look down on vs look down one's nose

look down on

verb
  • To regard or treat as inferior. 

  • To view [people or events on Earth] from the vantage point of the afterlife (originally, Heaven) 

look down one's nose

verb
  • To regard as inferior or distasteful; to hold in contempt. 

How often have the words look down on and look down one's nose occurred in a corpus of books? (source: Google Ngram Viewer )