The code for those sliders to access the linking books is listed in Gehn's journal that you found in his lab. The code is randomly generated and is different for each game. It is five numbers, between 1 and 25, listed in ascending sequence. The Rivenese number system is used here so you'll have to decipher that. Then start with the last, highest, number and slide the right-most slider to it and proceed in a like manner with the next highest, etc. Then push the button; the sliders will all slide to their original position and, if the code is correct, the door will open.
As MacDee said, the marble puzzle has to be completed to supply power to the linking book. Without that power, gaining entry to the book is all in vain.