Mutiple Device Authorization Question

I recently purchased an ADE book to read on my Windows desktop PC and Apple iPad.  I downloaded the book to my PC without setting up an Adobe ID.  I then downloaded Bluefire Reader on my iPad and set up an Adobe ID.  I tried to download the book to the iPad, but was told I could not because it was downloaded to the Windows version that didn't have an Adobe ID.  I then tried to authorize the Windows software with the Adobe ID created through the iPad and was told I could not use that ID because it was not originally set up on the Windows version.

How do I use the Adobe ID and read the book on both devices?  I'd rather not have to set up a new Adobe ID.

Thanks for your help.

Walter