C 55° ] 
is fuppofed to become infinitely fmali, and is gene- 
rally exprefi'ed by Two or more Terms, fome of 
which become infinitely lefs than the reft, and there- 
fore being negle&ed as of no Importance, the re- 
maining Terms form, what is called the ‘Difference 
of the Quantity propofed. The Terms that are neg- 
lected in this manner are the very fame which arife 
in confequence of the Acceleration or Retardation 
of the generating Motion, during the infinitely fmali 
Time in which the Element is generated ; and there- 
fore thefe Differences are in the fame Ratio to each 
other as the generating Motions or Fluxions. Hence 
the Concluftons in this Method are accurately true, 
without even an infinitely fmali Error, and agree 
with thofe that are deduced by the Method of 
Fluxions. 
It is ufual in this Method to confider a Curve as a 
Polygon of an infinite Number of S’des, which, being 
produced, give the Tangents of the Curve, and, by 
their Inclination to each other, meafure its Cur- 
vature. But it is neceftary in fome Cafes, if we 
would avoid Error, to refolve the Element of the 
Curve into feveral infinitely fmali Parts, or even 
fometimes into Infinitelimals of the Second Order 5 
and Errors that might otherwife arife in its Applica- 
tion, may, with due Care, be corrected by a proper 
Ufe of this Method itfelf, of which fome Inftances 
are given. If we were to fuppofe, for Example, the 
leaft Arc that can be deferibed by a Pendulum to 
coincide with its Chord, the Time of the Vibration 
derived from this Suppofition will be found er- 
roneous; but by refolving that Arc into more and 
more infinitely fmali Parts, we approach to the true 
Time 
1 
