[ 55 3 
TT» BF _____ yjr 2 
For, ftnce v 5 —V * * 
r s — /* 
R 2 
5 if, for 
i?% we fubftitute its Value ~ ~ ~~~ ? we ^ ave ^ " — 
1 <2. 
/>" 2 X 
2 M L> a — P l z 
- •• TAft. , oiv=V*t' — lML « "- : And, 
as by Dr. Hook's Principle, L : / : - ^ or ^ — 
P L, > = F x fZ-j-yj — , or, <y - / x 
2 Ma~ 
pi 
But — , by Galileos Do&rine, is a conftant Quan- 
\/ U 2 
tity 5 and therefore <1/ is proportional to j/ . JLL 
2 M a — fit 
75 ’ 
or, to // 
Coroll. 4. The Time /• of bending the Spring thro’ 
any Space /, is proportional to the Arch G F di- 
vided by V a '-> l being the right Sine of the Arch, 
and R—f/ - M F\ being the Radius. 
G F T 
For, by the Theorem, t = Tx — j and -- — is 
a conftant Quantity. 
Coroll. 5. The Diminution of the Product of the 
Weight of the Body into the Square of the Velocity, 
or (to ufe the Expreffion of fome late Writers) the 
Diminution of the Vis vivd> that is, M V 1 — Mv z , 
by bending a Spring thro' any Space /, is always 
C 2 p l 2- c 2 p 1 
equal to LA -, or to j where A is the Height 
from which a heavy Body will fall in vacuo in a 
Second of Time, and C is the Celerity gained by 
that Fall. 
For, 
4 
