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<title>Draft letter from John Collins to Newton, written c. 13-16 July 1670</title>
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<extent><hi rend="italic">c.</hi> <num n="word_count" value="565">565</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">13–16 July 1670, <hi rend="italic">c.</hi> 570 words, 1 f.</note>
<note n="pages">1 f.</note>
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<p>Published in H.W. Turnbull (ed), <hi rend="italic">The Correspondence of Isaac Newton</hi>, vol. 1 (Cambridge: 1959), pp. 32-3</p>
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<change when="2012-06-15"><name>Daniele Cassisa</name> started tagged transcription</change>
<change when="2012-10-15" type="metadata">Catalogue information compiled from CUL Janus Catalogue by <name xml:id="mjh">Michael Hawkins</name></change>
<change when="2013-02-13">Proofed by <name>Robert Iliffe</name></change>
<change when="2013-02-25" status="released">Code audit by <name sameAs="#mjh">Michael Hawkins</name></change>
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<pb xml:id="p007r" n="7r" facs="#i21"/><fw type="shelfmark" place="topRight" hand="#unknown">7.</fw>
<p xml:id="par1">M<hi rend="superscript">r</hi> Newton</p>
<p xml:id="par2"><choice><abbr>S<hi rend="superscript">r</hi></abbr><expan>Sir</expan></choice></p>

<p xml:id="par3">I received yours with Kinckhuysens Introduction, and <lb xml:id="l1"/>perceive you have taken great paines which god willing shall be <lb xml:id="l2"/>inserted into <choice><abbr>y<hi rend="superscript">e</hi></abbr><expan>the</expan></choice> Translation and printed with it, hereby you have <lb xml:id="l3"/>much obliged the young Students of Algebra <addSpan spanTo="#addend001r-01" place="pageTop" startDescription="the top of the page" endDescription="f 7r" resp="#mjh"/>and the Bookseller who was at <choice><abbr>y<hi rend="superscript">e</hi></abbr><expan>the</expan></choice> <choice><abbr>commencem<hi rend="superscript">t</hi></abbr><expan>commencement</expan></choice> on Munday and Tuesday but was so taken up and concerned you were so too that he did not see you, but remaines your <del type="strikethrough">Debt</del> much obliged <choice><abbr>D<hi rend="superscript">r</hi></abbr><expan>Debtor</expan></choice> <del type="cancelled">where of Will som</del><anchor xml:id="addend001r-01"/>, I formerly intimated <lb xml:id="l4"/>that I thou<del type="over"><gap reason="illgblDel" unit="chars" extent="1"/></del><add indicator="no" place="over">gh</add>t <del type="strikethrough">he</del> <add indicator="no" place="supralinear">Kinck</add> had too slightly handled the doctrine of Surd <lb xml:id="l5"/>Numbers, <add indicator="yes" place="supralinear">and that the same might be transcribed from others</add> I find you in the same opinion for in one of your <lb xml:id="l6"/>Marginall Notes you say thus, The Author having slipped over <lb xml:id="l7"/>the Addition Substraction Multiplication and Division of all <lb xml:id="l8"/>but quadratick Surds &amp;c <del type="cancelled">and</del> <add indicator="no" place="supralinear">*</add> <addSpan spanTo="#addend001r-02" place="p007r-lower" startDescription="lower down f 7r" endDescription="higher up f 7r" resp="#mjh"/>* and he acknowledgeth as much <del type="cancelled"><unclear reason="del" cert="low">tantly</unclear></del> by consequence himselfe referring <lb xml:id="l9"/>the Reader to Wassenare Onwissen Wistconstenaer however <lb xml:id="l10"/>he cheifely thereby intended <choice><abbr>y<hi rend="superscript">e</hi></abbr><expan>the</expan></choice> <del type="strikethrough">Cube</del> rootes of Binomialls which you have supplyed<anchor xml:id="addend001r-02"/> being unwilling the young Student <lb xml:id="l11"/>should be referred to other bookes <add indicator="yes" place="supralinear">which are scarce</add> for the Doctrine of Surds <newtonSymbol xmlns="http://www.newtonproject.sussex.ac.uk/ns/nonTEI" value="large tick"/> <tei:addSpan xmlns:tei="http://www.tei-c.org/ns/1.0" spanTo="#addend001r-03" place="p007r-lower" startDescription="lower down f 7r" endDescription="higher up f 7r" resp="#mjh"/><newtonSymbol xmlns="http://www.newtonproject.sussex.ac.uk/ns/nonTEI" value="large tick"/> I <tei:del xmlns:tei="http://www.tei-c.org/ns/1.0" type="cancelled"><tei:unclear reason="del" cert="low">make bold</tei:unclear></tei:del> will a little further presume <tei:del xmlns:tei="http://www.tei-c.org/ns/1.0" type="over"><tei:gap reason="illgblDel" unit="chars" extent="1"/></tei:del><tei:add xmlns:tei="http://www.tei-c.org/ns/1.0" indicator="no" place="over">a</tei:add>nd <tei:del xmlns:tei="http://www.tei-c.org/ns/1.0" type="cancelled">to</tei:del> <tei:add xmlns:tei="http://www.tei-c.org/ns/1.0" indicator="yes" place="supralinear">therefore</tei:add> crave your <tei:lb xmlns:tei="http://www.tei-c.org/ns/1.0" xml:id="l12"/><tei:choice xmlns:tei="http://www.tei-c.org/ns/1.0"><tei:abbr>iudgem<tei:hi rend="superscript">t</tei:hi></tei:abbr><tei:expan>iudgement</tei:expan></tei:choice> of what you thinke necessary to be taken either out of <tei:lb xmlns:tei="http://www.tei-c.org/ns/1.0" xml:id="l13"/>Scheubelius, Van Ceulen, or Humes which <tei:add xmlns:tei="http://www.tei-c.org/ns/1.0" indicator="yes" place="supralinear">bookes</tei:add> I herewith send <tei:lb xmlns:tei="http://www.tei-c.org/ns/1.0" xml:id="l14"/>and having another Scheubelius <tei:del xmlns:tei="http://www.tei-c.org/ns/1.0" type="cancelled">you</tei:del> here, you need not returne <tei:lb xmlns:tei="http://www.tei-c.org/ns/1.0" xml:id="l15"/>that sent, wherewith be pleased to accept of another <tei:foreign xmlns:tei="http://www.tei-c.org/ns/1.0" xml:lang="lat">Libellus de</tei:foreign> <tei:lb xmlns:tei="http://www.tei-c.org/ns/1.0" xml:id="l16"/><tei:foreign xmlns:tei="http://www.tei-c.org/ns/1.0" xml:lang="lat">Machina Aquatica</tei:foreign> There are two other Authors have excellently <tei:lb xmlns:tei="http://www.tei-c.org/ns/1.0" xml:id="l17"/>handled Surds, those are Frans van der Huyps in <tei:add xmlns:tei="http://www.tei-c.org/ns/1.0" indicator="no" place="supralinear">his</tei:add> Low Dutch <tei:lb xmlns:tei="http://www.tei-c.org/ns/1.0" xml:id="l18"/>Algebra <tei:del xmlns:tei="http://www.tei-c.org/ns/1.0" type="cancelled">and</tei:del> in 1654 and <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> Seiur d Taneur <tei:add xmlns:tei="http://www.tei-c.org/ns/1.0" indicator="yes" place="supralinear">in french</tei:add> in his <tei:lb xmlns:tei="http://www.tei-c.org/ns/1.0" xml:id="l19"/>Tract of irrationall quantities and Commentaries on 10 Euclid <tei:lb xmlns:tei="http://www.tei-c.org/ns/1.0" xml:id="l20"/>at Paris in 1640.<tei:anchor xmlns:tei="http://www.tei-c.org/ns/1.0" xml:id="addend001r-03"/></p>
<tei:p xmlns:tei="http://www.tei-c.org/ns/1.0" rend="indent0" xml:id="par4"><tei:hi rend="large">I</tei:hi> am glad to know you have a better way for the Musicall <tei:lb xml:id="l21"/>Progression then the latter you sent up <tei:add indicator="yes" place="supralinear"><tei:del type="strikethrough">p<tei:gap reason="illgblDel" unit="chars" extent="5"/></tei:del> (being the same I mentioned not having □</tei:add> <tei:addSpan spanTo="#addend001r-04" place="marginLeft" startDescription="the left margin" endDescription="f 7r" resp="#mjh"/>□ seriously considered your Letter reserving it to better leisure)<tei:anchor xml:id="addend001r-04"/> <tei:add indicator="no" place="infralinear">you</tei:add> having hinted so much in an <tei:lb xml:id="l22"/>intermediate letter, but sorry it put you to so much trouble, being very <tei:lb xml:id="l23"/>loath to <tei:del type="strikethrough">imp<tei:gap reason="illgblDel" unit="chars" extent="2"/> ex<tei:gap reason="illgblDel" unit="chars" extent="2"/>r<tei:gap reason="illgblDel" unit="chars" extent="1"/>se</tei:del> intrude upon your Patience, Mengolus an excellent <tei:lb xml:id="l24"/>Mathematician and Musitian hath a treatise of Musick in the Presse <tei:lb xml:id="l25"/>and there is newly come over by the Post (sent to the Societie) a little <tei:lb xml:id="l26"/>treatise of his in Italian of the Suns Parallax and refraction <tei:lb xml:id="l27"/><tei:add indicator="no" place="interlinear">which I have not yet seen</tei:add></tei:p>
<tei:p xmlns:tei="http://www.tei-c.org/ns/1.0" rend="indent0" xml:id="par5">I was apt to beleive that Ferguson had done more <tei:add indicator="yes" place="supralinear">then Kinckhuysen</tei:add> in these 3 particulars</tei:p>
<tei:p xmlns:tei="http://www.tei-c.org/ns/1.0" rend="indent0" xml:id="par6">1 In <tei:del type="strikethrough"><tei:unclear reason="del" cert="low">setting</tei:unclear></tei:del> <tei:add indicator="no" place="supralinear">applying one generall rule to</tei:add> both kinds of Cubick Æquations, to wit <tei:add indicator="no" place="supralinear">as well</tei:add> those that are solved by meane Proportionall Proportionalls as those that require Trisection</tei:p>
<tei:p xmlns:tei="http://www.tei-c.org/ns/1.0" rend="indent0" xml:id="par7">2 In rendring the rootes of Cubick and Biquadratick Æquations <tei:lb xml:id="l28"/>properly that is to say in giving the rootes when <tei:add indicator="yes" place="supralinear">they are explicated by</tei:add> fractions or Surds <tei:lb xml:id="l29"/>exactly, and not by a <tei:foreign xml:lang="lat">quamproximé</tei:foreign></tei:p>
<tei:p xmlns:tei="http://www.tei-c.org/ns/1.0" rend="indent0" xml:id="par8">3 In emprooving the generall Method</tei:p>
<tei:p xmlns:tei="http://www.tei-c.org/ns/1.0" rend="indent0" xml:id="par9">But having failed in the first I conceive it opportune to shew at <tei:lb xml:id="l30"/>least <tei:del type="strikethrough">that he ha</tei:del> wherein he hath failed, and if you please (which is <tei:lb xml:id="l31"/>by you offred and seemes desirable) supply his defect</tei:p>
<tei:p xmlns:tei="http://www.tei-c.org/ns/1.0" rend="indent0" xml:id="par10">Lastly why you should desire to have your Name unmentioned I see <tei:lb xml:id="l32"/>not, but if it be your will and command so to have it, it shall be <tei:lb xml:id="l33"/>observed by</tei:p>
<tei:pb xmlns:tei="http://www.tei-c.org/ns/1.0" xml:id="p007v" n="7v" facs="#i22"/>
<tei:p xmlns:tei="http://www.tei-c.org/ns/1.0" xml:id="par11">To M<tei:hi rend="superscript">r</tei:hi> Newton July 13 1670</tei:p>
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