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Alfo, ‘DE‘‘ + C‘D'=CE'‘ = CF'‘—BF t 
-h CB\ that is, + /■ + 2 Is + s* = 
2 A M L . / 5 2 $ M L 2 a. M L , 
— p— + / 5 or — ™ — = — 2 Is— s'; 
or 2 g ML = 2 *ML — Tsx 17 “+“*. 
Coroli. j8. If the Motion of the Body ceafeupon 
bending the Spring thro' the Space BD~s, that 
is, if g = o s then the Height to which the Body 
might afcen din vacuo, with the Velocity v, or a = 
P i X 2 l -f- * 
2 ML * 
For, by the lad, when g = 0 , 2 « M L = 
T s x 2 / 4 - s. 
Coroll. 3 9- If the Force of the Spring when 
bent thro 5 the Space C B y be equal to Af the Weight 
of the Body 5 the Height to which the Body would 
afcend in vacuo with the Velocity <v, is to the Space 
thro’ which it will bend the Spring, by ftriking 
upon it at B with that fame Velocity, as 2 / + j- 
to 2 /, or a. : s ; : 2 / +-j : 2 L 
For, by the lad, «.= ' L + -• 5 and ~ being 
equal to f 5 and, if p = M y «. 
— j x Sl+J 
2 / - 
Coroll. 40. Ify> — Af, and do alfo continue 
conftantly the fame while the Spring is bending 
from B to T> (both which Suppodtions are necel- 
farily made in reducing the Aftion of a Spring to 
that of Gravity upon an afcending Body), the Spring 
mud be of an infinite Length j and /, the Space 
thro- 
