How we cite our quotes: (Essay.Paragraph)
Quote #1
The instability, injustice, and confusion introduced into the public councils, have, in truth, been the mortal diseases under which popular governments have everywhere perished; as they continue to be the favorite and fruitful topics from which the adversaries to liberty derive their most specious declamations. (10.1)
Simply ensuring freedom ain't enough. If the United States was going to survive without the States fracturing one against the other, they needed to be brought into one order. Disorder is the enemy of society, by this logic.
Quote #2
Hence it is that such democracies have ever been spectacles of turbulence and contention; have ever been found incompatible with personal security or the rights of property; and have in general been as short in their lives as they have been violent in their deaths. (10.13)
Madison's pretty much saying that democracy is one of the most chaotic forms of government imaginable. He's probably also looking back to the democracy of Athens, which is probably what he's referring to here.
Quote #3
A dependence on the people is, no doubt, the primary control on the government; but experience has taught mankind the necessity of auxiliary precautions. (51.4)
Madison's asserting that there needs to be an extra level of control above the heads of the will of the people. Governments need to be stable and persist through turbulent times and bad leaders.