I'd like to compile a list of books that aren't only good books on the history of mathematics—but books that are themselves mathematical explanations. For example, imagine a biography on Cantor. This biography would be a good historical book—but also provide (maybe even walk-through) all of the relevant Cantor proofs. It'd teach you both history and mathematics.
Unfortunately, I don't have any ideas. My experience with mathbooks is strictly textbooks with, at best, a "Did You Know It?" esque insert at the top of a page or something.
My targets are any and all topics, honestly.