[ 33 * 3 
In Chap. II. a Triangle that has Two of its Sides 
given in Pofition, is fuppofed to be generated by ail 
Ordinate moving parallel to itfelf along the Bafe. 
When the Bafe increafes uniformly, the Triangle 
increafes with an accelerated Motion, becaufe its 
fucceflive Increments are Trapezia , that continually 
increafe. Therefore, if the Motion with which the 
Triangle flows, was continued uniformly from any 
Term for a given Time, a lefs Space would be de- 
feribed by it than the Increment of the Triangle 
which is adually generated in that Time by Axiom I. 
but a greater Space than the Increment which was 
actually generated in an equal Time preceding that 
Term, by Axiom II. and hence it is demonftrated, 
that the Fluxion of the Triangle is accurately mea- 
fured by the Redangle contained by the correfpond- 
ing Ordinate of the Triangle, and the right Line 
which meafures the Fluxion of the Bafe. The Incre- 
ment which the Triangle acquires in any Time, is 
refolved into Two Parts; that which is generated in 
confequence of the Motion with which the Triangle 
flows at the Beginning of the Time, and that which 
is generated in confequence of the Acceleration of 
this Motion for the fame Time. The latter is juftly 
negleded in meafuring that Motion (or the Fluxion 
of the Triangle at that Term), but may ferve for 
meafuring its Acceleration, or the Second Fluxion of 
the Triangle. The Motion with which the Triangle 
flows, is fimilar to that of a Body defeending in free 
Spaces by an uniform Gravity, the Velocity of 
which, at any Term of the Time, is not to be mea- 
fured by the Space deferibed by the Body in a given 
Time, cither before or after that Term, bccaufc the 
. U u Mo- 
