( »8o ) 
Examp’es of the fecond kind you have in the fame Compen- 
dium, in finding the Length of Curve Lines p i 5. and in 
finding the Ordinates, Areas and Lengths of Mechanical 
Curves p. 18. 19. And he tells you, that by the fame Method, 
Tangents may be drawn to mechanical Curves p. 19. And 
in his Letter of Decemb. 10. 167 z. he adds, that Problems 
about the Curvature of Curves Geometrical or Mechanical are 
refolv’d by the fame Method. Whence its manifefl, chat he 
had then extended the Method to the fecond and third Mo- 
ments. For when the Areas of Curves are confidered as 
Fluents ( as is ufual in this Analyfls ) the Ordinates exprefs the 
firft Fluxions, the Tangents are given by the fecond Fluxions, 
and the Curvatures by the third, And even in this Analyfls 
p . 16. where Mr. Newton faith, Momentum e(l fuperflcies cum de 
folidis,&Linea cum de [uperficiebus ,&P unttum cum de lineis agitur , 
it is all one as if he had faid, that when Solids are confide- 
red as Fluents, their Moments are Superficies, and the Mo- 
ments of thofe Moments (or fecond Moments) are Lines, and 
the Moments of thofe Moments (or third Moments) are 
Points, in the Senfe of Cavalier ius. And in his Princtpia 
PhilofophU , where he frequently confiders Lines as Fluents 
defcribed by Points, whofe Velocities increafe or decreafe, 
the Velocities are the firft Fluxions, and their Increafe the 
fecond. And the Probleme, Data aquatione fluentes quantity 
tes involvente flux tones invenire & vice verfa, extends to all 
the Fluxions, as is manifefl by the Examples of the Solution 
thereof, published by Dr .Wallis fom.z. p 391, 392., 396. 
And in Lib. II. Princip. Prop. xiv. he calls the fecond Diffe- 
rence the Difference of Moments. 
Now that you may know what kind of Calculation 
Mr. Newton ufed in, or before the Year 1669. when he wrote 
this Compendium of his Analyfls , I will here fet down his 
Demonflration of the firft Rule abovementioned. Sit 
:> ' Curvx 
