Take a look at them (right mouse button in the inventory) and take the ramrod from beneath the pistol. Afterwards examine the side of the chest (zoom).
Localize the lock and use the key found in the chest. You will notice that there is a hidden drawer there, but the lock is blocked. Take a look at the hole on the side of the chest (on the left). Put the ramrod inside it and unlock the mechanism. Now just open the drawer and take the old manuscript.
Of course take a look at it while in zoom (right mouse button in the inventory). Look at the pages (arrows at the right and left edges or by clicking at the next page) - you will see that fragments of a map are sewed to the pages. Go out of the zoom and use the tweezers to get the threads out of the book (combine the two in the inventory). Now open the manuscript in zoom once again and click on the first map fragment. This way you will take all of them out of the book. Now you can read the clear manuscript and get to know something about the Tree of Life.
It's time to put the map fragments into one (right mouse button in the inventory). You can drag it with the left button and place them on the board and turn 90 degrees with the right button. Additionally at the edge there will be an icon letting you see the other side of a piece, as the map has two sides and it's worth to turn all the pieces so they show the same side (the right way to assemble the both sides is shown above, you choose which is easier for you).
Leave the bay and take another look at the 3D printer (zoom). Check each of the red lights. You will learn that the machine is missing powder, resin and dye. Open the left side and take the empty container.