( 20 6 ) 
to generate an Area, and the Area into a Line by local Mo- 
tion to generate a Solid. But the fumming up of Indivi- 
fibles to compofe an Area or Solid was never yet admitted in- 
to Geometry. Mr. Newton’s Method is a'^fo of greater Ufe 
and Certainty, being adapted either to the ready finding out 
of a Propofition by fuch Approximations as will create no 
Error in theConclufion, or to the demonftrating it exa&ly: 
Mr Leibnitz s is only for finding it out. When the Work 
fuGceeds not in finite Equations Mr. Newton has recourfe to 
converging Series, and thereby his Method becomes incom- 
parably more univerfal than that of Mr. Leibnitz , which is 
confin’d to finite Equations : for he has no Share in the Me- 
thod of infinite Series. SomeYears after the Method of Series 
‘ was invented, Mr. Leibnitz invented a Propofition for tranf* 
muting curvilinear Figures into other curvilinear Figures of 
equal Areas, in order to fquare them by converging Series: 
but the Methods of fquaring thole other Figures by fuch Series 
were not his. By the help of the new Analyfis Mr. Newton 
found out moft of the Propofitions in his Principia Philofophht 
but becaufe the Ancients for makingthings certain admitted 
nothing into Geometry before it was demonflrated fyntheti- 
cally, he demonflrated the Propofitions fynthetically, that 
the Syfleme of the Heavensmigbt be founded upon good Geo- 
metry. And this makes it now difficult for unskilful Men to 
fee the Analyfis by which thofe Propofitions were found out. 
It has been reprefented that Mr. Newt on , in the Scholium 
at the End of his Book of Quadratures, has put the third, 
fourth, and fifth Terms of a converging Series refpetftively 
equal to the fecond, third, and fourth Differences of the firft 
Term, and therefore did not then underfland the Method of 
fecond, third, and fourth Differences. Butin the firfl Pro- 
pofition of that Book he {hewed how to find the firft, fecond, 
third and following Fluxions in infinitum; and therefore when 
he wrote that Book, which was befotfe the Year 1676, he 
did underfland the Method of all the Fluxions, and by con- 
2 fequence 
