Translation of "辨人禽界，立天地心"
I originally had this as a comment but it seems like it has become an answer.



Confucianism likes to talk about the separation of man (人) and beast (禽), so that would be the crux of the first sentence, i.e.: separating the human and animal worlds. 

立天地心 should be talking about setting a standard or a principle for heaven and earth, there are many translations that put similar ideas as: ordaining a conscience for Heaven and Earth.



In relation to your edit:

There are a couple of well-known translations for 为天地立心，为生民立命， 为往圣继绝学，为万世开太平


  To ordain conscience for Heaven and Earth
    To secure life and fortune for the people
    To continue lost teachings for past sages
    To establish peace for all future generations


another would be:


  To ordain conscience for Heaven and Earth
    To secure life and fortune for the populace
    To carry on lost teachings of ancient sages
    To build peace for posterity