not the ratio of two natural numbers was a shock to them which they only reluctantly accepted. A testimony of this is the modern terminology of irrational number for referring to a number that is not the quotient of two integers, since "irrational" means originally "not reasonable" or "not accessible with reason".

The fact that length ratios are not represented by rational numbers was resolved by Eudoxus of Cnidus (408-355 BC), a student of Plato,