( >95 ) 
Tot eft aliquid awplius praftari in eo genere quod max 'mi font 
ufus ad omnis generis Froblemata, ic Teems to be the only Im- 
provement which he had then in his Mind for extending the 
Method to all forts of Problems. The Improvement by the 
differential Calculus was not yet in his Mind, but muff be 
referred to the next Year. 
Mr. Nevaton in his next Letter, dated Ocfol.z^. 1 6:6, 
mentioned the Analjfis communicated by Dr. Barrow to 
Mr. Collins in the Year 1669, and alfo another Trad written 
in 1671. about converging Series, and about the other Me- 
thod by which Tangents were drawn after the Method of 
Slufius , and Maxima and Minima were determined, and the 
Quadrature of Curves was made more eafy, and this without 
flicking at Radicals, and by which Series were invented 
which brake bfF and gave the Quadrature of Curves in finite 
Equations when it might be. And the Foundation of thefc 
Operations he comprehended in this Sentence exprefl enig- 
matically as above. Data £ quatione fluentes quotcunque quantitates 
irrvolvente 1 flux tones invenire, & vice verfa. Which puts it pad 
all Difpute that he had invented the Method of Fluxions be- 
fore that time. And if other things in that Letter be consi- 
dered, it will appear that he had then brought it to great 
Perfection, and made it exceeding general ; the Propofiti- 
ons in his Bock of Quadratures, and the Methods of convex 
ging Series and of drawing a Curve Line through any Num- 
ber of given Points, being then known to him. For when 
the Method of Fluxions proceeds not in finite Equations, 
he reduces the Equations into converging Series by the bino- 
mial Theoreme, and by the Extra&ion of Fluents out of 
Equations involving or not involving their Fluxions. And 
when finite Equations are wanting., he deduces converging 
Series from the Conditions of the Probleme, by afluming the 
Terms of the Series gradually, and determining them by 
thofe Conditions. And when Fluents are to be derived from 
Fluxions, and the Law of the Fluxions is wanting, he find f s 
5 i 1 that 
