appoint vs engage

appoint

verb
  • To equip (someone) with (something); to assign (someone) authoritatively (some equipment). 

  • To name (someone to a post or role). 

  • To set, fix or determine (a time or place for something such as a meeting, or the meeting itself) by authority or agreement. 

  • To fix the disposition of (property) by designating someone to take use of (it). 

  • To furnish or equip (a place) completely; to provide with all the equipment or furnishings necessary; to fit out. 

engage

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

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

  • To enter into battle. 

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