( 547 ) 
it. This is a particular Cafe of the Tnverfe Method, but 
for its great ufefulnefs I thought it deferved particularly 
to be taken notice of. This Problem is treated of in ge- 
neral ill the i oth Propofition, The Method of folving it 
in finite Terms is only tentative; and when that does not 
Succeed, recourfe mu ft necefiarily be had to the Solution 
by a Series in the 8 th Propofition. In the i itb and i ith 
Proportions I have fliew’d how Seriefes may be conveni- 
ently found, in fome particular Gales when Fluxions are 
propofed. 
In, the (econd Part I have endeavour'd to (hew the 
Ufefulnefs of thefe Methods in the Solution of feveral 
Problems; The 13 th Propofitiorv is much the fame with 
Sir IfiAC Newtons Methodus Differentials, when the Or- 
dinates are at equal Diftances .• and in an Example at the 
End of this Propofition 1 have fhew’d how eafily Sir Ifaac 
Newton s Series for exprefling the Dignity of a Binomial 
may be found by this Incremental Method. The 14^ 
Propofition fhews in fome meafure how this Method may 
beofufe in fumming up of Arithmetical Seriefes. In the 
1 jtb Propofition I fhew by fome Examples how the Pro- 
portions of the Fluxions are to be found in Geometrical 
figures 5 from whence immediately flows the Method of 
finding the Radiufes of their inofculating Circles, the In- 
vention of the Points of contrary Flexure, and the Solu- 
tion of other Problems of the like nature. In the 16th 
Propofition l fhew how the Method of Fluxions is to be 
applied to the Quadrature of all forts of Curves. In 
the following Propofition I give a general Solution of the 
Problem of the Ifoperimeter, which has been treated of 
by the two famous Mathematical Brothers the Bernoulli's. 
In the 1 8 th Propofition I give the Solution of the Problem 
about the Catenaria , not only when the Chain is of a gi- 
ven Thicknefs every where, but in general, when its 
Thicknefs alters according to any given Law, In the 
