How we cite our quotes: (Article.Sentence)
Quote #4
There shall be a firm and perpetual peace between his Brittanic Majesty and the said states, and between the subjects of the one and the citizens of the other, wherefore all hostilities both by sea and land shall from henceforth cease. (7.1)
Okay, it's not quite friendship, but you can't be friends with someone who's still shooting at you. Go ahead; try. Actually, don't. That's a terrible idea.
So you see the point. They need to conclude hostilities before they can move on to the healing process.
Quote #5
The navigation of the river Mississippi, from its source to the ocean, shall forever remain free and open to the subjects of Great Britain and the citizens of the United States. (8.1)
This is like one of those situations where a parent has to let both siblings use the same set of Star Wars action figures. Both countries wanted the Mississippi, which was really important for travel back then. So this provision insured that, legally speaking, both sides would have to cooperate. It's setting the stage for a kind of friendship to develop.