[ 56 ] 
C B 2 _ 
R 2 
For, by Coroll 2 . V 2 — v 2 — V 2 x 
~ ; and i? % by the Conftruftion, being equal to 
v 2 — v 2 -y*r-x — 
P J r zMLa 
V z C 2 
But, by Galileos Theory, — = ~ ; therefore, 
V'—v'=. L211, andMF*-Mv' = ‘ c * fl * 
zM la 
2 LA 
C 2 pi 
2 A * 
Cor oil. 6. The Diminution of the T/i 1 iiiw, by 
bending a Spring thro’ any Space /, is always pro- 
p l 2 
portional to — , or to / : And, if either the Spring 
be given, or «iL be given in different Springs, the 
la 
Lofs of the Vis viva will be as /% or as p 2 . 
For, by Coroll 5 . MV 2 — Mv 2 — 
c 2 p i z 
"2 L A 
C 2 pi 
T ~A ’ 
M V 2 
C ^ 
and — being a conftant Quantity, MV' 
is as 
A 
p / 2 
r 
p l : And. if -j~ be given } 
p 2 
rri or 
M V 2 — Mv 2 will be as l 2 ; or as l 2 x 
■L. “ 
p 2 
as l 2 x jr > or as 2 . 
Coroll 7- The Lois of the Vis viva , by bendin 
a Spring thro’ its whole Length, or by wholly clofin 
C 2 P L 
it, is equal to ~W > and is proportional to V L : 
And, if V L be given, the Lofs of the Vis viva is 
always the fame. 
This 
UQ Cf9 
