danger vs menace

danger

noun
  • An instance or cause of likely harm. 

  • The stop indication of a signal (usually in the phrase "at danger"). 

  • Exposure to likely harm; peril. 

menace

noun
  • A perceived threat or danger. 

  • An annoying and bothersome person or thing. 

  • The act of threatening. 

verb
  • To endanger (someone or something); to imperil or jeopardize. 

  • To threaten (an evil to be inflicted). 

  • To make threats against (someone); to intimidate. 

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