As you play through the story of Atelier Ryza 2: Lost Legends & the Secret Fairy you will discover that the compass you find in the first ruin serves an interesting purpose. It can lead you to Ruin Fragments, living memories of times past. If you can collect all the Fragments in a ruin then you will be able to piece together important information, unlocked new skills, and earn other rewards.
In your Exploration Diary, which you can open from the world map if you highlight a ruin, you can find a record of the Ruin Fragments, and the Ruin Vestiges that you can also find. By examing both of them, you can link them together, completing the information that they contain.
The very first time you need to do this is the Mausoleum of Eternity, so we have some screenshots below that will show you all the locations where you can find the information, and then the correct layout of the Fragments.
Each Fragment has its own icon, so simply match the icon to their placement on the vestiges in the image below. The Fragments and the Vestiges will both contain keywords that give you clues about which ones match up. The will not be exactly the same, but you can work it out with a little bit of logic and patience.
If you would prefer to take the easy route, then just copy the exact image below for the correct solution.