C 6 + ] 
Coroll. 29. If the Quantity of Motion MV bend 
a Spring thro’ its whole Length, and be con fumed 
thereby, no other Quantity of Motion equal to the 
former, as n M x , will clofe the fame Spring, 
and be wholly confumed thereby. 
This is proved in the fame manner as Coroll. 15, 
putting only L for /. 
Coroll. 30. But a Quantity of Motion lefs or 
greater than M V, in any given Ratio, may clofe 
the fame Spring, and be wholly confumed in doling 
it : And the Time fpent in doling the Spring will be 
refpe&ively lefs or greater, in the fame given Ratio. 
This is eafily proved from Coroll. 1 6 . 
Coroll. 31. If the Motion of the Body ceaie, 
when the Spring is wholly clofed, the initial Vis 
C * p L 
viva, or M V % , is equal to —- ~ A — l And 2 a M~ 
PL. 
For, by Cor oil. 22. V = C p d . T -. or V z — 
J 2 M A 
C 2 P L _ _ C 2 P L V 2 P L 
2. M A* 0f MV 2A 2a » 
Coroll. 32. In the fame Cafe, the initial Vis 
viva is as the Redangle under the Strength and 
Length of the Spring. 
C 2 P T. 
For, by the preceding Corollary, MV 2 = 
2 A 
c 2 
and — is a 2 
„ _ d ivcn Quantity? wherefore MV 2 is 
as P L . 
p 
Coroll. 33. In the fame Cafe, if be given, the 
initial Vis viva is as P % or as Z» 2 . 
This 
