Septimus freezes during quest
Solution 1:
Here is what is supposed to happen:
Septimus is about to pick up the book, but Hermaeus Mora decides that his usefulness has come to and end and he is disintegrated. You then pick up the book yourself.
According to the UESP page for Discerning the Transmundane, this is a known bug, and your best bet is to just kill Septimus.