( 34 ' ) 
their Differences ; thus in the prefent Example, the firft 
Increments * in the Series 1.3. 6. 10. 15*, &c. are found by 
taking the Differences of the Numbers x in the Series i. 
4.10.20.35’, drc- and the fecond Increments * in the 
Series 1. 2. 3. 4. 5", are found in the like manner, by 
taking the Differences of the Numbers and fo of the 
third and other Increments. This Method confiflsof two 
parts; One is concerned in jfhewing how to find the Re- 
lations of the Increments of feveral variable Quantities, 
having given the Relations of the Quantities themfelves; 
and the Other is concerned in finding the Relations of the 
Integral Quantities themfelves freed from the confidera- 
tion of their Increments, having given the Relations of 
the Increments : either fimply, or they being any how 
compounded with their Integral Quantities. In the Me- 
thod of Fluxions Quantities are not confider’d with their 
parts, but with the Velocities of the Motions they are 
fuppofed to be formed by ; or to fpeak more accurately, 
they are confider’d with the Quantities of the Motions by 
which they are fuppofed to be generated ; for the Fluxions 
are proportional to the Velocities, only when the moving 
Quantities, which produce the flowing Quantities confi- 
der’d, are equal. Thefe Quantities of Motion, or Velo- 
cities when the moving Quantities are equal, are what 
Sir lfaac Newton calls Fluxions- As in the Method of 
Increments there are fecond, third, and other Increments; 
fo in the Method of Fluxions there are fecond, third, and 
other Fluxions ; the Fluxions themfelves being confider’d 
as Quantities that are formed by Motion, the Quantity 
of which Motion is their Fluxions. As the Method of 
Increments confifts of two Parts; one being concern’d in 
finding the Increments from the Integrals given, and the 
other in finding the Integrals having given the Increments ; 
fb does the Method of Fluxions confift of two Parts ; 
the one fhewing how to find the Fluxions, having the 
H h h Flu- 
