Letter from Newton to John Collins, dated 17 November 1674

38.

Novemb 17th 1674. Cambridge.

SrSir

Hearing ytthat Mr Kersies book is out of Press, I desire you would send me yethe Fourth part. I have ordered John Stiles to satisfy you for it. Mr Dary is very sollicitous about Mathematiques. The rules wchwhich I lately sent him for resolving æquations by Logarithms to be communicated to you, he applys to quadratic equations: whereas they are only to be applied to æquations wchwhich have many intermediate terms wanting, four or five at least. And yethe more intermediate terms are wanting, the sooner they approach to truth. He is desirous of yethe best way of determining Logarithms by yethe Hyperbola & yethe solution of another Probleme of yethe same kind, but I have nothing valuable to communicate therein wchwhich you are not already acquainted wthwith. So wthwith my thanks to you for all yoryour kindnesses I rest

YorYour obliged & humble Servant

Is. Newton

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

\begin{matrix} \begin{array}{r} 30 \\ 31 \\ 30 \\ 8 \end{array} \\ \begin{matrix} \begin{array}{r} 21 \\ 28 \\ 31 \\ 10 \end{array} \\ 90 \end{matrix} \end{matrix}

\begin{array}{r} 1 & 3650 \\ 2 & 7300 \\ 3 & 10950 \\ 4 & 14600 \\ 5 & 18250 \\ 6 & 21900 \\ 7 & 25500 \\ 8 & 29200 \\ 9 & 32850 \end{array}

\begin{array}{l} 198000 & 54 \underline{| 246} \\ \underline{18250} \\ 15500 & 21 \\ \underline{14600} & 22 \\ 9000 \\ \underline{7300} \\ 17000 \\ \underline{14600} \\ 24000 \end{array}

\begin{array}{r} 53, 414 \\ \underline{40} \\ \begin{matrix} 2136,560 \\ \underline{1825,0} \end{matrix} & (\begin{matrix} ,584 \end{matrix} \\ \begin{matrix} 311 56 \\ \underline{292 00} \end{matrix} \\ \begin{matrix} 19 560 \end{matrix} \end{array}

\begin{matrix} \begin{array}{l} 350 \\ \underline{31} \\ 35 \\ \underline{105} \\ \begin{matrix} 10850 \\ \underline{7300} \end{matrix} & (\begin{matrix} 2,975 \end{matrix} \\ \begin{matrix} 35500 \\ \underline{32850} \end{matrix} \\ \begin{matrix} 26500 \\ \underline{24500} \end{matrix} \\ \begin{matrix} 20000 \end{matrix} \end{array} \\ \begin{array}{l} 16 \\ \underline{24} \\ 4875 \\ \underline{4} \\ \begin{matrix} \begin{matrix} 195000 \\ \underline{18250} \end{matrix} & (\begin{matrix} 53 \underline{| 414} \end{matrix} \end{matrix} \\ \begin{matrix} 12500 \\ \underline{10950} \end{matrix} \\ \begin{matrix} 15500 \\ \underline{14600} \end{matrix} \\ \begin{matrix} 9000 \\ \underline{7300} \end{matrix} \\ \begin{matrix} 17000 \end{matrix} \end{array} \end{matrix}

\begin{matrix} \begin{matrix} \begin{array}{l} 23 \\ 54,246 \\ \underline{33} \\ 162738 \\ \underline{162738} \\ \begin{matrix} \begin{matrix} 1790118 \\ \underline{14660} \end{matrix} & (\begin{matrix} 490 \end{matrix} \end{matrix} \\ \begin{matrix} 33011 \\ \underline{32850} \end{matrix} \\ \begin{matrix} 1610 \end{matrix} \end{array} \end{matrix} \\ \begin{matrix} \begin{array}{l} 53,414 \\ \underline{15} \\ 267070 \\ \underline{53414} \\ \begin{matrix} \begin{matrix} 801210 \\ \underline{7300} \end{matrix} & (\begin{matrix} \underline{| 247} \end{matrix} \end{matrix} \\ \begin{matrix} 17121 \\ \underline{14600} \end{matrix} \\ \begin{matrix} 25210 \end{matrix} \end{array} \end{matrix} \end{matrix}

\begin{matrix} \begin{array}{l} 460 \\ \underline{43} \\ 1380 \\ \underline{184} \\ \begin{matrix} 19780 \\ \underline{18250} \end{matrix} & (\begin{matrix} 5 \underline{| 191} \end{matrix} \\ \begin{matrix} 15300 \\ \underline{14600} \end{matrix} \\ \begin{matrix} 7000 \\ \underline{3650} \end{matrix} \\ \begin{matrix} 33500 \\ \underline{32850} \end{matrix} \\ \begin{matrix} 6500 \end{matrix} \end{array} \\ \begin{matrix} \begin{array}{r} 21 \\ 31 \\ 31 \\ 22 \\ \overline{105} \end{array} \\ \begin{array}{r} 9 \\ 30 \\ 31 \\ 26 \\ \overline{96} \end{array} \end{matrix} \end{matrix}

\begin{matrix} \begin{array}{l} 16,602 \\ \underline{90} \\ \begin{matrix} \begin{matrix} 1494180 \\ \underline{14600} \end{matrix} & (\begin{matrix} ,409 \end{matrix} \end{matrix} \\ \begin{matrix} 34180 \end{matrix} \end{array} \end{matrix}

\begin{matrix} \begin{array}{l} 83,795 \\ \underline{105} \\ \begin{matrix} \begin{matrix} 418 975 \\ \underline{8379 5} \end{matrix} \end{matrix} \\ \begin{matrix} \begin{matrix} 8798,475 \\ \underline{7300} \end{matrix} & (\begin{matrix} 2,410 \end{matrix} \end{matrix} \\ \begin{matrix} \begin{matrix} 1498 4 \\ \underline{1460 0} \end{matrix} \end{matrix} \\ \begin{matrix} \begin{matrix} 38 40 \\ \underline{36 50} \end{matrix} \end{matrix} \\ \begin{matrix} \begin{matrix} 19 00 \end{matrix} \end{matrix} \end{array} \end{matrix}

\begin{matrix} \begin{array}{l} 81,014 \\ \underline{96} \\ \begin{matrix} \begin{matrix} 486 084 \\ \underline{7291 26} \end{matrix} \end{matrix} \\ \begin{matrix} \begin{matrix} 7777,344 \\ \underline{7300} \end{matrix} & (\begin{matrix} 2 \underline{| 130} \end{matrix} \end{matrix} \\ \begin{matrix} \begin{matrix} 477 3 \\ \underline{365 0} \end{matrix} \end{matrix} \\ \begin{matrix} \begin{matrix} 11 230 \\ \underline{10 950} \end{matrix} \end{matrix} \\ \begin{matrix} \begin{matrix} 2800 \end{matrix} \end{matrix} \end{array} \end{matrix}

39.

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

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

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