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This is evident from the preceding Corollary. 
Coroll. 34 . If the Vis viva MV X bend a Spring 
thro’ its whole Length, and be confumed in doling 
it, any other Vis viva equal to the former, as nn 
Mx — - j will dofe the fame Spring, and be con- 
71 n 
fumed thereby. 
This is evident from Coroll. 32. 
Coroll. 3 5 - But the Time of doling the Spring by 
the Vis viva nn Mx ~, will be to the Time of 
71 n 
doling it by the Vis viva MV % as n to 1. 
For, by Coroll. 11. fince the Spring is given, the 
Time is as V M. 
Coroll. 3 6. If the Vis viva MV- be wholly confumed 
in doling a Spring of the Strength P, and Length/# j 
the Vis viva , nn MV 2 , will be fufficient to dofe, 
1. Either a Spring of the Strength nnP, and 
Length L. 
2. Or a Spring of the Strength n P> and Length 
n L. 
3. Or of the Strength P, and Length nn L. 
4. Or, if n be a whole Number, the Number n 
of Springs, each of the Strength P y and Length L , 
one after another. 
For, MV 1 : nn MV 1 :: P L : nnP L ; and 
therefore, by Coroll. 32. the Vis viva , nnMV z , 
will dofe any Spring that has nnP L for the Pro- 
dud of its Strength and Length. But nnP L is 
compofed either of nn P x L y or of n P x n L y or 
of P x nn L. 
Alfo the Lofs of the Vis viva , in bending a given 
Spring, being always the tame, by Coroll. 7. and 
the Vis viva , MV 2 being wholly loft in bending 
I a finszle 
4^’ 
