How we cite our quotes: (Act.Scene.Line). Line numbers correspond to the 2008 Norton edition.
Quote #1
PROSPERO
The direful spectacle of the wreck, which touched
The very virtue of compassion in thee,
I have with such provision in mine art
So safely ordered that there is no soul—
No, not so much perdition as an hair,
Betid to any creature in the vessel (1.2.33-38)
Though Prospero seems to be performing evil with his magic, it's actually not black magic, as he has been careful to make sure that everyone aboard the ship was safe. His intentions are good, even if his magic doesn't always seem to be.
Quote #2
PROSPERO
Know thus far forth.
By accident most strange, bountiful Fortune,
Now my dear lady, hath mine enemies
Brought to this shore; and by my prescience
I find my zenith doth depend upon
A most auspicious star, whose influence
If now I court not but omit, my fortunes
Will ever after droop. (1.2.212-219)
Prospero's magic does not rely on his ability alone. Instead, nature has a great impact on his ability, and he is humbled and attendant to this fact. He also realizes that, though he is powerful, he is not omnipotent, and he is respectful of nature.
Quote #3
PROSPERO
It was a torment
To lay upon the damned, which Sycorax
Could not again undo. It was mine art,
When I arrived and heard thee, that made gape
The pine and let thee out. (1.2.343-347)
Prospero's magic is indeed great, as he was able to undo Sycorax's own spell, which she was not able to undo herself. Besides informing us of Prospero's power, this illustrates that he's not above vanity—he's willing to remind Ariel (and the audience) of just how powerful he is. This passage also reminds us that Prospero is willing to use his magic for his own personal gain; instead of granting Ariel's freedom after rescuing the sprite from the pine tree, he keeps Ariel as his servant until he can find a way off the island.