The image bears a striking resemblance to
The second drawing is one of the symbolic membership badges used by the Order of the Dragon. One of the most famous members of the Order was Vlad II Dracul, father of Vlad Tepes -> Dracula -> Alucard. 'Dragon' is where the 'Dracul' comes from.
So, a coincidence? I think not! Have there been any other ideas about why the quote is used (besides what the words themselves might symbolize in Hellsing)? Does anyone know enough about alchemy to guess what meaning a dragon biting its own tale (or choking/killing itself) has in this illustration? Are there any other links between alchemy and the Order of the Dragon?