incidentally vs paradoxically

incidentally

adv
  • By chance; in an unplanned way. 

  • In an incidental manner; not of central or critical importance. 

  • Parenthetically, by the way. 

paradoxically

adv
  • In a paradoxical manner; so as to create a paradox. 

How often have the words incidentally and paradoxically occurred in a corpus of books? (source: Google Ngram Viewer )