <lb xml:id="l13"/>themselves attained by more <add indicator="yes" place="supralinear">easy</add> Principles than yours yet you having already taken the Paines in your owne method, and the Result <lb xml:id="l14"/>though not the Journey the same <add indicator="yes" place="supralinear">in both</add>, <del type="cancelled">yo</del> I thinke notwithstanding you <lb xml:id="l15"/>would doe well to publish the same in Latin or permitt a <lb xml:id="l16"/>Translation and the comming foorth thereof in <choice><abbr>Eng<hi rend="superscript">s</hi></abbr><expan>English</expan></choice>, you will at <lb xml:id="l17"/>first perceive that Leibnitz out of these Data <formula><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mn>AQ</mn><mo>=</mo><mn>r</mn></mrow></math></formula> the radius and <tei:formula xmlns:tei="http://www.tei-c.org/ns/1.0"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mrow><msub><mn mathvariant="normal">Q</mn><mn>1</mn></msub><mn>N</mn></mrow><mo>=</mo><mn>z</mn></mrow></math></tei:formula> hath a designe to find the Ordinate <tei:formula xmlns:tei="http://www.tei-c.org/ns/1.0"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mmultiscripts><mn mathvariant="normal">B</mn><mn>1</mn><mprescripts/><mn>1</mn></mmultiscripts><mn mathvariant="normal">D</mn></mrow></math></tei:formula> by <tei:lb xmlns:tei="http://www.tei-c.org/ns/1.0" xml:id="l18"/>an Analyticall Calculation, by ayd of the Square of the Chord <tei:formula xmlns:tei="http://www.tei-c.org/ns/1.0"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>AD</mn></math></tei:formula> <tei:lb xmlns:tei="http://www.tei-c.org/ns/1.0" xml:id="l19"/>which will be found <tei:formula xmlns:tei="http://www.tei-c.org/ns/1.0"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mo>=</mo><mfrac><mrow><mn>4</mn><mo>⁢</mo><msup><mn>r</mn><mn>4</mn></msup></mrow><mrow><mrow><mn>r</mn><mo>⁢</mo><mn>r</mn></mrow><mo>+</mo><mrow><mn>z</mn><mo>⁢</mo><mn>z</mn></mrow></mrow></mfrac></mrow></math></tei:formula>, for the finding whereof suppose <tei:choice xmlns:tei="http://www.tei-c.org/ns/1.0"><tei:abbr>y<tei:hi rend="superscript">e</tei:hi></tei:abbr><tei:expan>the</tei:expan></tei:choice> <tei:lb xmlns:tei="http://www.tei-c.org/ns/1.0" xml:id="l20"/>Chord of the <tei:choice xmlns:tei="http://www.tei-c.org/ns/1.0"><tei:abbr>Complem<tei:hi rend="superscript">t</tei:hi></tei:abbr><tei:expan>Complement</tei:expan></tei:choice> to the Semicircle to be likewise d<tei:supplied xmlns:tei="http://www.tei-c.org/ns/1.0" reason="damage" evidence="external" cert="medium">rawn</tei:supplied>, and <tei:lb xmlns:tei="http://www.tei-c.org/ns/1.0" xml:id="l21"/>then there is given the ratio of those Chords such as <tei:formula xmlns:tei="http://www.tei-c.org/ns/1.0"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>r</mn></math></tei:formula> <tei:supplied xmlns:tei="http://www.tei-c.org/ns/1.0" reason="damage" evidence="external" cert="medium">to <tei:formula><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>z</mn></math></tei:formula> an</tei:supplied>d the <tei:lb xmlns:tei="http://www.tei-c.org/ns/1.0" xml:id="l22"/>Sum of their Squares <tei:formula xmlns:tei="http://www.tei-c.org/ns/1.0"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mo>=</mo><mrow><mn>4</mn><mo>⁢</mo><mn>r</mn><mo>⁢</mo><mn>r</mn></mrow></mrow></math></tei:formula> and out of such data by a<tei:supplied xmlns:tei="http://www.tei-c.org/ns/1.0" reason="damage" evidence="external" cert="medium">n ana</tei:supplied>lyticall <tei:lb xmlns:tei="http://www.tei-c.org/ns/1.0" xml:id="l23"/>processe <tei:formula xmlns:tei="http://www.tei-c.org/ns/1.0"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mo mathsize="150%">□</mo><mn>AD</mn></mrow></math></tei:formula> is found <tei:formula xmlns:tei="http://www.tei-c.org/ns/1.0"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mo>=</mo><mfrac><mrow><mn>4</mn><mo>⁢</mo><msup><mn>r</mn><mn>4</mn></msup></mrow><mrow><mrow><mn>r</mn><mo>⁢</mo><mn>r</mn></mrow><mo>+</mo><mrow><mn>z</mn><mo>⁢</mo><mn>z</mn></mrow></mrow></mfrac></mrow></math></tei:formula>, And then it holds <tei:lb xmlns:tei="http://www.tei-c.org/ns/1.0" type="intentional" xml:id="l24"/><tei:formula xmlns:tei="http://www.tei-c.org/ns/1.0"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mrow><mrow><mo mathsize="150%">□</mo><mn>AN</mn></mrow><mo lspace="1em" rspace="1em">∶</mo><mrow><mo mathsize="150%">□</mo><mn>NQ</mn></mrow></mrow><mo lspace="1em" rspace="1em">∷</mo><mrow><mrow><mo mathsize="150%">□</mo><mn>AD</mn></mrow><mo lspace="1em" rspace="1em">∶</mo><mrow><mo mathsize="150%">□</mo><mrow><msub><mn mathvariant="normal">D</mn><mn>1</mn></msub><msub><mn mathvariant="normal">B</mn><mn>1</mn></msub></mrow></mrow></mrow></mrow></math></tei:formula> which he calls <tei:formula xmlns:tei="http://www.tei-c.org/ns/1.0"><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mn>y</mn><mn>2</mn></msup></math></tei:formula> <tei:lb xmlns:tei="http://www.tei-c.org/ns/1.0" xml:id="l25"/><tei:add xmlns:tei="http://www.tei-c.org/ns/1.0" indicator="no" place="marginLeft">ie</tei:add> <tei:formula xmlns:tei="http://www.tei-c.org/ns/1.0"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mrow><mrow><mrow><mn>r</mn><mo>⁢</mo><mn>r</mn></mrow><mo>+</mo><mrow><mn>z</mn><mo>⁢</mo><mn>z</mn></mrow></mrow><mo lspace="1em" rspace="1em">∶</mo><mrow><mn>z</mn><mo>⁢</mo><mn>z</mn></mrow></mrow><mo lspace="1em" rspace="1em">∷</mo><mrow><mfrac><mrow><mn>4</mn><mo>⁢</mo><msup><mn>r</mn><mn>4</mn></msup></mrow><mrow><mrow><mn>r</mn><mo>⁢</mo><mn>r</mn></mrow><mo>+</mo><mrow><mn>z</mn><mo>⁢</mo><mn>z</mn></mrow></mrow></mfrac><mo lspace="1em" rspace="1em">∶</mo><mfrac><mrow><mn>4</mn><mo>⁢</mo><msup><mn>r</mn><mn>4</mn></msup><mo>⁢</mo><mn>z</mn><mo>⁢</mo><mn>z</mn></mrow><mrow><mrow><mtable frame="solid" columnspacing="0"><mtr><mtd><mn>2</mn></mtd></mtr></mtable><mtable><mtr><mtd><mn>r</mn><mo>⁢</mo><mn>r</mn></mtd></mtr></mtable></mrow><mtable><mtr><mtd><mo>+</mo><mrow><mn>z</mn><mo>⁢</mo><mn>z</mn></mrow></mtd></mtr></mtable></mrow></mfrac></mrow></mrow></math></tei:formula> the roote <tei:lb xmlns:tei="http://www.tei-c.org/ns/1.0" xml:id="l26"/>whereof is <tei:formula xmlns:tei="http://www.tei-c.org/ns/1.0"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mfrac><mrow><mn>2</mn><mo>⁢</mo><mn>z</mn><mo>⁢</mo><msup><mn>r</mn><mn>2</mn></msup></mrow><mrow><mrow><mn>r</mn><mo>⁢</mo><mn>r</mn></mrow><mo>+</mo><mrow><mn>z</mn><mo>⁢</mo><mn>z</mn></mrow></mrow></mfrac><mo>=</mo><mn>y</mn></mrow></math></tei:formula> as he makes it <tei:lb xmlns:tei="http://www.tei-c.org/ns/1.0" type="intentional" xml:id="l27"/>The reason of my Writing <tei:add xmlns:tei="http://www.tei-c.org/ns/1.0" indicator="yes" place="supralinear">is to rectify a mistake viz</tei:add> that when he sayes <tei:quote xmlns:tei="http://www.tei-c.org/ns/1.0" xml:lang="lat">habita ergo recta <tei:formula><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mrow><mmultiscripts><mn mathvariant="normal">B</mn><mn>1</mn><mprescripts/><mn>1</mn></mmultiscripts><mn mathvariant="normal">D</mn></mrow><mfenced><mrow><mo>=</mo><mfrac><mrow><mn>2</mn><mo>⁢</mo><mn>z</mn><mo>⁢</mo><msup><mn>r</mn><mn>2</mn></msup></mrow><mrow><msup><mn>r</mn><mn>2</mn></msup><mo>+</mo><msup><mn>z</mn><mn>r</mn></msup></mrow></mfrac></mrow></mfenced></mrow></math></tei:formula> et recta <tei:formula><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mrow><mmultiscripts><mn mathvariant="normal">B</mn><mn>2</mn><mprescripts/><mn>1</mn></mmultiscripts><mn mathvariant="normal">B</mn></mrow><mfenced><mrow><mo>=</mo><mfrac><mrow><mn>4</mn><mo>⁢</mo><msup><mn>r</mn><mn>3</mn></msup><mo>⁢</mo><mn>z</mn><mo>⁢</mo><mn>β</mn></mrow><mrow><mtable frame="solid" columnspacing="0"><mtr><mtd><mn>2</mn></mtd></mtr></mtable><mtable><mtr><mtd><mrow><msup><mn>r</mn><mn>2</mn></msup><mo>+</mo><msup><mn>z</mn><mn>2</mn></msup></mrow></mtd></mtr></mtable></mrow></mfrac></mrow></mfenced></mrow></math></tei:formula> habebitur valor <tei:lb xml:id="l28"/>rectanguli, <tei:formula><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mmultiscripts><mn mathvariant="normal">D</mn><mn>1</mn><mprescripts/><mn>1</mn></mmultiscripts><msub><mn mathvariant="normal">B</mn><mn>2</mn></msub><mn mathvariant="normal">B</mn></mrow></math></tei:formula> multiplicatis eorum Valori<tei:del type="over"><tei:gap reason="illgblDel" unit="chars" extent="1"/>b</tei:del><tei:add indicator="no" place="over">b</tei:add>us in se invicem <tei:lb xml:id="l29"/>habebitur inquam <tei:formula><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>8</mn><mo>⁢</mo><msup><mn>r</mn><mn>5</mn></msup></mrow><mrow><mtable frame="solid" columnspacing="0"><mtr><mtd><mn>3</mn></mtd></mtr></mtable><mtable><mtr><mtd><mover><mrow><msup><mn>r</mn><mn>2</mn></msup><mo>+</mo><mrow><msup><mn>z</mn><mn>2</mn></msup></mrow></mrow><mo stretchy="true">‾</mo></mover></mtd></mtr></mtable></mrow></mfrac></math></tei:formula></tei:quote> (this is not the Product but <tei:lb xmlns:tei="http://www.tei-c.org/ns/1.0" xml:id="l30"/>should be <tei:formula xmlns:tei="http://www.tei-c.org/ns/1.0"><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mtext/><mspace width="0.5em"/><mfrac><mrow><mn>8</mn><mo>⁢</mo><msup><mn>r</mn><mn>5</mn></msup><mo>⁢</mo><mn>z</mn><mo>⁢</mo><mn>z</mn><mo>⁢</mo><mn>β</mn></mrow><mrow><mtable frame="solid" columnspacing="0"><mtr><mtd><mn>3</mn></mtd></mtr></mtable><mtable><mtr><mtd><mover><mrow><msup><mn>r</mn><mn>2</mn></msup><mo>+</mo><mrow><msup><mn>z</mn><mn>2</mn></msup></mrow></mrow><mo stretchy="true">‾</mo></mover></mtd></mtr></mtable></mrow></mfrac></mrow></math></tei:formula>, And whereas he sayes the Ordinate <tei:lb xmlns:tei="http://www.tei-c.org/ns/1.0" xml:id="l31"/><tei:formula xmlns:tei="http://www.tei-c.org/ns/1.0"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>NP</mn></math></tei:formula> is <tei:formula xmlns:tei="http://www.tei-c.org/ns/1.0"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>8</mn><mo>⁢</mo><msup><mn>r</mn><mn>5</mn></msup><mo>⁢</mo><msup><mn>z</mn><mn>2</mn></msup></mrow><mrow><mtable frame="solid" columnspacing="0"><mtr><mtd><mn>3</mn></mtd></mtr></mtable><mtable><mtr><mtd><mover><mrow><msup><mn>r</mn><mn>2</mn></msup><mo>+</mo><mrow><msup><mn>z</mn><mn>2</mn></msup></mrow></mrow><mo stretchy="true">‾</mo></mover></mtd></mtr></mtable></mrow></mfrac></math></tei:formula> this I thinke should also be <tei:formula xmlns:tei="http://www.tei-c.org/ns/1.0"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>8</mn><mo>⁢</mo><msup><mn>r</mn><mn>5</mn></msup><mo>⁢</mo><mn>z</mn><mo>⁢</mo><mn>z</mn><mo>⁢</mo><mn>β</mn></mrow><mrow><mtable frame="solid" columnspacing="0"><mtr><mtd><mn>3</mn></mtd></mtr></mtable><mtable><mtr><mtd><mrow><mover><mrow><msup><mn>r</mn><mn>2</mn></msup><mo>+</mo><mrow><mn>z</mn><mo>⁢</mo><mn>z</mn></mrow></mrow><mo stretchy="true">‾</mo></mover></mrow><mmultiscripts><mphantom><mn>1</mn></mphantom><mprescripts/><mphantom><mn>1</mn></mphantom><mn>2</mn></mmultiscripts></mtd></mtr></mtable></mrow></mfrac></math></tei:formula> <tei:lb xmlns:tei="http://www.tei-c.org/ns/1.0" type="intentional" xml:id="l32"/>I hope you will be pleased to settle me as to this doubt, not else at present but that I am</p> 
<tei:p xmlns:tei="http://www.tei-c.org/ns/1.0" rend="right" xml:id="par4">Your much obliged <tei:lb type="intentional" xml:id="l33"/>Servitor <tei:lb type="intentional" xml:id="l34"/>John Collins</tei:p>    
<tei:p xmlns:tei="http://www.tei-c.org/ns/1.0" xml:id="par5">Viviani at Florence hath a treatise <tei:foreign xml:lang="lat">de</tei:foreign> <tei:lb type="intentional" xml:id="l35"/><tei:foreign xml:lang="lat">Loco Solido</tei:foreign> &amp;c in the Presse, and here <tei:lb type="intentional" xml:id="l36"/>father Bonds theory of the inclination of the <tei:lb type="intentional" xml:id="l37"/>Magnet is almost finished</tei:p>
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<tei:p rend="center" xml:id="par6"><tei:hi rend="larger">T</tei:hi>o M<tei:hi rend="superscript">r</tei:hi> Isaac Newton</tei:p>
<tei:p rend="center insetLeft5" xml:id="par7">fellow of Trinity Colledge <tei:lb type="intentional" xml:id="l38"/>In</tei:p>
<tei:p rend="center insetLeft10" xml:id="par8">Cambridge</tei:p>
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