f 
Toon after publifhed in the Tranfattions It proved to be the 
fame with that of Mr Newton. it was founded upon three 
Lemmas, the firfl of which was this, Differentia duarum digni- 
tatum ejufdem gradus applicata ad dffrentiam latcrum dat partes - 
; • y* — x J 
ffngularei gradus infer ibt is ex bimmio laterum, ut = ym 
y — x 
-r ? df 
T y x + xx t that is, in the Notation of Mr. Leibnitz — = 
; ‘ '' dj 
— 3 yy. A Copy of Mr; Newtons Letter of Decemb. io. 1 6yz 
Was fent to Mr. Leibnitz by Mr. Oldenburg amongfl the Papers 
of Mr James Gregory, at the fame time with Mr. Newtons Let- 
ter of June 13. 1 676. And Mr. Newton having deferibed in 
thefe two Letters that he had a very general Analyfis, confi- 
ding partly of the Method of converging Series, partly of 
another Method, by Whidi he applied thofd Series to the 
Solution of almofi all Problems (except perhaps fome nume- 
ral ones like thofe of Diophantus ) and found the Tangents, 
Areas, Lengths, folid Contents, Centers of Gravity, and 
Curvities of Curves, and curvilinear Figures Geometrical or 
Mechanical, without flicking at Surds ; and that the Method 
of Tangents of Slufius was but a Branch or Corollary of this 
other Method : Mr. Leibnitz, in his returning Home through 
Holland, was meditating upon the Improvement of the Me- 
thod of Slufius. For in a Letter to Mr. Oldenburgh, dated 
from Amflerdam Nov. % 16^, he wrote thus Methodus 
Tangent turn a Slufio public ata nondum rei fafligium tenet . Pot eft 
aliquid amplius pr Atari in eo genere quod maximi foret nfus ad 
omnis generis Problemata : etiam ad meam {fine extraPlionihus) 
AEquationum ad feries reduPHonem. Nimirum poffet brevis qua- 
dam calculari circa Tangentes Tabula , eoufque continuanda donee 
progrejfto Tabula af par et \ ut earn feilicet quifque quoufque libucrit 
fine calculo continuare pojfit . This was the Improvement of 
the Method of Slufius into a general Method, which 
Nit. Leibnitz, was then thinking upon, and by his Words, 
Pot eft 
