The ideas that are associated with the words justice, magnanimity and correspondence are peace and friendship,
The excerpt is:
We have appealed to their native justice and magnanimity, and we have conjured them by the ties of our common kindred to disavow these usurpations, which would inevitably interrupt our connections and correspondence.
A synonym of magnanimity is generosity.
Magnanimous means generous or forgiving, especially towards a rival or less powerful person.
Justice can be defined as fairness in the way people are dealt with.
Correspondence means a close similarity, connection, or equivalence.