"...Prospero not only has a magic robe and a magic staff (both of which are explicitly called for ), but, like Friar Bacon and Doctor Faustus and other stage magicians before him, he also has a magic book. Further, the play presents Prospero's always-offstage book as crucial to his rule over the island, the magical instrument that enables him to control the spirits who come from their confines when Prospero calls..."
http://muse.jhu.edu/login?uri=/journals/shakespeare_quarterly/v052/52.1mowat.html

Prospero's Books
The Tempest
Complete Shakespeare Play
&
Greenaway Transcription
http://www.omencity.com/xitez/prospero/tempesttext.html

"Avalanches of hot, loose gravel and molten sand fall out of the book to scorch the library floor.":

1. The Book of Water
2. A Book of Mirrors
3. A Book of Mythologies
4. A Primer of the Small Stars
5. An Atlas Belonging to Orpheus
6. A Harsh Book of Geometry
7. The Book of Colours
8. The Vesalius Anatomy of Birth
9. An Alphabetical Inventory of the Dead
10. A Book of Travellers' Tales
11. The Book of the Earth
12. A Book of Architecture and Other Music
13. The Ninety-Two Conceits of the Minotaur
14. The Book of Languages
15. End-plants
16. A Book of Love
17. A Bestiary of Past, Present and Future Animals
18. The Book of Utopias
19. The Book of Universal Cosmography
20. Lore of Ruins
21. The Autobiographies of Pasiphae and Semiramis
22. A Book of Motion
23. The Book of Games
24. Thirty-Six Plays
http://www.members.optusnet.com.au/~zaphod/ProsperoTheBooks.html

The case for believing that Prospero was directly inspired by John Dee:
http://books.google.com/books?id=yJc2nCMYkWMC&pg=PA130&lpg=PA130&dq=john+dee+prospero+yates&source=bl&ots=QCC2lHcxVX&sig=9pGl2jDrog_fr4j3V5Ua-J_8i2E&hl=en&sa=X&oi=book_result&resnum=5&ct=result