engage vs entrance

engage

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

  • 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 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. 

entrance

verb
  • To delight and fill with wonder. 

  • To put into a trance. 

noun
  • The act of taking possession, as of property, or of office. 

  • The place of entering, as a gate or doorway. 

  • The right to go in. 

  • The bow, or entire wedgelike forepart of a vessel, below the water line. 

  • The action of entering, or going in. 

  • The entering upon; the beginning, or that with which the beginning is made; the commencement; initiation. 

  • The beginning of a musician's playing or singing; entry. 

  • The causing to be entered upon a register, as a ship or goods, at a customhouse; an entering. 

  • The angle which the bow of a vessel makes with the water at the water line. 

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