L 6 . 3 
This appears after the fame manner as the pre- 
ceding, by making n a fraaional Number inftead of a 
^CorolT 1 8. If the Motion of the Body ceafe, 
when the Spring is bent thro’ any Space A the initial 
or to 
Vis viva, or MV--, is equal to -feyf , 
C 2 ±L : And a a M = ^ = { '■ 
2 A ^ 
For, by Coroll. 8 . V =• C l V \~ M l a ^ ^2. ma. 
pi 
c 2 /. p _ c ^ pi 
or V‘ 2 ML A 2MA 
c 2 P / 2 C 2 pi V 2 P l z 
■ Therefore M V 2 
v 2 pi 
2 LA 2 A 2 La 2 a . 
Coroll- 19- In the fame Cafe, the initial Vis viva 
Pi 2, 7 p 
is proportional to — = pi and if —be given, 
the Vis viva is as / 2 , or asy> 2 . 
For, in the preceding Corollary, ~ being a given 
Quantity, the Vis viva is as — — = p l > and, if — ■ 
be given, it will be as / % or as p 2 ; iorafmuch as p 
and / increafe in the fame Proportion. 
Coroll. 20. If the Vis viva , MV 2 , bend a Spring 
thro’ the Space /, and be totally con fumed thereby, 
any other Vis viva , equal to the former, as n n 
M x — , will bend the fame Spring thro’ the fame 
Space, and be totally confumed thereby. 
For, the Spring being the fame, -jr* is given ; 
aud therefore by Coroll. 1 9* the Vis viva, widen 
will 
