On the Vis viva. Q277 
For 4c P S=au’?;4cps=bV*;4cqt=dv’, 
by cor. 2. theor. 3.; hence, by addition, 4 cx 
(PS+pstqt, &e.)=au?> t+bV*t+dv’*, &e. 
Q.E.D. 
Cor. 1. If g be the sum of the vires vive of 
the bodies, whose masses are a, b,d, &c.g 
will have a constant proportion to au*+bV* +4 
dv’, &c. 
Cor. 2. Let n—a+b+d, Kc. r= its velocity 
when g denotes its vis viva, and we have by 
cor. 1. nz?=au?+bV?+d v’, &c. ; hence 7— 
pate MATT Rs 
ScnHotium. It appears from the last 
corollary, that a system of bodies in motion 
has an assignable quantity of vis viva, even 
when the momentum of it, or the motion of its 
centre of gravity is equal to nothing. 
TrErorEM V. Let P, Q, R, &c. (plate 4, 
fig. 2) be a system of bodies in motion, whose 
common centre of gravity is G, moving in 
absolute space, in the direction Gg: put y= 
the velocity of G in Gg; u= the velocity, 
with which P approaches to, or recedes from 
G in the relative space P,Q, R; V the same 
‘Kind of velocity in respect of Q, and v in re- 
spect of R; and let a, 6, d, denote the masses 
of P,Q, and R: then the vis viva of the sys- 
tem will be as (a+b4d).y*+tau*+bV*+dv*. 
