Appendix Containing Newton's Proofs of his Priority

Author: Isaac Newton

Source: MS Add. 3968, f. 253r-253v, Cambridge University Library, Cambridge, UK

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<253r>

APPENDIX.

By the foregoing Papers \{illeg} & Records/ it may be understood that M^r Leibnitz in the year 1676 received rea{illeg} did not understand the higher Geometry when he was the first time in England, w^ch was in {illeg} February 1673 nor began to study it while his correspondence w^th M^r Oldenburg continued uninterrupted w^ch was till Iune 6^th 16 of the same year. Then he began to be instructed in the higher Geometry by M^r Hygens, beginning w^th his Horologium oscillatorium oscillatorium {sic} then newly published about a month before. The next year in Iuly 1674 he received his correspondence w^th M^r Oldenburg & began to boast of his skill in the higher Geometry, pretending \in {sic} {illeg} |in his next| Letter of Octob 6/ to have found a Series which gave him the length of any arc Arc whose sine was given, tho the proportion of the sine to arc to the whole circumference was not yet known. But the method of finding this series he did not yet know: for in his Letter of 12 May 1676 he {illeg} wrote presently \earnestly/ to M^r Oldenburg to procure from M^r Collins the Demonstration of this series, that is, \{for}/ the method of finding it, & promised a reward for the communication same. M^r Newton in his Letter of 13 Iune following \at the request of M^r Oldenburg & M^r Collins/ sent him the reward {illeg} Demonstration & M^r Leibnitz in his next Letter dated 27 Aug. 1676 sent back the promised reward. And this reward was a Series invented by M^r |Ia.| Gregory & sent by him to M^r Collins, & in a Letter dated 15 Feb. 167 $\frac{0}{1}$ & by M^r Collins & M^r Oldenburg \communicated/ to M^r Leibnitz twice; first in a Letter dated 15 Apr. 1715 & then in a Copy of a Letter dated M^r Gregories Letter {illeg} above mentioned w^ch was inserted into the extract excerpta ex D. Gregorij Epistolis sent by M^r Oldenburg to M^r Leinitz {sic} 26 Iulij 1676. / {One} A{nd}\ M^r Newton commended the invention of this Series but did not then know that it {illeg} it it was invented by Gregory & sent by to M^r Leibnitz from London. About {illeg} \And/ a|A|fter this M^r Leibnitz printed this series \as his own/ in Acta Eruditorum for Febr. 1682, without mentioning the correspondence by w^ch this series was sent \to/ him twice from London he had received it from hence. ♀ < insertion from lower down f 253r > ♀ He also in his Letter of 27 August 1676 put in his claim to several series w^ch \he had received from/ M^r Newton had sent to him Idem, but upon M^r Newtons correcting him, he desisted from his claim. < text from higher up f 253r resumes > And these things are plane matter of fact. For M^r O Leibnitz by a Letter dated 20 May 1675 & still extant in his own hand writing, acknowledged the receipt of the Letter of Apr. 15. |And| These two Letters \as they/ are printed in the Commers|c|ium Epistolicum have been examined in collated w^th the originalls before many forreigners who went to \the howse of/ the R.S. to see the collation of the Commercium Epistolicum with the Originals from w^ch it was published. And thus much concerning the series pretended to be invented by M^r Leibnitz

As for his Methodus differentialis {illeg} he did not begin to leave \understand/ the higher Geometry before the yeare 1674, & when he wrote his Letters of 27 Aug: 1676 he it doth appear that he understood any thing of it before the year 1677. He{illeg}|e| did not understand \was learning/ the higher Geometry before \in/ the year 1674. M^r Newton in his Letter of 13 Iune 1676 wrote that|us| Analysis beneficio Æquationum infinitarum ad omnia, pene dixerim, problemata si numeralia Diophanti & similia excipias) sese extendit. M^r Leibnitz in his {illeg} Letter of 27 Aug. 1676 replied: Quod dicere videmini pleras difficultates (exceptis Problematibus Diophantæis) ad series reduci Infinitas reduci; id mihi non videtur. Sunt enim multa adeo mira et implexa ut ne ab Æquationibus pendeant, ne ex Quadraturis. Qualia sunt (ex multis alijs) Problemata methodi Tangentium inversæ. And therefore he had not yet a method for attempting such Problems. He had just then receivd The Excerpta ex Gregorij Epistolis & therein was a copy of M^r Newtons Letter to M^r Leibnitz \Collins/ dated 10 Decem 1672 & \another/ of M^r Gregorys Letter to M^r Collins dated 5 Sept. 1670. In the first M^r Newton d|r|epresented that he had a general method of solving Problems \(such as were those {illeg}/ w^ch stuck not at Curves Surdes, & {illeg} readily gave the method of Tangents of Gregory & Slusius & \in/ the second M^r Gregory represented that his method was derived from D^r Barrows. And this was enough to let M^r Leibnitz know that there was such a general method & that the way to it was to improve D^r Barrows method of Tangents as Gregory had done so as to make it <253v> produce the method of Slusius, & then to improve it further so as to make it proceede without stopping at fractio surds. And in my letter of October 24 1676 I repeated