Wow, today's word is a very exciting one: ratio. Obviously, this noun has yielded some very important borrowings in English such as ratio, ration, rational, etc., and also reason, which comes via Old French raison.
In Latin, this noun is derived from the verb reor, which has ratus as its participle. The verb reor means "I reckon, I think," and so ratio is the verbal noun that expresses that same idea: reckoning, thinking, etc. The word seems to derive from the proto-Indo-European root *ar- meaning "to fit, align." For this interpretation, see the *ar page at the UT Indo-European website (a great online resource). It is possible that the Latin word res shares the same root as well - so reor would mean "I think," ratio is the "thought" or the "thinking," while res would be the object of that thought, the "thing" itself.
Like the word modus, which can be a unit of quantity (size, length, circumference, etc.) or, more generally, a way or manner of doing things, ratio can mean a numerical relationship or it can refer, more generally, to any sort of relationship or condition. Compare the way that in English "I reckon" can refer to a numerical calculation or to some other kind of thought process.
Here are some examples of today's word in Latin sayings and proverbs; for more information, see the page at the Scala Sapientiae, which contains notes on some of the proverbs cited below, as well as additional proverbs:
Ratione, non vi.
Dux vitae ratio.
Ratione vivendum est.
Nec satis rationis in armis.
Nihil sine ratione faciendum est.
Ratio fatum vincere nulla valet.
Ratione duce per totam vitam eundum est.
Habenda est ratio hominum, rei et temporis.
Ratione, non ira.
Quid est in homine ratione divinius?
Mors ultima ratio.
Exemplo plus quam ratione vivimus.
Nil melius vere quam cum ratione tacere.
Ratio contra vim parum valet.
Non prodest ratio, ubi vis imperat.
Domina omnium et regina ratio.
Nunc est dicendum, nunc cum ratione silendum.
Ratio est radius divini luminis.
Deus est ratio quae cuncta gubernat.
Ratione praestamus beluis.