How we cite our quotes: (Book.Chapter.Bekker #s); all Bekker line numbers are approximate, since they are keyed to the original Greek.
Quote #4
The just, therefore, is what is lawful and what is equal; the unjust is what is unlawful and what is unequal. (5.1.1129b1)
Aristotle defines the just and the unjust in two ways here. First, according to the law: the just embrace legal code, whereas the unjust are lawbreakers. Then, he brings in the societal component: the unjust always grasp for more than their share of the pie (and are therefore "unequal"). This understanding of what's just and unjust will be important later, when Aristotle talks about the different kinds of justice (i.e. corrective and distributive).
Quote #5
The laws pronounce on all things, in their aiming at the common advantage, either for all persons or for the best or for those who have authority, either in accord with virtue or in some other such way. As a result, we say that those things apt to produce and preserve happiness and its parts for the political community are in a manner just. (5.1.1129b15-19)
Aristotle sees the law as the main preserver of equity and peace in society. It's the job of lawgivers to look into all aspects of human behavior and life in order to make the kinds of laws that will produce good citizens (by setting clear and reasonable boundaries) and promote justice (correcting inequalities, punishing lawbreakers).
Quote #6
Worst, then, is he who treats both himself and his friends in a corrupt way, but best is he who makes use of virtue not in relation to himself but in relation to another. For this is a difficult task. This justice, then, is not a part of virtue but the whole of virtue, and the injustice opposed to it is not a part of vice but the whole of vice. (5.1.1130a6-11)
Aristotle makes sure we understand how incredibly different it is to be just. We have to set aside self-interest and consider others as we would consider ourselves. Because it's so extraordinarily hard, justice requires extraordinary powers of goodness. But the effort's worth it, because the alternative is frankly quite terrifying. Giving in to unjust behavior makes us into one nasty piece of work.