One usual meaning given to the expression "irrational number" is "number not logical or reasonable". In particular in Spanish, where the usual term is "número irracional" (without logic, madness).
This goes against what is the main characteristics of these numbers in mathematics: not possible to express them as a ratio (fraction, division) of numbers.
The etymology that google displays is:
where the latin term "rationalis" has four possible definitions:
- accounts (attributive)
- rational, reasonable, of or possessing reason
- that has a ratio
- syllogistic
Of these four options, it seems that the most near to the mathematical concept must be "that has a ratio", not the one about "reasonable".
For these reasons, it seems that the Spanish term "número irracional" (in Spanish) and similar descriptions in English or other languages are very inadequate, being better say "número no fracional" or similar.
Knows someone the history and etymology of the term?
Euclid used the word ἄλογον (alogon), the Latin word was a translation. When used in the Greek text of the Bible, "alogon" is translated as "absurd" or (King James Version) "unreasonable".
SEE: Euclid, Elements, x.1.3