incidentally vs serendipitously

incidentally

adv
  • By chance; in an unplanned way. 

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

  • Parenthetically, by the way. 

serendipitously

adv
  • By serendipity; by blind luck in combination with wisdom; by fortunate accident. 

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