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.
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.
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.
PROSPERO What, I say, My foot my tutor?—Put thy sword up, traitor, Who mak'st a show, but dar'st not strike, thy conscience Is so possessed with guilt. Come from thy ward, For I can here disarm thee with this stick And make thy weapon drop. (1.2.568-574)
Prospero here uses his magic to protect him in a very simple way, though obviously he is much more powerful than this action implies. He is willing to use his magic as a dumb-show when necessary, in this case to convince Ferdinand that he's not playing around.
FERDINAND The ditty does remember my drowned father. This is no mortal business, nor no sound That the earth owes. I hear it now above me. (1.2.483-485)
Magic is more than mortal, though it tends to impact mortals. Ferdinand draws the connection that magic might also have a bit of the divine in it (otherwise it would be against God, and kind of blasphemous).
Act 4, Scene 1
ARIEL I told you, sir, they were red-hot with drinking, So fun of valour that they smote the air For breathing in their faces, beat the ground For kissing of their feet; yet always bending Towards their project. Then I beat my tabour, At which, like unbacked colts, they pricked their ears, Advanced their eyelids, lifted up their noses As they smelt music: so I charmed their ears That, calf-like, they my lowing followed through Toothed briers, sharp furzes, pricking gorse, and thorns, Which entered their frail shins. At last I left them I' th' filthy-mantled pool beyond your cell, There dancing up to th' chins, that the foul lake O'erstunk their feet. (4.1.190-205)
Ariel's actions often emphasize the whimsical parts of magic, like luring bad guys into pools that smell of horse urine. These tricks are perhaps more suited to Ariel's connection to nature than Prospero's austere practicality.
FERDINAND This is a most majestic vision, and Harmoniously charmingly. May I be bold To think these spirits? PROSPERO Spirits, which by mine art I have from their confines called to enact My present fancies. (4.1.131-136)
Prospero is not above using his magic to his own fancy. We are asked to think about the limitation of his power here—he can make spirits look like gods, but he has no access to the real gods. Is the implication that even Prospero's magic hits a glass ceiling when it comes to the divine?
PROSPERO Our revels now are ended. These our actors, As I foretold you, were all spirits and Are melted into air, into thin air; And like the baseless fabric of this vision, The cloud-capped towers, the gorgeous palaces, The solemn temples, the great globe itself, Ye all which it inherit, shall dissolve, And, like this insubstantial pageant faded, Leave not a rack behind. We are such stuff As dreams are made on, and our little life Is rounded with a sleep. (4.1.165-175)
In describing the results of his magic, Prospero creates a metaphor for the theater: What happens in the playhouse is not any more real than magic, but it has the same effect.
Act 5, Scene 1
But this rough magic I here abjure, and, when I have required Some heavenly music, which even now I do, [Prospero gestures with his staff] To work mine end upon their senses that This airy charm is for, I'll break my staff, Bury it certain fathoms in the earth, And deeper than did ever plummet sound I'll drown my book. (5.1.59-66)
Here, Prospero promises to break his staff and give up his magic forever but immediately after delivering this speech, Prospero holds Alonso in a "charm" and later orders Ariel to make sure the seas are calm so the cast can enjoy a peaceful and safe passage back to Italy. So, is Prospero actually ready to give up his "rough magic"?
PROSPERO You elves of hills, brooks, standing lakes, and groves, And you that on the sands with printless foot Do chase the ebbing Neptune and do fly him When he comes back; you demi-puppets that By moonshine do the green sour ringlets make, Whereof the ewe not bites, and you whose pastime Is to make midnight mushrooms, that rejoice To hear the solemn curfew; by whose aid, Weak masters though you be, I have bedimmed The noontide sun, called forth the mutinous winds, And 'twixt the green sea and the azured vault Set roaring war; to the dread rattling thunder Have I given fire and rifted Jove's stout oak With his own bolt; the strong-based promontory Have I made shake and by the spurs plucked up The pine and cedar; graves at my command Have waked their sleepers, oped, and let 'em forth By my so potent art. (5.1.42-59)
Before Prospero announces his plans to retire, he delivers a stunning speech that recalls the ways in which he's used his art to harness the forces of nature.