Draft letter from John Collins to Newton, written c. 13-16 July 1670

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M^r Newton

S^r

I received yours with Kinckhuysens Introduction, and perceive you have taken great paines which god willing shall be inserted into y^e Translation and printed with it, hereby you have much obliged the young Students of Algebra < insertion from the top of the page > and the Bookseller who was at y^e commencem^t on Munday and Tuesday but was so taken up and concerned you were so too that he did not see you, but remaines your Debt much obliged D^r where of Will som < text from f 7r resumes > , I formerly intimated that I thou{illeg}|gh|t he \Kinck/ had too slightly handled the doctrine of Surd Numbers, \and that the same might be transcribed from others/ I find you in the same opinion for in one of your Marginall Notes you say thus, The Author having slipped over the Addition Substraction Multiplication and Division of all but quadratick Surds &c and \*/ < insertion from lower down f 7r > * and he acknowledgeth as much {tantly} by consequence himselfe referring the Reader to Wassenare Onwissen Wistconstenaer however he cheifely thereby intended y^e Cube rootes of Binomialls which you have supplyed < text from higher up f 7r resumes > being unwilling the young Student should be referred to other bookes \which are scarce/ for the Doctrine of Surds < insertion from lower down f 7r > I {make bold} will a little further presume {illeg}|a|nd to \therefore/ crave your iudgem^t of what you thinke necessary to be taken either out of Scheubelius, Van Ceulen, or Humes which \bookes/ I herewith send and having another Scheubelius you here, you need not returne that sent, wherewith be pleased to accept of another Libellus de Machina Aquatica There are two other Authors have excellently handled Surds, those are Frans van der Huyps in \his/ Low Dutch Algebra and in 1654 and y^e Seiur d Taneur \in french/ in his Tract of irrationall quantities and Commentaries on 10 Euclid at Paris in 1640. < text from higher up f 7r resumes >

I am glad to know you have a better way for the Musicall Progression then the latter you sent up \p{illeg} (being the same I mentioned not having □/ < insertion from the left margin > □ seriously considered your Letter reserving it to better leisure) < text from f 7r resumes > /you\ having hinted so much in an intermediate letter, but sorry it put you to so much trouble, being very loath to imp{illeg} ex{illeg}r{illeg}se intrude upon your Patience, Mengolus an excellent Mathematician and Musitian hath a treatise of Musick in the Presse and there is newly come over by the Post (sent to the Societie) a little treatise of his in Italian of the Suns Parallax and refraction |which I have not yet seen|

I was apt to beleive that Ferguson had done more \then Kinckhuysen/ in these 3 particulars

1 In {setting} \applying one generall rule to/ both kinds of Cubick Æquations, to wit \as well/ those that are solved by meane Proportionall Proportionalls as those that require Trisection

2 In rendring the rootes of Cubick and Biquadratick Æquations properly that is to say in giving the rootes when \they are explicated by/ fractions or Surds exactly, and not by a quamproximé

3 In emprooving the generall Method

But having failed in the first I conceive it opportune to shew at least that he ha wherein he hath failed, and if you please (which is by you offred and seemes desirable) supply his defect

Lastly why you should desire to have your Name unmentioned I see not, but if it be your will and command so to have it, it shall be observed by

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To M^r Newton July 13 1670