It is (our) duty . . . to pay especial attention to the principles of government which shall be inculcated therein (at the University), and to provide that none shall be inculcated which are incompatible with those on which the Constitutions of this State, and of the United States were genuinely based, in the common opinion; and for this purpose it may be necessary to point out specially where these principles are to be found legitimately developed.