As the group of them began to explore the library again, they would find all the books just as they had been left.  There was another little room nearby - a quick inspection would reveal that it appeared to be a studying hole, where a few basic amenities for the most dedicated of students could use.  There were a few notebooks laying around here - but a quick flip through the writing would reveal that the little hole was likely used by a singular person.

On the opposite side of the balcony there were a couple other rooms to be looked into.  Another one of which appeared to be oddly filled with various weapons, similar to the one upstairs - however the yellowish blades were clearly some sort of bronze.  Various glaives, spears, swords, shields, and other weapons were put on display in the room.  A more thorough examination would reveal that the weapons were likely there to be examined rather than used based on the way they were mounted on the wall.

The final room had another table in the center, and a constellation being held up by some sort of mechanical mechanism.  If the princess decided to enter the room, she'd see that the table in the center were really several large dials.  The first set the furthest out seemed to have the numbers one to 50.  The second dial went from one to seven.  The third dial really was a set of four smaller dials, each going from one to ten.  There was also a staircase nearby heading downstairs towards the crystal and more of the library if Izzy was finished examining the upper story.