<55r>

Cambridge.
Sept. 5. 1676.

Sr

I received ye Packet you sent & return you ye manuscript papers wth my thanks for them & for Mr Frenicle's book. In yor paper about Mr Gregory I have presumed to race out two things as you will perceive; the first because though about 5 or 6 years ago{illeg}|e| I wrote a discourse in wch I explained ye doctrine of infinite æquations, yet I have not hitherto read it but keep it by me: the last because in my generall method mentioned in yor 4th section, I have occasion to make use of no other wa{illeg}|y| of extracting ye roots of a{illeg}|ff|ected æquations then that you are already acquainted with. If you should have occasion to see Dr Pell or (if he be not in London) to write to him at any time, pray prsent my service to him & let him know that (though I know not h{illeg}|o|w far Mr Gregory has improved ye Method of infinite series yet) so far as I know any thing of it I account it of no great advantage for resolving affected æquations \in numbers/. Some use it may have sometimes this way but I neither invented it nor recommend it much for this end, but for {illeg}g{illeg} extending Algebra to such sorts of Problems as have {had} are not the common ways of computing extend not to. And therefore his method for resolving æquations interfering so little wth mine, I could wish (even though they interfered much more) that he would not stay to expect ye publishing of mine, as I perceive by one of ye papers you send|t| me he does: For I would {illeg} not be an instrument of hindring ye publick so long from enjoying any a thing so valuable. I have nothing in ye press, only Kin{illeg}ckhuysens Algebra I would have got printed here to satisfy ye expectation of some friends in London, but or Press cannot do it. This I suppose is ye book Dr Lloyd means. It is now in ye hands of a Bookseller here to get it printed: but if it doe come out I shall ad nothing to it. A{illeg}|s| for my paper I sent about infinite series, I know not whether it will be proper to print it. I leave it to yor discretion. In my apprehension it may do as well to suppress it, but if you think otherwise I desire you would give me notice before it go into ye Press, because of altering an expression or two. Mr Baker's patience as well as his skill I admire. His method I see is to find first X the summ of ye 4 quantities & then ye quantities severally, wch I think is ye method you were suggesting to me at London. The other Problem <55v> I think I told you required no art but much calculation to resolve it, & therefore I have never thought of it since I saw you. There is nothing requisite to ye solution but this: To find two equations expressing ye nature of ye two curve lines, supposing their bases coincident & their ordinat{illeg}|es| parallel; & then the to {sic} end putting ye same letter \suppose x/ for ye bases in both æquations, & another letter suppose y for ye ordinates, to exterminate one of those letters. & reduce ye {illeg} For ye resulting equation will give ye|o|u ye several valors of ye other letter, wch valors limit all ye intersection points of ye two curves. I doubt I shal put you to too much trouble to transcribe Mr Leibnitz's whole letter if it be so long, & therefore I shall desire you to send me only a general account of it, wth such passages as you think may concern me, if there be any thing that concerns me.

Sr

I am

Yor humble Servant

Is. Newton.

<55av>

For Mr John Collins at
the Farthing Office
in Fanchurch
Street in

London

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

|Mr Newton about finding the Æquation to a chance Constructio|