(A*9 ) 
fired Mr. Newton to explain to him the Method of finding 
thofe very two Series, 
When Mr. Neirton had received this Letter, he wrote back 
that all the faid four Series had been communicated by him 
to Mr. Leibnitz 5 the two firft being one and the fame Series in 
which the Letter / was put for the Logarithm with its Sign 
+ or — ; and the third being the Excels of the Radius above 
the verfcd Sine, for which a Series had been fent to him. 
Whereupon Mr. Leibnitz* defifted from his Claim. Mr. Newton 
alfo in the fame Letter dated Offob. 14. 1676. further explain- 
ed his Methods of Regreflion, as Mr. Leibnitz, had defired. 
And Mr. Leibnitz in his Letter of June zi. 1 677. defired a 
further Explication : but foon after,upon reading Mr. Newtons 
Letter a fecond time, wrote back July tz. 1 677. that he now 
underftood what he wanted ; and found by his old Papers 
that he had formerly ufed one of Mr. Newtons Methods of 
Regreflion, but in the Example which he had then by chance 
madeufe of, there being produced nothing elegant, he had, 
out of his ufual Impatience, negleded to ule it any further. 
He had therefore feveral dired Series, and by confequence a 
Method ol finding them, before he invented and forgot the 
inverfe Method. And if he had fearched his old Papers di- 
ligently, he might have found this Method alfo there ; but 
having forgot his own Methods he wrote for Mr, Newtons. 
When Mr. Newton in his Letter dated June 15. 1676. had 
explained his Method of Series, he added .* Ex his videre eft 
quantum fines Analfieos per hujufmodi infinitas aquat tones ampli- 
antur : quippe qu<£ earum beneficio ad omnia pent dixerim proble- 
rnata ((i numeralia Diophattfi fafimilia excipias) fife extendit. 
Non tamen ontnino univerfalis evadit , nifi per ulteriores quafdam 
Methodos eliciendi Series infinitas . Sunt enim queedam Troblema • 
ta in quibus non licet ad Series infinitas per Divifionem vel Extra - 
clionem radicum fimplrcium affeffarumve pervenire . Sed quomodo 
in iftis cafibus frocedendum fit jam non vacat dicere ; ut neque 
alia qu<£aam trade re, qua circa Reduttionem infinitanm Serierum 
z I i in 
