C 67 ] 
the Radius CF, defcribe the Quadrant C G F E A* 
Then will our prefent Cafe be exa&ly reduced to 
that of the Theorem ; C B, CF), reprcfentirrg the 
Spaces thro’ which the Spring is bent ; B F and 
F) E the Velocities in the Points B and F) •, G F 
and GE the Times of bending the Spring thro" the 
Spaces CB, CF) ; and CG reprefenting the imagi- 
nary Velocity V, with which the Body might have 
flmck the Spring at C. 
Tor, by the Theorem, B F z : C G * v * : F* ; 
and v 2 : V 2 : : <* : a. Therefore CG*=BF~x 
~ . But B F % ==2 a x by the Conftru&ion ; 
and, confequently, CG * = x L = 
~ a p L — , as in the Conftru&ion of the Theorem. 
From this Cafe we fhall draw a few Corollaries, 
as well for their Ufefulnefs upon other Occaftons, 
as to fhew how the Theory of Springs may be fafely 
applied to the A&ion of Gravity upon afcending or 
falling Bodies. 
Cor oil. 37* If the Body M y with the Velocity'!;, 
fufficient to carry it to the Height a, ftrike at B , 
upon a Spring already bent thro’ the Space C B~ 1 5 
and do thereby bend it thro 1 feme farther Space 
B F) = s 5 at the End of which Space, or at F ), 
the Body has a Velocity fufficient to carry it to fome 
Height, as g ; then g = LL..FF— p s x 2 1 +* 
For, by the Theorem, a : g : ; BF 2 : F)E % or 
®£ * = BF’ x— = 1 “ . " L x ± or® E‘ — 
At & 
2 s M L 
I 2 
P 
Alfo, 
