Letter from John Collins to Newton, dated 9 September 1676
9th September 1676
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 ye raising of a Resolvend, by ayd of tables of Logmes 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/, yo I thinke notwithstanding you would doe well to publish the same in Latin or permitt a Translation and the comming foorth thereof in Engs, you will at first perceive that Leibnitz out of these Data the radius and hath a designe to find the Ordinate by an Analyticall Calculation, by ayd of the Square of the Chord AD which will be found , for the finding whereof suppose ye Chord of the Complemt 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 and out of such data by a{n ana}lyticall processe is found , And then it holds
which he calls |ie| the roote whereof is as he makes it
The reason of my Writing \is to rectify a mistake viz/ that when he sayes habita ergo recta et recta habebitur valor rectanguli, multiplicatis eorum Valori{illeg}b|b|us in se invicem habebitur inquam (this is not the Product but should be , And whereas he sayes the Ordinate NP is this I thinke should also be
I hope you will be pleased to settle me as to this doubt, not else at present but that I am
Your much obliged
Servitor
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