In what ways is Prospero considered a "Renaissance Man" in The Tempest?
The term "Renaissance Man" connotes the concept of an individual knowledgeable in many different areas of study. It refers to a time starting around the 1400's when Italy began to be the dominant cultural force in Europe in developing the arts and sciences. The individuals involved at that time in the various fields of study became skilled in many different fields; the preeminent example being Leonardo Da Vinci (1452-1519) who was both scientist and artist.
In Shakespeare's The Tempest, the character of Prospero is described as a deposed statesman. Although the rightful Duke of Milan, he was additionally interested in his "secret studies" of magicianship that he exercises on his island where he is exiled. As statesman and magician, he manipulates events to punish the evildoers, and set his daughter up in a secure marriage. He renounces his powers, but only after he has set all right.
The Tempest was Shakespeare's last play, and was written as a celebration for the marriage of Elizabeth (daughter of English King James I) and Frederick V, of what is now Germany. Many have considered Prospero as a characterization of William Shakespeare himself. Although he lived late in the Renaissance, he could be considered a Renaissance Man, having managed land, businesses, and written a play and poem or two. Another facet could have been what we consider a "wedding planner," or at least the person providing the entertainment, having written the play in celebration of the young royal couple. Best wedding present ever.