# Draft letter from Newton to John Wallis concerning the publication of his 'Epistola posterior'

S^{r}

The amendments w^{ch} need be made are only these \I meet w^{th} no other amendments w^{ch} need be made beside these w^{ch} follow./

pag. 368 lin. ult. pro 1665 lege 1666.

pag. 392 lin. ult. pro $-2\stackrel{.}{\mathrm{x}}\mathrm{o}\mathrm{o}\stackrel{.}{\mathrm{y}}\stackrel{.}{\mathrm{y}}$ {illeg} $+\stackrel{.}{\mathrm{x}}\mathrm{o}\mathrm{o}\stackrel{.}{\mathrm{y}}\stackrel{.}{\mathrm{y}}+\mathrm{x}{\mathrm{o}}^{3}\stackrel{.}{\mathrm{y}}\stackrel{.}{\mathrm{y}}$ lege $-2\stackrel{.}{\mathrm{x}}\mathrm{o}\mathrm{o}\stackrel{.}{\mathrm{y}}\mathrm{y}-\stackrel{.}{\mathrm{x}}\mathrm{o}\mathrm{o}\stackrel{.}{\mathrm{y}}\stackrel{.}{\mathrm{y}}-\mathrm{x}{\mathrm{o}}^{3}\stackrel{.}{\mathrm{y}}\stackrel{.}{\mathrm{y}}$

pag. 393 l. 2. pro $+\mathrm{x}\mathrm{o}\stackrel{.}{\mathrm{y}}\stackrel{.}{\mathrm{y}}+\stackrel{.}{\mathrm{x}}\mathrm{o}\stackrel{.}{\mathrm{y}}\stackrel{.}{\mathrm{y}}$ lege $-\mathrm{x}\mathrm{o}\stackrel{.}{\mathrm{y}}\stackrel{.}{\mathrm{y}}-\stackrel{.}{\mathrm{x}}\mathrm{o}\stackrel{.}{\mathrm{y}}\stackrel{.}{\mathrm{y}}$.

The plague was in Cambridge in both y^{e} years 1665 & 1666 but it was in y^{t} year 1666 y^{t} I was in y^{e} Country. \absent from Cambridge & therefore I have set down an amendm^{t} of y^{e} year./ I wrote to you lately that I found y^{e} method of converging series in the winter between y^{e} years 1665 & 1666. For y^{t} was y^{e} earliest mention \of it/ I could find then amongst my papers. But meeting since w^{th} the notes w^{ch} \in y^{e} year 1664/ upon my first reading of Vieta's works Schooten's Miscelanies & yo^{r} Arithmetica Infinitorum \{illeg}/ I took out of those books (w^{ch} was done in y^{e} year 1664) I & finding among these notes my deduction of y^{e} these series \for the circle & Hyperbola & some other figures/ out of yours in yo^{r} Arithmetica Infinitorum for squaring y^{e} circle & Hyperbola: I collect y^{t} it was in y^{e} year 1664 that I deduced these series out of yo^{rs} for squaring \the circle/ these {illeg} figures with some others |Then is also among these notes Mercators series for squaring the Hyperbola found by y^{e} same method w^{th} {illeg} some others.| But I cannot find y^{t} I understood y^{e} invention of these series by division & extraction of roots or made any further progress in this business before the writer w^{ch} was between y^{e} years 1665 & 1666. But in y^{t} winter & y^{t} spring following by y^{e} use of Division & extraction of roots I brought that method to be general, & then the plague made me leave c|C|ambridge. But I do not think it requisite that you should make a particular mention of these things. I believe you have said enough in y^{e} beginning of yo^{r} 91^{th} Chapter.

In yo^{r} third Chapter you have given us a collation of the Arabic cyphers with ours both old & modern. The other day looking into Tave{illeg}|r|niere's travells into India pa lib. 1 pag {illeg}|2|3 I met w^{th} y^{e} cyphers now used all over India. They are these.

$\begin{array}{ccccccccccccc}\mathrm{q}& \mathrm{\u0240}& \mathrm{\epsilon}& \mathrm{\u096a}& \mathit{y}& \mathrm{\u0292}& \mathit{9}& \mathrm{\ufea1}& \u096d& \mathrm{q}.& \mathrm{q}..& \mathrm{q}...& \mathrm{q}....\\ 1& 2& 3& 4& 5& 6& 7& 8& 9& 10& 100& 1000& 10000\end{array}$

Our old \figures/ 2, 4 & 5 \& 8 (thus marked ɀ $\underset{X}{\_}$ {sic} $\mathit{y}$ ﺡ)/ seem to be borrowed from these.

I communicated the Postscript of yo^{r} letter to o^{r} Vicechancellor together w^{th} such other Papers as yo^{r} messenger shewed me. That His answer was that he had been so much pressed by the heads of Colleges upon several occasions to admit nothing of this kind without full evidence y^{t} y^{e} \{pe{illeg}|titi|oner}/ was \a true/ {illeg} object of charity, that \feared \some of/ y^{e} Heads would be displeased if he {should}/ he could not give leave without better evidence then he had in this case \least he should meet w^{th} a new check from y^{e} Heads/. He exprest a great respect to yo^{r} letter & said that he lived within five miles of Sandwich & knew the hands of most of y^{e} gentry there & had the case come recommended by some of them whome he could have confided in he would have admitted it, but for y^{e} seale of y^{e} corporation he represented that he knew they sometimes granted it upon too {sleight} occasions to get rid of troublesome people & therefore he could lay no great stress upon that. Nor did he think the heads of Colleges could be satisfied w^{th}out better Testimonials. M^{r} Deeds he said he knew, but seemed to lay \no/ stress upon his testimony. I beleive he mistook the man, because I since heare there are more of that name. He desired that you should be \will/ satisfied about the business & so telling him that I would represent it to you I took my leave & giving yo^{r} Messenger ten shillings was fain to dismis him with this answer. Last summer when y^{e} Vicechancellor stood to be o^{r} Burgess I voted against him & so have \can challenge/ no interest in him tho he is very fair & civil to me. My heart{illeg}y thanks for the sheets of your book I am very glad it is so near finishing. You have done o^{r} nation a great honour in putting so useful a work into Latin for y^{e} perusal of foreigners.