These institutions, intermediate between the primary schools and university, might then be the passage of entrance for Youths into the University, where their classical learning might be critically compleated, by a study of the authors of highest degree. And it is at this stage only that they should be recieved at the university.
In this sentence the writers describe the fundamental necessity of high schools and prep schools. It is interesting to note that the need for prep schools arises from the rigorous curriculum that the writers decide on. It is really interesting to read this, especially when high school today does exactly what the writers yearned for.