[ U l 3 
Time in which it is defcribed. By fuppofing the 
Tangent of the Curve to be the Production of the 
rectilineal Element of the Curve, the Subtenfe of 
the Angle of Contact is found equal to the Second 
Difference or Fluxion of the Ordinate; but in this 
Inquiry, the Tangent ought to be fuppofed to be 
equally inclined to the two Elements of the Curve 
that terminate at the Point of Gonta& 5. and then the 
Subtenfe of the Angle of Contact will be found 
equal to half the Second Difference of the Ordinate, 
which is its true Value. 
Sir Ifaac Newton , however, inveftigates the Flu- 
xions of Quantities in a more unexceptionable man- 
ner. He firfl: determines the finite fimultaneous In- 
crements of the Fluents, and, by comparing them, 
inveftigates the Ratio that is the Limit of the various 
Proportions which they bear to each other, while 
he fuppofes them to decreafe together till they vanifh. 
When the generating Motions are variable, the Ratio 
of the fimultaneous Increments that are generated 
from any Term, is exprefled by feveral Quantities, 
fome of which arife from the Ratio of the generating 
Motions at that Term, and others from the fubfe- 
quent Acceleration or Retardation of thefe Motions. 
While the Increments are fuppofed to be diminifhed, 
the former remain invariable, but the latter decreafe 
continually, and vanifh with the Increments; and 
hence the Limit of the variable Ratio, of the Incre- 
ments (or their ultimate Ratio) gives the prccife 
Ratio of the generating Motions or Fluxions. Moft 
of the Propofitions in the preceding Chapters may be 
more briefly demonftrated by this Method, (of which 
feverai 
