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
For he who rules is already in relation to another and within the community. And on account of this same thing too, justice alone of the virtues is held to be another's good, because it relates to another. For it does what is advantageous to another, either to a ruler or to someone who shares in the community. (5.1.1130a2-5)
Justice can only exist in community. Aristotle will make a big deal out of this in his Ethics, especially when he discusses the possibility of committing an injustice to oneself (which he says we can't do). Justice only exists in community because it only exists for people governed by law.
Quote #5
For roughly speaking the majority of the lawful things are those commanded on the basis of the whole of virtue: the law commands us to live in accord with each virtue and forbids us to live in accord with each corruption. Things productive of the whole of virtue are all those legislative acts pertaining to the education to the common good. (5.2.130b23-26)
Aristotle tells us that the law exists not just for the correction of injustice after the fact. It also aims to create the model citizen through an encoding of virtue into law. This "education" can be coercive (note the language: "commands" and "forbids"), which highlights the urgency of conforming to virtuous behavior when living together as a community.
Quote #6
The just in this sense [the corrective] has a different form the previous one, for the just in the distribution of things held in common always accords with the proportion spoken of. And in fact if the distribution comes out of common resources, it will accord with the same ratio that the contributions have toward each other. (5.4.1131b26-28)
It's no surprise that community is at the heart of all conversations of justice in Aristotle's Ethics. If you recall, justice can only exist between people who live together in a society governed by laws. Without this communal life, there would be little opportunity to interact, for better or worse.
For a just society to exist, then, the good belonging to everyone needs to be shared out equitably. But that doesn't mean that everyone deserves to get the same amount. Aristotle proposes the idea of an equitable proportion for all, in which we get back the same proportion of good that we contribute to society. There may be many problems with this concept, but it's at least reasonable on the surface.