Don't forget military engineer. I've read a letter he sent as a sort of resume, and it basically talks about his engineering, ability to design nasty marmachines and fortifications, his musical ability and other incredible erudition. Then at the end of the letter, it pretty much says (and I paraphrase), "oh, and I can paint too." I love that.

Leonardo Da Vinci and Albrecht Dürer are my two favorite Renaissance figures, for reasons that only partly involve their art.