What do we learn of the importance of studies to Prospero in The Tempest?

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If you are asking about the play as a whole, I can think of a couple of places where we learn about how important studying was to Prospero.

First of all, it seems that his love for studying helped get him onto the island -- it helped him lose his dukedom.  This is because he spent so much time studying that his brother Antonio pretty much took over all the duties of the ruler.  So Prospero studied instead of ruling.  (Act I, Scene 2)

And Prospero the prime duke, being so reputed
In dignity, and for the liberal arts
Without a parallel; those being all my study,
The government I cast upon my brother
And to my state grew stranger, being transported
And rapt in secret studies.

The other one is where (Act III, Scene 1) Miranda tells Ferdinand that they have some time to be together and for Ferdinand to rest because Prospero will be studying for something like three hours yet.

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