Appendix Containing Newton's Proofs of his Priority Isaac Newton c. 848 words The Newton Project Oxford 2020 Newton Project, University of Oxford

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 c. 1710-1720, in English, with some Latin, c. 848 words, 1 f. 1 f.

in English, with some Latin

 MS Add. 3968, f. 253r-253v, Cambridge University Library, Cambridge, UK UKCambridgeCambridge University Library Portsmouth Collection MS Add. 3968, f. 253r-253v c. 1710-1720 England English Latin Isaac Newton ScienceMathematics Transcription by Marie Soulier Transcription by Michelle Pfeffer Transcription continued by Robert Ralley Transcription completed by Robert Ralley. Code audited by Michael Hawkins.
253 APPENDIX.

By the foregoing Papers & Records it may be understood that Mr Leibnitz in the year 1676 received rea did not understand the higher Geometry when he was the first time in England, wchwhich was in February 1673 nor began to study it while his correspondence wthwith Mr Oldenburg continued uninterrupted wchwhich was till Iune 6th 16 of the same year. Then he began to be instructed in the higher Geometry by Mr Hygens, beginning wthwith his Horologium oscillatorium oscillatorium then newly published about a month before. The next year in Iuly 1674 he received his correspondence wthwith Mr Oldenburg & began to boast of his skill in the higher Geometry, pretending in 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 wrote presently earnestly to Mr Oldenburg to procure from Mr Collins the Demonstration of this series, that is, for the method of finding it, & promised a reward for the communication same. Mr Newton in his Letter of 13 Iune following at the request of Mr Oldenburg & Mr Collins sent him the reward Demonstration & Mr Leibnitz in his next Letter dated 27 Aug. 1676 sent back the promised reward. And this reward was a Series invented by Mr Ia. Gregory & sent by him to Mr Collins, & in a Letter dated 15 Feb. 16701 & by Mr Collins & Mr Oldenburg communicated to Mr Leibnitz twice; first in a Letter dated 15 Apr. 1715 & then in a Copy of a Letter dated Mr Gregories Letter above mentioned wchwhich was inserted into the extract excerpta ex D. Gregorij Epistolis sent by Mr Oldenburg to Mr LeinitzLeibnitz 26 Iulij 1676. One And Mr Newton commended the invention of this Series but did not then know that it it it was invented by Gregory & sent by to Mr Leibnitz from London. About And aAfter this Mr Leibnitz printed this series as his own in Acta Eruditorum for Febr. 1682, without mentioning the correspondence by wchwhich this series was sent to him twice from London he had received it from hence. ♀♀ He also in his Letter of 27 August 1676 put in his claim to several series wchwhich he had received from Mr Newton had sent to him Idem, but upon Mr Newtons correcting him, he desisted from his claim. And these things are plane matter of fact. For Mr 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 Commerscium Epistolicum have been examined in collated wthwith 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 wchwhich it was published. And thus much concerning the series pretended to be invented by Mr Leibnitz

As for his Methodus differentialis 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. Hee did not understand was learning the higher Geometry before in the year 1674. Mr Newton in his Letter of 13 Iune 1676 wrote thatus Analysis beneficio Æquationum infinitarum ad omnia, pene dixerim, problemata si numeralia Diophanti & similia excipias) sese extendit. Mr Leibnitz in his Letter of 27 Aug. 1676 replied: Quod dicere videmini plerasque difficultates (exceptis Problematibus Diophantæis) ad series reduci Infinitas reduci; id mihi non videtur. Sunt enim multa adeo mira et implexa ut neque ab Æquationibus pendeant, neque 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 Mr Newtons Letter to Mr Leibnitz Collins dated 10 Decem 1672 & another of Mr Gregorys Letter to Mr Collins dated 5 Sept. 1670. In the first Mr Newton drepresented that he had a general method of solving Problems (such as were those wchwhich stuck not at Curves Surdes, & readily gave the method of Tangents of Gregory & Slusius & in the second Mr Gregory represented that his method was derived from Dr Barrows. And this was enough to let Mr Leibnitz know that there was such a general method & that the way to it was to improve Dr Barrows method of Tangents as Gregory had done so as to make it produce 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