depose vs engage

depose

verb
  • To take or swear an oath. 

  • To testify; to bear witness; to claim; to assert; to affirm. 

  • To put down; to lay down; to deposit; to lay aside; to put away. 

  • To interrogate and elicit testimony from during a deposition; typically done by a lawyer. 

  • To remove (a leader) from (high) office, without killing the incumbent. 

  • To give evidence or testimony, especially in response to interrogation during a deposition 

engage

verb
  • To guarantee or promise (to do something). 

  • 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 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. 

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