"Ratio" comes from Latin "reri" and PIE "re-" meaning "to reason or count". The mathematical sense can only be dated to the 1600s

This is unexpected for me because ancient Greeks discovered irrational numbers, namely the square root of 2. I expected *ratio* and its other forms to be much older and much more entwined with the origin of *rational*. Edit: A more [in depth answer on StackExchange](https://english.stackexchange.com/questions/217956/does-rational-come-from-ratio-or-ratio-come-from-rational)