9th September 1676

Mr Newton

I received yours with the returne of the Papers inclosed, it is likely being in hast I did not so warily word Dr Pells sense of the infinite Series, which whatsoever it be it matters not, for he is utterly a Stranger to that kind of doctrine, he doth indeed affirme he can gett the Sum of many Algebraick Nomes giving a roote in order to the raising of a Resolvend, by ayd of tables of Logarithmes or Sines, the great promises in his Idea being attended with few or noe performances or Communications suitable causeth his esteeme much to fall &c Mr Oldenburgh is gone into the Country for 10 dayes however hath sent you a Coppy of the Letters both of Leibnitz and Schurnhaus, who are persons of great worth and Candour, and though they pretend or assert that the doctrine of infinite Series may be enlarged or the Series themselves attained by more easy Principles than yours yet you having already taken the Paines in your owne method, and the Result though not the Journey the same in both, I thinke notwithstanding you would doe well to publish the same in Latin or permitt a Translation and the comming foorth thereof in English, you will at first perceive that Leibnitz out of these Data AQ=r the radius and Q1N=z hath a designe to find the Ordinate B11D by an Analyticall Calculation, by ayd of the Square of the Chord AD which will be found =4r4rr+zz, for the finding whereof suppose the Chord of the Complement to the Semicircle to be likewise d{rawn}, and then there is given the ratio of those Chords such as r {to z an}d the Sum of their Squares =4rr and out of such data by a{n ana}lyticall processe AD is found =4r4rr+zz, And then it holds
ANNQADD1B1 which he calls y2 ie rr+zzzz4r4rr+zz4r4zz2rr+zz the roote whereof is 2zr2rr+zz=y as he makes it
The reason of my Writing is to rectify a mistake viz that when he sayes habita ergo recta B11D=2zr2r2+zr et recta B21B=4r3zβ2r2+z2 habebitur valor rectanguli, D11B2B multiplicatis eorum Valoribus in se invicem habebitur inquam 8r53r2+z2 (this is not the Product but should be 8r5zzβ3r2+z2, And whereas he sayes the Ordinate NP is 8r5z23r2+z2 this I thinke should also be 8r5zzβ3r2+zz112
I hope you will be pleased to settle me as to this doubt, not else at present but that I am

Your much obliged
John Collins

Viviani at Florence hath a treatise de
Loco Solido &c in the Presse, and here
father Bonds theory of the inclination of the
Magnet is almost finished


To Mr Isaac Newton

fellow of Trinity Colledge


© 2024 The Newton Project

Professor Rob Iliffe
Director, AHRC Newton Papers Project

Scott Mandelbrote,
Fellow & Perne librarian, Peterhouse, Cambridge

Faculty of History, George Street, Oxford, OX1 2RL - newtonproject@history.ox.ac.uk

Privacy Statement

  • University of Oxford
  • Arts and Humanities Research Council
  • JISC