Lots of good things said here. You would just have to know if he's the type of person that would rather you say it, or if he's the type of person that had a tendency to blow up when confronted with it.
I'm not embarrassed about it at all. I would love for friends and family to be more interested in my illness. Being that it sounds like he knows what it is, like that he's gone to the doctor and has been diagnosed...it might not be so bad, and he might actually cling to you.
The book you read is an awesome book. You're an awesome person for doing what most people don't.
I don't remember who said it, but....the person that told you to ask him leading questions etc., the next time he says something you might want to let him know you're a safe place to land, and someone he can count on, and tell him that from the hinting around he's been doing...that you guessed, because it's a common disease. So the paranoia doesn't set in...you might not want to mention the book until after you've had the real discussion about it. But because you read it, you'll be ready for the conversation and what to do next.