On the Vis viva. 283 
&e, denote the absolute velocities of P, Q, R, 
&e, and proceed as in nga RET of 
the theorem. | 
Txurorem VII. saat APE: dial BQE, 
(ithe 4, fig. 3), be two homogeneous and 
elastic bodies in motion, which meet at: E; 
put’ Fand f for the quanitities of vis viva which 
are exerted during the streke, on APE and 
B pe to change their figures, and let their 
masses be denoted by a and 6; and it will be q 
as F: fi: b: a; that is, these quantities of 
vis viva will be inversely as = quantities of 
matter on which they a cme 
For, ‘since the bodies APE and BQE 
are homogencous, their powers of resistance 
are “equal ; “therefore the point BH, and their 
common centre of gravity G, are at rest in 
the relative space AP QB, by cor. 2. theor. 
6; and the motion of AP EH, as well as that 
of BQE, is opposed by a force acting at G 
in the contrary directions GP and GQ, by 
mechanics, prop. 44. cor. 4; hence we have 
as Pp: Qq: 2b: 4, “by cor. 3. theor. 3 ; but 
ary Te Pe Qq, by cor. 2. theor 2; 
because the resisting powers are equal in both 
directions ; therefore as I’: f:: b: a. Q.E.D. 
| Cor. 1. The vis viva, exerted on an elas- 
tic body , does not become inactive by chang- 
ing the figure of that body. On the contrary 
n2 
