1. a basis or cause, as for some belief, action, fact, event, etc. ...
3. the mental powers concerned with forming conclusions, judgments, or inferences.
So, its the difference between "reasoning", which we do in math and logic all the time, and "belief" or "motive". That is "reason" did indeed have a specific mathematical meaning at that time, and it still does today.
http://dictionary.reference.com/browse/reason
1. a basis or cause, as for some belief, action, fact, event, etc. ...
3. the mental powers concerned with forming conclusions, judgments, or inferences.
So, its the difference between "reasoning", which we do in math and logic all the time, and "belief" or "motive". That is "reason" did indeed have a specific mathematical meaning at that time, and it still does today.
One might also google "mathematical reasoning"...