<1r>

Sr

I am very much obliged to you for ye pains in transcribing my \two/ Letters of 1676 & much more for your kind concern of {illeg} right being done me by publishing them. I have perused your transcripts {illeg}|o|f them & e{illeg}|x|amined ye calculations & corrected some few places wch were amiss. The chief was in pag. 13 lin 29 where $\theta +1=r$ was written for $\frac{\theta +1}{n}=r$. Which mistake made ye examples in ye next page seem faulty, tho they were not so. In ye end of ye 20{th} page & beginning of ye next, it may be convenient to print ye words after this manner

Possum utiqꝫ cum conicis sectionibus conicis Geometrice comparare curvas omnes \(numero infinities infinitas)/ quare ordinatim applicatæ sunt
$\begin{array}{l}\frac{d{z}^{\eta -1}}{e+f{z}^{\eta }+g{z}^{2\eta }}\phantom{\rule{1em}{0ex}}\text{vel}\phantom{\rule{1em}{0ex}}\frac{d{z}^{2\eta -1}}{e+f{z}^{\eta }+g{z}^{2\eta }}\phantom{\rule{1em}{0ex}}\text{&c}\\ \frac{d{z}^{\frac{1}{2}\eta -1}}{e+f{z}^{\eta }+g{z}^{2\eta }}\phantom{\rule{1em}{0ex}}\text{vel}\phantom{\rule{1em}{0ex}}\frac{d{z}^{\frac{3}{2}\eta -1}}{e+f{z}^{\eta }+g{z}^{2\eta }}\phantom{\rule{1em}{0ex}}\text{&c}\\ \frac{d}{z}\sqrt{e+f{z}^{\eta }+g{z}^{2\eta }}\phantom{\rule{1em}{0ex}}\text{vel}\phantom{\rule{1em}{0ex}}d{z}^{\eta -1}×\sqrt{e+f{z}^{\eta }+g{z}^{2\eta }}\phantom{\rule{1em}{0ex}}\text{&c}\\ \frac{d{z}^{\eta -1}}{\sqrt{e+f{z}^{\eta }+g{z}^{2\eta }}}\phantom{\rule{1em}{0ex}}\text{vel}\phantom{\rule{1em}{0ex}}\frac{d{z}^{2\eta -1}}{\sqrt{e+f{z}^{\eta }+g{z}^{2\eta }}}\phantom{\rule{1em}{0ex}}\text{&c}\end{array}$

The explications of the two sentences wch wchere concealed in letters set out of order \pag 13 & pag 24/ may|wil|l be best set in ye margin. And in pag 13 over against the words [quam solertissimus Slusius ante annos duos tresve tecum coomunicavit, de qua tu (suggerente Collinio) {illeg} rescripsisti \eandem/ mihi etiam innotuisse] may be set this note in the margin this Note. Verba Collinij {illeg} Hoc intellexit Newtonus ex Epistola Collinij, \die 18/ Junij 18 1673, ad ipsum data, cujus \hæc sunt/ verba sunt, As to Slusius metho{d} of Tangents it was by the|i|m well understood when pu|he| published h{is} boo{illeg}|k| De Mesolabio but \he/ did not then divulge it because he wou{ld} not prevent his friend Riccio who afterwards declining mathema{ti}cal studies desired Slusius to divulge it, who not obteining leisu{re} to write of it at large promised to send it to Mr Oldenb{urgh} to publish in ye Transactions. Before it arrived I writ to you {to} understand what you knew of it & having received ye{illeg} An{swer,} imparted it to Mr Oldenburgh to send to Slusius to let him {know} that it was understood in England tho perchance not so lo{ng or} so soon as himself had attained it.

As to the time of my finding the method of conv{ex} series, the exacte{illeg}|s|t account I can give of it is this, T{illeg} the year {illeg} 1664 not long before \michaelemas &/ Christmass I {illeg} read your {illeg}|y|our {sic} works & \& found ye intercalation of your series \I think/ that winter. {illeg}/ in the notes I then look {on} {illeg} {illeg} infinitorum I {illeg}ala{illeg} \& {obser}{illeg}/ <1v> quanties into converging series by division & extraction of roots & thereby of squaring all curves. And then (that is in ye beginning of the year 1666) I retired from the University into Lincolnshire to avoijd the plague danger of ye plague.

|To Dr Wallis|