The periodic table is not meant to be a complete work. The Bible is meant as a complete work. Thus the order not to take from or add to.
The periodic table is meant to be incomplete. We just needed a way to organize the elements, so the periodic table was made, in full knowledge that there were other elements out there. With this in mind, we adjusted the table so that it could hold new elements created or discovered.
It is not a fair comparison, for the two are completely different in completeness. The Bible is meant to be finished---it's done. The periodic table can still be added to when new elements are found. It doesn't mean anything is changing in science; those new elements were always out there. We simply found them. The only thing that changed was our knowledge of them.