<6r>

Jul 11th 1670.
Trin. Coll.

Sr

I have here sent your Kink-Huysons Algebra wth those notes wch I have intermixed wth {illeg}|th|e Authors discourse. I know not whither I have hit your meaning or noe but I have added & altered those things wch I thought convenient to bee added or altered, & I guesse that was your desire I should doe. All & every part \of what/ I have written I leave wholly to your choyse whither it shall bee printed together wth your translation or not. what If you think fit to print any of it ye directions I have writ in english will shew you where it is to bee inserted. But if you have a mind not to change ye Author soe much, I would not have you recede from yor intentions upon ye accompt of wt I have done. For I assure you I writ wt I send you not so much wth a desi{illeg}|g|ne yt they should bee printed at|s| yt yor desires should bee satisfied to have me revise ye booke. And so soone as you have read ye papers I have my end of writing them. In a letter you hinted somthing to bee supplyed out of Ferguson's Labyrinthus about ye extraction of cubick roots; if you meant pure rootes, I have done yt in as breif plaine & full a manner as I can. But if you meant affected roots, tis already done by Kinck-Huyson {illeg}|p|ag 91 as well as by Ferguson. Indeed Ferguson seemes to have done {illeg}|m|ore in so much as to comprehend all cases of cubick roots \equations/ wthin ye same rules; but that [more] is inartificiall because it supposes ye extraction of cubick roots ou{illeg}|t| of imaginary binomiums, wch how to doe hee hath not taught u{illeg}|s|, {illeg} his rule taught in pag 4 not extending to it. Thus his second example, ${1}^{æ}=6\chi +4$ supposeth ye cubick roote of $2+\sqrt{}-4$ to bee extracted wch indeed is $-1+\sqrt{}-1$, but I would know by wt direct {illeg}|m|ethod hee teacheth to find i{illeg}|t|. Not but that it may bee done, & I know how to doe it, but I think it not worth ye inserting into Kinck huyson, yet if you think it convenient (& indeed it may bee congruently enough inserted into him at pag 91) I will send you it done in my next letter. There remains but one thing more & thats about the Title page if you print these alterations wch I have made in the Author: For it may bee esteemed unhandsom & injurious to Kinck huysen to father a booke upo wholly upon him wch is soe much alter'd from what hee had made it. But I think all will bee safe if after ye words [nunc e Belgico Latinè versa,] bee added [et ab alio Authore locupletata.] or some other such note.

Somthing I have yet to say & that's about your paper concerning ye aggregate of the termes of a musicall progression: Namely yor way deduced from Mercators squareing of ye Hyperbola is ye same wth ye last of those two I had sent you together before. Onely I had taken a greate deale of paines to bring it to such a forme might bee most convenient for pr{illeg}|a|ctise & soe had made it soe intricate as to other respects that is noe wonder if you did not discerne its fountaine or by wt method I had composed it. I begg you pardon therefore for that obscurity: but I have since commi{illeg}|tt|ed a greater fault then that; & that's a neglect of writing to you, Yet I doubt not but that you have goodnesse enough to pardon all. In confidence of wch I rest

Yor most humble Servant

Is: Newton.

< insertion from the left margin >

I had sent yor booke immediately upon ye receipt of yor letter but that I staid two or three days {illeg}|e|xpecting to see Mr Pitts. As for ye coppys of Kinck-huysen you mentioned to send to me, I know tis usually not wthout some unwillingnesse that Math: books are printed. And I would not soe far discourage ye printing of it as to have {illeg} any coppys reserved for mee. I had rather purchase yor freinship then bookes. Yet if you please to send mee one coppy I shall acknowledg my selfe your debter for that together wth Dr Wallis his Mechanicks & ye rest, I. N.

< text from f 6r resumes >
<6av>

These

To Mr John Collins
at his house neare the three Crowns
in Bloosbury {sic} in

London.
wth a parcell.

|by Tho Powell at ye Greendragon in bishopgat|