How we cite our quotes: (Book.Chapter.Bekker #s); all Bekker line numbers are approximate, since they are keyed to the original Greek.
Quote #7
One form of partial justice...is found in the distributions of honor or money or any of the other things divisible among those who share in the regime (for in these things it is possible for one person to have a share that is either unequal or equal to another's). The other form of such justice is the corrective one involved in transactions...(5.2.1130b30-1131a1)
This "partial" type of justice is different from justice as a whole—which Aristotle defines as the whole of virtue in relation to others—and deals specifically with equality. Distributive justice ensures that everyone in a community has access to goods held in common. Corrective justice applies to interactions between people, whether they're voluntary (where both parties agree to interact) or involuntary (where one party doesn't agree, as in assault). In both cases, the law intervenes to maintain balance in society.
Quote #8
Hence when people dispute with one another, they find refuge before a judge. To go to a judge is to go to the just, for a judge wishes to be, as it were, the just ensouled. And people seek a judge as the middle way, and some call them mediators, on the grounds that, if they hit the middle term, they will have hit on the just. (5.4.1132a20-24)
In his thinking about justice, Aristotle shows how corrective justice aims to re-distribute the harm done in a dispute so that each party has a more equal share of it. The judge's job, then, is to inflict loss on the person who tries to gain more than his fair share of something from someone.
We're not speaking only in terms of money here; "gain" might mean injuring someone and gratifying our passions by doing so. While the judge can't take away the injury, he can strike down the unjust person in some way, so that the hurt's equal on both sides. But it takes a right-thinking person to be able to find that balance, so the judge really does have to be a model of correct reason and just behavior.
Quote #9
The just exists for those for whom there is also law pertaining to them, and law exists among those for whom there is injustice. For justice is a judgment about the just and the unjust. (5.6.1134a30-33)
You've probably never gotten this basic in your thinking about justice, but Aristotle challenges us to think about that molecular political unit that makes both law and justice a Thing: the community. If we don't live together (i.e. share a life in common), there would be no need to regulate anything. Without laws, there are no lawbreakers. While we might disagree (people can still hurt others, even in the absence of laws), Aristotle's correct in an absolute sense: justice and injustice in a specific sense can only exist when we group up and agree on the terms of living together.