ratio

ratio, rationis is a third declension feminine noun, plural rationes, rationum, rationibus, and one of the widest-ranging words in Latin. It comes from reor, ratus, "to reckon", and the first sense is literally arithmetical: a reckoning, a bill, an account to be rendered, hence rationem reddere and rationem habere, to take account of something.

From counting it moves to system and method (hac ratione, by this method; ratio belli, the plan of campaign), and from method to the faculty of reasoning itself. It is the word Cicero uses to carry the Greek logos, which is why "rational", "ratio", "ration", "rate" and, through French, "reason" all belong to it. The practical warning: a reader who translates every ratio as "reason" will turn a passage about book-keeping or military planning into nonsense. Let the context pick which of the three senses is in play.