Sorry Lily! I almost forgot... So, I don't know exactly the difference between "order" and "ordering", but - I've searched a bit on the web - I think "ordering" is better.
So, should I change the translation in: "orderings and sections"?
I think "ordines" could be "classes, orders/orderings, divisions" --- according to what jairhass said about the "Jewish division of the OT into three orders (Law, Prophets, Writings)".