C 343 ) 
ted their Conclufions in the Method of Exhauftions, by a 
Veduffio ad Abfurdum. 
Having premifed thus much in general concerning the 
two Methods here treated of, to come to a particular 
Defcription of this Book; In the Preface I give a fhorc 
Defcription of the Method of Increments, and an Account 
of Sir l[aac Nenrtons Notion of the Fluxions which I 
have already fpoke of The Book confifts of two Parts, 
and contains 118 Pages in Quarto; the Propofitions be- 
ing number’d throughout from the Beginning. In the 
firft Part I explain the Principles of both Methods : and 
in the fecond Part I fhew the Ufefulnefs of them in 
fome particular Examples* 
After having explain’d the Notation I make ufe of in 
the Introduction, in the firft Propofition I explain the 
direct Method both of Increments and of Fluxions. The 
fecond Propofition fhews how to transform an Equation 
wherein Integrals and their Increments, or wherein Fluents 
and their Fluxions are concern’d ; fo as in the Room of 
the Integrals or Fluents, to fubflitute their Compliments 
to a given Quantity with their Increments or their Fluxi- 
ons, they increafing in a contrary Senfe to the Quantities 
in the firft Suppofition. In the third Propofition I fhew 
how to transform a fluxional Equation, fo as to change 
the Characters of the Fluents, making that Quantity to 
flow uniformly which in the firft Suppofition flow’d un- 
equally, having fecond, third and other Fluxions, and 
making that Quantity which in the firft Suppofition flow’d 
uniformly, now to flow unequally, fo as to have fecond 
and third Fluxions, &c. This Propofition is of great 
ufe in the inverfe Method, when you would invert the 
Expreflion of the Relation of the flowing Quantities ; for 
Example, if in the Suppofition z flows uniformly and 
x variably, by the inverfe Method of Fluxions you will 
find x expreft by the Powers of z : but if you would find# 
H h lu expreft 
