Konig's paper was written at about the same time as Richard's (see
above, p.142).  Like Richard, Konig deals with the set of finitely
definable numbers; but, instead of using a diagonal construction, he
considers the complement of that set.  If the set of real numbers
could be well-ordered, the set of not finitely definable real numbers
would have a first element, which, after all, would be finitely
definable.  Konig's conclusion is that the set of real numbers cannot
be well-ordered.