Arithmetic of the Medieval Universities

 "The Greeks were concerned with the education of free men as future citizens"

"The Romans, like the Greeks, seem to have accepted a few basic subjects as worthy of the efforts of free

men and to have expected the young citizens to concentrate on such subjects."

""Logistic is the theory which deals with numerable objects and not with numbers. Arithmetic was a study of the universities; logistic was not. Logistic was practical and utilitarian, a study for children and slaves; logic was a liberal art, a study for free men."

The order and the selected subjects are different in Roman and Greek. In the first quote, I do not understand what is meaning of free man. And in the third quote, I still do not understand the difference between logistic and logic.