<38r>

Novemb 17th 1674. Cambridge.

Sr

He{illeg}|a|ring yt Mr Kersies book is out of Press, I desire you would send me ye Fourth {illeg}|p|art. I have ordered John Stiles to satisfy you for it. Mr Dary is very sollicitous about Mathematiques. The rules wch I lately sent him for resolving æquations by Logarithms {illeg} to be communicated to you, he applys to {illeg}|q|uadratic equations: whereas they are only to be applied to æquations wch have many intermediate terms wanting, four or five at least. And ye more intermediate terms are wanting, the sooner they approach to truth. He is desirous of ye best way of determining Logarithms by{illeg} ye Hyperbola {illeg} & ye solution of another Probleme of ye same kind, but I have nothing valuable to communicate \therein/ wch you are not already acquainted wth. So wth my thanks to you for all yor kindnesses I rest

Yor obliged &
humble Servant

Is. Newton
<38v>

As 36500 Is to 10 times the Number of Dayes so is any Principall to the Interest

$\begin{array}{c}\begin{array}{rr}30& \\ 31\\ 30\\ 8\end{array}\\ \begin{array}{c}\begin{array}{r}21\\ 28\\ 31\\ 10\end{array}\\ 90\end{array}\end{array}$ $\begin{array}{rrr}1& 3650& \\ 2& 7300\\ 3& 10950\\ 4& 14600\\ 5& 18250\\ 6& 21900\\ 7& 25500\\ 8& 29200\\ 9& 32850\end{array}$ $\begin{array}{ll}198000& 54\underset{‾}{|246}\\ \underset{‾}{18250\phantom{0}}\\ \phantom{0}15500\phantom{0}& & 21\\ \underset{‾}{\phantom{0}14600\phantom{0}}& & 22\\ \phantom{000}9000\phantom{0}\\ \underset{‾}{\phantom{000}7300\phantom{0}}\\ \phantom{000}17000\\ \underset{‾}{\phantom{000}14600}\\ \phantom{000}24000\end{array}$ $\begin{array}{r}\phantom{0}53,414\phantom{0}\\ \underset{‾}{\phantom{000000}40\phantom{0}}\\ \begin{array}{c}2136,560\\ \underset{‾}{1825,0\phantom{00}}\end{array}& \left(\begin{array}{}\phantom{.}\\ ,584\\ \phantom{.}\end{array}\right\\ \begin{array}{c}\phantom{0}311\phantom{,}56\phantom{0}\\ \phantom{0}\underset{‾}{292\phantom{,}00\phantom{0}}\end{array}\\ \begin{array}{c}\phantom{00}19\phantom{,}560\end{array}\end{array}$
$\begin{array}{c}\begin{array}{l}\phantom{0000}350\phantom{0}\\ \underset{‾}{\phantom{0000}31\phantom{0}\phantom{0}}\\ \phantom{000}35\phantom{000}\\ \underset{‾}{\phantom{0}105\phantom{0}\phantom{000}}\\ \begin{array}{c}10850\\ \underset{‾}{\phantom{}7300\phantom{0}}\end{array}& \left(\begin{array}{}\phantom{.}\\ 2,975\\ \phantom{.}\end{array}\right\\ \begin{array}{c}\phantom{0}35500\\ \underset{‾}{\phantom{0}32850}\end{array}\\ \begin{array}{c}\phantom{00}26500\\ \underset{‾}{\phantom{00}24500}\end{array}\\ \begin{array}{c}\phantom{0000}20000\end{array}\end{array}\\ \begin{array}{l}16\phantom{00000}\\ \underset{‾}{24\phantom{00000}\phantom{0}}\\ \phantom{00}4875\phantom{0}\\ \underset{‾}{\phantom{00000}4\phantom{0}}\\ \begin{array}{cc}\begin{array}{c}195000\\ \underset{‾}{\phantom{}18250\phantom{0}}\end{array}& \left(\begin{array}{}\phantom{.}\\ 53\underset{‾}{|414}\\ \phantom{.}\end{array}\right\end{array}\\ \begin{array}{c}\phantom{0}12500\\ \underset{‾}{\phantom{0}10950}\end{array}\\ \begin{array}{c}\phantom{000}15500\\ \underset{‾}{\phantom{000}14600}\end{array}\\ \begin{array}{c}\phantom{00000}9000\\ \underset{‾}{\phantom{00000}7300}\end{array}\\ \begin{array}{c}\phantom{000000}17000\end{array}\end{array}\end{array}$ $\begin{array}{c}\begin{array}{c}\begin{array}{l}\phantom{00}23\phantom{00000}\\ \phantom{0}\\ \phantom{00}54,246\phantom{00}\\ \underset{‾}{\phantom{0054,2}33\phantom{00}}\\ \phantom{0}162738\phantom{0}\\ \underset{‾}{162738\phantom{0}}\\ \begin{array}{cc}\begin{array}{c}1790118\\ \underset{‾}{\phantom{}14660\phantom{00}}\end{array}& \left(\begin{array}{}\phantom{.}\\ 490\\ \phantom{.}\end{array}\right\end{array}\\ \begin{array}{c}\phantom{0}33011\\ \underset{‾}{\phantom{0}32850}\end{array}\\ \begin{array}{c}\phantom{000}1610\phantom{00}\end{array}\end{array}\end{array}\\ \begin{array}{c}\begin{array}{}\phantom{0}\\ \phantom{0}53,414\phantom{00}\\ \underset{‾}{\phantom{054,2}15\phantom{00}}\\ 267070\phantom{0}\\ \underset{‾}{53414\phantom{00}}\\ \begin{array}{cc}\begin{array}{c}801210\\ \underset{‾}{\phantom{}7300\phantom{00}}\end{array}& \left(\begin{array}{}\phantom{.}\\ \underset{‾}{|247}\\ \phantom{.}\end{array}\right\end{array}\\ \begin{array}{c}17121\\ \underset{‾}{14600}\end{array}\\ \begin{array}{c}\phantom{0}25210\phantom{00}\end{array}\end{array}\end{array}\end{array}$ $\begin{array}{c}\begin{array}{l}\phantom{0000}460\phantom{0}\\ \underset{‾}{\phantom{00000}43\phantom{0}}\\ \phantom{0000}1380\phantom{0}\\ \underset{‾}{\phantom{000}184\phantom{0}\phantom{000}}\\ \begin{array}{c}\phantom{000}19780\\ \underset{‾}{\phantom{000}18250}\end{array}& \left(\begin{array}{}\phantom{.}\\ 5\underset{‾}{|191}\\ \phantom{.}\end{array}\right\\ \begin{array}{c}\phantom{00000}15300\\ \underset{‾}{\phantom{00000}14600}\end{array}\\ \begin{array}{c}\phantom{000000}7000\phantom{0}\\ \underset{‾}{\phantom{000000}3650\phantom{0}}\end{array}\\ \begin{array}{c}\phantom{000000}33500\phantom{0}\\ \underset{‾}{\phantom{000000}32850\phantom{0}}\end{array}\\ \begin{array}{c}\phantom{00000000}6500\end{array}\end{array}\\ \begin{array}{cc}\begin{array}{r}21\\ 31\\ 31\\ 22\\ \stackrel{‾}{105}\end{array}& \\ & \begin{array}{r}9\\ 30\\ 31\\ 26\\ \stackrel{‾}{96}\end{array}\end{array}\end{array}$
$\begin{array}{c}\begin{array}{}\phantom{0}\\ \phantom{0}16,602\phantom{00}\\ \underset{‾}{\phantom{054,2}90\phantom{00}}\\ \begin{array}{cc}\begin{array}{c}1494180\\ \underset{‾}{\phantom{}14600\phantom{00}}\end{array}& \left(\begin{array}{}\phantom{.}\\ ,409\\ \phantom{.}\end{array}\right\end{array}\\ \begin{array}{c}\phantom{00}34180\end{array}\end{array}\end{array}$ $\begin{array}{c}\begin{array}{}\phantom{0}\\ \phantom{0}83,795\phantom{00}\\ \underset{‾}{\phantom{054,}105\phantom{00}}\\ \begin{array}{c}\begin{array}{c}\phantom{0}418\phantom{,}975\\ \underset{‾}{\phantom{}8379\phantom{,}5\phantom{00}}\end{array}\end{array}\\ \begin{array}{cc}\begin{array}{c}8798,475\\ \underset{‾}{7300\phantom{,000}}\end{array}& \left(\begin{array}{}\phantom{.}\\ 2,410\\ \phantom{.}\end{array}\right\end{array}\\ \begin{array}{c}\begin{array}{c}1498\phantom{,}4\\ \underset{‾}{1460\phantom{,}0}\end{array}\end{array}\\ \begin{array}{c}\begin{array}{c}\phantom{00}38\phantom{,}40\\ \underset{‾}{\phantom{00}36\phantom{,}50}\end{array}\end{array}\\ \begin{array}{c}\begin{array}{c}\phantom{000}19\phantom{,}00\end{array}\end{array}\end{array}\end{array}$ $\begin{array}{c}\begin{array}{}\phantom{0}\\ \phantom{0}81,014\phantom{00}\\ \underset{‾}{\phantom{054,0}96\phantom{00}}\\ \begin{array}{c}\begin{array}{c}\phantom{}486\phantom{,}084\\ \underset{‾}{\phantom{}7291\phantom{,}26\phantom{00}}\end{array}\end{array}\\ \begin{array}{cc}\begin{array}{c}7777,344\\ \underset{‾}{7300\phantom{,000}}\end{array}& \left(\begin{array}{}\phantom{.}\\ 2\underset{‾}{|130}\\ \phantom{.}\end{array}\right\end{array}\\ \begin{array}{c}\begin{array}{c}\phantom{0}477\phantom{,}3\\ \underset{‾}{\phantom{0}365\phantom{,}0}\end{array}\end{array}\\ \begin{array}{c}\begin{array}{c}\phantom{00}11\phantom{,}230\\ \underset{‾}{\phantom{00}10\phantom{,}950}\end{array}\end{array}\\ \begin{array}{c}\begin{array}{c}\phantom{0000\phantom{,}}2800\end{array}\end{array}\end{array}\end{array}$

<39r>

$\begin{array}{l}\begin{array}{lllll}\phantom{0}54:& \phantom{0}4:& 11\frac{1}{2}& & \phantom{\rule{2em}{0ex}}125:0:0\\ & \phantom{0}9& 10\phantom{\frac{0}{0}}& \phantom{\rule{2em}{0ex}}\text{33 dayes}\\ \phantom{0}53:& \phantom{0}8:& \phantom{0}3\frac{1}{2}& \\ \phantom{000:}& \phantom{0}4\phantom{:}& 11\frac{1}{2}& \phantom{\rule{2em}{0ex}}\text{15 Dayes}\end{array}\\ \begin{array}{llll}108:& 07:& 11\frac{1}{2}& \\ \phantom{0}16:& 12:& \phantom{0}0\frac{1}{2}& \end{array}\end{array}$

$\begin{array}{r}\begin{array}{ccccc}\hfill \text{Jan 10}& & \text{Over}\hfill & & \phantom{00}16:12:\phantom{0}0\frac{1}{2}\\ \hfill \text{Carried downe}\phantom{\rule{2em}{0ex}}83:15:11& & \begin{array}{l}\text{Interest to the 10 of}\phantom{\rule{0.5em}{0ex}}{\text{Ap}}^{\text{ll}}\\ \text{being 90 dayes}\end{array}\hfill & & \phantom{0}\phantom{00}0:\phantom{0}8:\phantom{0}2\frac{1}{2}\\ & & \text{By Cash then}\phantom{\rule{0.5em}{0ex}}{\text{p}}^{\text{d}}\hfill & & \phantom{00}66:15:\phantom{0}8\phantom{\frac{1}{2}}\\ \phantom{_______________________________________}& & \phantom{_______________________________________}& & \begin{array}{}\\ \phantom{00}83:15:11\phantom{\frac{1}{2}}\end{array}\end{array}\\ \begin{array}{ccccc}\hfill & & \text{Brought downe}\hfill & & \phantom{00}83:15:11\phantom{\frac{1}{2}}\\ \hfill \begin{array}{r}\text{Aug 22}\phantom{\rule{3em}{0ex}}\phantom{0}5:\phantom{0}3:\phantom{\frac{1}{2}}10\\ 81:\phantom{0}0\phantom{:}\phantom{0}3\frac{1}{2}\end{array}& & \begin{array}{l}\text{Interest thereof to 22}\\ \text{Aug being 105 dayes}\phantom{\frac{0}{0}}\end{array}\right\}\hfill & & \phantom{0}\phantom{00}0:\phantom{0}2:\phantom{0}2\frac{1}{2}\\ \phantom{_______________________________________}& & \phantom{_______________________________________}& & \begin{array}{}\\ \phantom{00}86:\phantom{0}4:\phantom{0}1\frac{1}{2}\end{array}\end{array}\\ \begin{array}{ccccc}\phantom{_______________________________________}& & \text{Brought downe}\hfill & & \phantom{00}81:\phantom{0}0:\phantom{0}3\frac{1}{2}\\ \hfill & & \text{Cash then paid}\hfill & & \phantom{00}64:14:\phantom{0}1\phantom{\frac{1}{2}}\\ & & \begin{array}{l}\text{Interest the to 26}\phantom{\rule{0.5em}{0ex}}{\text{Nov}}^{\text{r}}\phantom{\rule{0.5em}{0ex}}\text{being}\\ \text{96 dayes}\phantom{\frac{0}{0}}\end{array}\hfill & & \phantom{00}22:\phantom{0}4:10\frac{1}{2}\\ \hfill \text{Carried downe}\phantom{\rule{2em}{0ex}}880:14:\phantom{0}5\frac{1}{2}& & \phantom{_______________________________________}& & \begin{array}{}\\ \phantom{0}867:19:\phantom{0}3\phantom{\frac{1}{2}}\end{array}\\ _____________________________________& & \text{By Cash}\phantom{\rule{0.5em}{0ex}}{\text{p}}^{\text{d}}\phantom{\rule{0.5em}{0ex}}\text{26 Nov}\hfill & & \phantom{00}12:15:\phantom{0}2\frac{1}{2}\\ & & \phantom{_______________________________________}& & \begin{array}{}\\ \phantom{0}880:14:\phantom{0}5\frac{1}{2}\end{array}\\ \hfill \begin{array}{r}99:\phantom{0}4:\phantom{0}8\frac{3}{4}\\ \phantom{\frac{0}{0}}\end{array}& & \begin{array}{l}\text{Interest to 18 May}\\ \text{1667 being 173 dayes}\phantom{\frac{0}{0}}\end{array}\right\}\hfill & & \phantom{00}41:15:\phantom{0}6\phantom{\frac{1}{2}}\\ \begin{array}{l}\text{Interest from}\\ \text{5 feb to 18 May}\\ \text{being 102 dayes}\end{array}\right\}\hfill & & \text{May 18 Paid}\hfill & & \begin{array}{c}\phantom{0}350:\phantom{0}0:\phantom{0}0\phantom{\frac{1}{2}}\end{array}\\ & & \phantom{_______________________________________}& & \begin{array}{}\\ 1272:\phantom{0}9:11\frac{1}{2}\end{array}\end{array}\end{array}$

<39v>

These

For Mr John Collins at the
Farthing Office in Fenchurch
Street in

London.

|send by Stiles at the green dragon in bishope gate on thursday|

© 2019 The Newton Project

Professor Rob Iliffe
Director, AHRC Newton Papers Project

Scott Mandelbrote,
Fellow & Perne librarian, Peterhouse, Cambridge

Faculty of History, George Street, Oxford, OX1 2RL - newtonproject@history.ox.ac.uk

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