On the Vis viva. 2$1 
Cor. 2. Let P and Q be the centres of gra- 
vity of the bodies, when they come into con- 
tact at E; p and q their centres of gravity, when 
they are at rest in the space PABQ by Cor. 
2, Theor. 5; then as action and reaction 
are equal at EK, GE will be constant in all 
cases ; because G and the space PABQ move 
with equal velocities ; and from the nature of 
the centre of gravity it will be as PG: pg:: 
QG:qg. Now let the bodies APE, BQE 
be homogeneous and pliant ; and it is evident, 
that one of the points P or Q moves faster than 
G; from whence it follows that pg and gq are 
less than PG and GQ; i. e. the points P and @ 
approach each other and the common centre 
of gravity G, while the mutual reaction of 
the bodies is exerted to reduce the vis viva of 
the system to that of its centre of gravity. 
Let us suppose in the next place APE to be 
an indefinitely hard body, and BQE to be 
soft; then APE will suffer no change of 
figure; PG (or PE+EG) will be constant ; 
that is, pg=PG; therefore qg=QG and 
pg=PQ, in which case the body BQE under- 
goes all the change. Lastly, if both the 
bodies be infinitely hard, neither will suffer 
any change; and PQ will remain invariable: 
but a force situated in @ will act equally on 
their respective centres of gravity in the, 
Nn 
