title_body: I have the Kindle app on two of my Mac computers.
upvoted_answer: Yes, the books will still appear within the Kindle app on the new computer, provided that you are signed in to your account.
  
  I believe you can be signed in to the kindle app on up to 6 devices, removing one device will not affect the books you have purchased (you may just need to re-download them on to the new device).