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a fingle Spiring P L ; the Lofs of the Vis viva, n n 
MV % , in doling one fuch Spring, will be MV 9 j 
and its Lofs in doling a fecond fuch Spring, will 
again be MV % , and foon: Confequently, the Num- 
ber nn of fuch Springs will be clofed one after an- 
other, by that time the Vis viva, n n MV % is 
wholly confumed. 
Scholium III. 
If the Spring, inftead of being at firft wholly un- 
bent, as we have hitherto confider'd it, be now fup- 
pofed to have been already bent thro" fome Space 
C B , before the Body ftrik.es it ,• and the Velocity of 
the Body be required, after the Spring is bent thro* 
any further Space, B T), Fig. 8. this Cafe, as well 
as the Three other above-mention d, will be found 
to come under our Theorem. 
For, if v be the Velocity with which the Body 
is fuppofed to ftrike againft the bent Spring at B , 
it is evident, that this may be confidefd, either as 
the original Velocity, or as the Remainder of a 
greater Velocity V, with which the Body might have 
ftruck upon the Spring at C, and which, upon bend- 
ing the Spring from C to B } would now be reduced 
to v. For, in either Cafe, the EfFed in bending 
the Spring from B to F) } will be exadly the fame. 
In order, therefore, to determine this imaginary 
Velocity V, let a middle Proportional, B F, betaken 
' M 
between CL x and 2 *, a being the Height to 
r 
which a Body will afccnd in vacuo with the Velo- 
city v* draw B F perpendicular to C B, and, with 
l the 
