Possible? MacBook Pro to iPad??

Hi. Is it possible to download Digial Editions on MacBook Pro and transfer to iPad?

I did download it to my Mac, although the link showed iPhone or iPad, maybe this is why it doesn't work?

I authorised the app on the Mac, but no way can I transfer books to my iPad.  In the app library the downloaded book just keeps replicating itself.  I can move it to Finder or Air Drop, but they do not transfer across to the iPad.

Am I wasting my time?

Your help would be appreciated, thank you.