Go down to the right immediately after entering and pick up the Capricorn Stellazzio, then continue into the passageway. Go up the lift where you'll find a Synthesist.

Go through the left doorway where you'll find the Item store. If you agree with the Young Man who is arguing with the clerk every time you'll get a Flare, agree with the clerk and you'll get a Meteor.

Press the button on the block next to the item shop. Talk with the scholar who is looking for a book, go to the other side and examine the stack of books, then go tell the scholar where his book is. Go down the hidden ladder after the scholar moves. Go to the far left side for an Elixir and the far right side for another Elixir.

Go back up and exit through the left door to reach the Weaponsmith. Talk with him and then go back through the Library, down and back to the entryway. Go left this time to get to the lower part of the Weaponsmith's room. Examine the levers and lower the Left lever twice. Examine the lowest lift and then the staff. Lower the Right lever twice then examine it to ride up to the top. Now you can buy from the Weaponsmith.