C 11° ] 
tions, the Theory of Motion is rendered applicable 
to this D.o&rine with the greateft Evidence, without 
fuppofmg Quantities infinitely little, or having rc- 
courfc to prime or ultimate Ratios. The Author 
iirfi demonstrates from them all the general Theorems 
concerning Motion, that are of Ufe in this Doctrine ; 
as that when the Spaces deferibed by Two variable 
Motions are always equal, or in a given Ratio , the 
Velocities are always equal, or in the fame given 
Ratio } and convcrfcly, when the Velocities of Two 
Motions are always equal to each other, or in a given 
Ratio , the Spaces deferibed by thofe Motions in the 
fame Time are always equal, or in that given Ration 
that when a Space is always equal to the Sum or 
Difference, of the Spaces deferibed by Two other 
Motions, the Velocity of the Firft Motion is always 
equal to the Sum or Difference of the Velocities of 
the other Motions; and converfely, that when a Ve- 
locity is always equal to the Sum or Difference of 
Two other Velocities, the Space deferibed by the 
Firft Motion is always equal to the Sum or Difference 
of the Spaces deferibed by thefe Two other Motions. 
In comparing Motions in this Do&rine, it is conve- 
nient and ufual to fuppofe one of them uniform ; 
and it is here demonftrated, that if the Relation of the 
Quantities be always determined by the fame Rule or 
Equation, the Ratio of the Motions is determined 
in the fame manner, when both are fuppofed vari- 
able. Thefe Propofitions are demonftrated ftri&ly 
by the fame Method which is carried on in the 
enfuing Chapters for determining the Fluxions of 
the Figures. 
In 
