[ 6o ] 
For, by the preceding Coroll, if the Spring be bent 
thro’ the Space /, and each of thefe Quantities of 
Motion be confumed thereby 5 IV Mi IV n M. : : 
MV', n M x — . But M V~ n M x — j and 
n n 
therefore, IV M— IV n M, or 1 — n, and M — 
n Mj and V~ — . Therefore the Quantity of Mo- 
v 
tion n M x “is not only equal to M V \ but is com- 
pofed of an equal Mafs, and an equal Velocity. 
Coroll. 16. But a Quantity of Motion lefs than 
M Vi in any given Ratio, may bend the fame Spring 
thro' the fame Space /, and the Time of bending it 
will be lefs in the fame given Ratio . 
For, let 1 to w be the given Ratio ; and let the 
leffer Quantity of Motion be x n V ; which is 
to MV, as 1 to n. Then, by Coroll. 14. the Spring 
being given, IV Mi IV — : ; MV 1 — — x n V~ 
VTm x 1 ^ vr ” VT* Therefore the Quantity of 
Motion x n V, being equal to ~^->will bend 
the Spring thro’ the fame Space /. 
Likewife, by the fame Corollary, MV is as Its 
and / being given, the Quantity of Motion is as t : 
Therefore the Time of bending the Spring will be lefs 
in the fame Ratio, as the Quantity of Motion is lefs. 
Coroll. 17. A Quantity of Motion greater than 
MV, in any Ratio given, may be confumed in bend- 
ing the Spring thro 3 the fame Space ; and the Time 
of bending it will be greater in rhe fame given 
Ratio . 
This 
