engage vs take on

engage

verb
  • To enter into conflict with (an enemy). 

  • To come into gear with. 

  • To enter into (an activity), to participate (construed with in). 

  • To draw into conversation. 

  • To mesh or interlock (of machinery, especially a clutch). 

  • To attract, to please; (archaic) to fascinate or win over (someone). 

  • To guarantee or promise (to do something). 

  • To engross or hold the attention of; to keep busy or occupied. 

  • To arrange to employ or use (a worker, a space, etc.). 

  • To bind through legal or moral obligation (to do something, especially to marry) (usually in passive). 

  • To enter into battle. 

take on

verb
  • To attempt to fight, compete with, or engage with. 

  • To assume or take responsibility for. 

  • To (attempt to) dribble round (an opposition player). 

  • To catch on, do well; to become popular. 

  • To obtain the services of (a person) in exchange for remuneration; to give someone a job. 

  • To begin to have or exhibit. 

  • To acquire, bring in, or introduce. 

  • To grieve or be concerned (about something or someone). 

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