Letter from Newton to John Collins, dated 17 November 1674

<38r>

Novemb 17^th 1674. Cambridge.

S^r

He{illeg}|a|ring y^t M^r Kersies book is out of Press, I desire you would send me y^e Fourth {illeg}|p|art. I have ordered John Stiles to satisfy you for it. M^r Dary is very sollicitous about Mathematiques. The rules w^ch 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 w^ch have many intermediate terms wanting, four or five at least. And y^e more intermediate terms are wanting, the sooner they approach to truth. He is desirous of y^e best way of determining Logarithms by^{illeg} y^e Hyperbola {illeg} & y^e solution of another Probleme of y^e same kind, but I have nothing valuable to communicate \therein/ w^ch you are not already acquainted w^th. So w^th my thanks to you for all yo^r kindnesses I rest

Yo^r obliged &
humble Servant

Is. Newton

<38v>

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

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

<39r>

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

$\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}83:15:11& & \begin{array}{l}\text{Interest to the 10 of}{\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}{\text{p}}^{\text{d}}\hfill & & \phantom{00}66:15:\phantom{0}8\phantom{\frac{1}{2}}\\ \phantom{\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_}& & \phantom{\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_}& & \begin{array}{c}\\ \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{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}\}\hfill & & \phantom{0}\phantom{00}0:\phantom{0}2:\phantom{0}2\frac{1}{2}\\ \phantom{\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_}& & \phantom{\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_}& & \begin{array}{c}\\ \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}{\text{Nov}}^{\text{r}}\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}880:14:\phantom{0}5\frac{1}{2}& & \phantom{\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_}& & \begin{array}{c}\\ \phantom{0}867:19:\phantom{0}3\phantom{\frac{1}{2}}\end{array}\\ \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_& & \text{By Cash}{\text{p}}^{\text{d}}\text{26 Nov}\hfill & & \phantom{00}12:15:\phantom{0}2\frac{1}{2}\\ & & \phantom{\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_}& & \begin{array}{c}\\ \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}\}\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}\}\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}{c}\\ 1272:\phantom{0}9:11\frac{1}{2}\end{array}\end{array}\end{array}$

<39v>

These

For M^r John Collins at the
Farthing Office in Fenchurch
Street in

London.

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