How we cite our quotes: (Act.Scene.Line). Line numbers correspond to the 2008 Norton edition.
Quote #1
BOATSWAIN
When the sea is. Hence! What cares these
roarers for the name of king? To cabin! Silence!
Trouble us not. (1.1.16-18)
In nature, none of the rules apply from the court. Court members must adjust to the fact that nature is the great equalizer.
Quote #2
PROSPERO
So dry he was for sway wi' th' King of Naples
To give him annual tribute, do him homage,
Subject his coronet to his crown and bend
The dukedom, yet unbowed—alas, poor Milan!—
To most ignoble stooping. (1.2.133-137)
Even when he was within the bounds of the court, Prospero saw there were certain formalities that were below him. It's not that the island alone influences Prospero to embrace a certain amount of natural dignity, but by his nature he was always a powerful and proud man.
Quote #3
CALIBAN
This island's mine, by Sycorax my mother,
Which thou tak'st from me. When thou cam'st first,
Thou strok'st me and mad'st much of me, wouldst
give me
Water with berries in 't, and teach me how
To name the bigger light and how the less,
That burn by day and night. And then I loved thee,
And show'd thee all the qualities o' th' isle,
The fresh springs, brine-pits, barren place and
fertile.
Cursed be I that did so! All the charms
Of Sycorax, toads, beetles, bats, light on you,
For I am all the subjects that you have,
Which first was mine own king; and here you sty me
In this hard rock, whiles you do keep from me
The rest o' th' island. (1.2.396-411)
In the rules of the court, Prospero would never have taken in Caliban this way—nor would Caliban do him service out of love (instead of duty). Initially, the rules of the courtly world were suspended on the island.