We can differentiate eqn. 1.18 with respect to time.
Since the m'are constant, the differentiation only acts on the r's giving
or
This implies that if the momentum 
is conserved, so
is the velocity of the center of mass 
.
So we have the equation
This says that the total momentum of a system is the same as when all the mass is concentrated at one point, at the system's center of mass!
If you can keep your eyes open a little longer, we can go further and differentiate this again:
So from 1.12 we finally have that
This says that the net force acting on an object is just the total mass times the acceleration of the center of mass.
Didn't we use already? Isn't this just Newton's second law?
We did use this already. When we did blocks going down inclined
planes which are non-particle-like objects. We did apply
F=ma to them. But err, we shouldn't have done this so cavlierly!
Newton's second
law really should have been defined for point objects. What we
just showed is that it also works for blocks, turnips, camels,
or what ever system you care to choose. You just have to use
the total mass of the system for "m" and the center of mass acceleration
for "a". The force 
is the net external force
acting the object.
I could have gone through all this math a few chapters ago, but it wasn't really necessary to solve problems. I'm including this to show you why would you did was OK. I also figured you might be in need of a good nap.
Now its time to wake up and do some more physics problems!
