Complex sentence: The earliest paper records of the Society are dated before 1770, and there are, moreover, mentions within the University records of a society existing and being open to students who took Logic, back when the University still resided within Glasgow Cathedral.
Split into simpler sentences: The earliest paper records of the Society are dated before 1770. There are moreover mentions within the University records of a society existing and being open to students who took Logic, back when the University still resided within Glasgow Cathedral.