divide vs engage

divide

verb
  • To be a divisor of. 

  • To vote, as in the British parliament and other legislatures, by the members separating themselves into two parties (as on opposite sides of the hall or in opposite lobbies), that is, the ayes dividing from the noes. 

  • To share (something) by dividing it. 

  • To separate into two or more parts. 

  • To mark divisions on; to graduate. 

  • To calculate the number (the quotient) by which you must multiply one given number (the divisor) to produce a second given number (the dividend). 

  • To play or sing in a florid style, or with variations. 

  • To disunite in opinion or interest; to make discordant or hostile; to set at variance. 

  • To split or separate (something) into two or more parts. 

  • Of a cell, to reproduce by dividing. 

noun
  • An act of dividing. 

  • A distancing between two people or things. 

  • A large chasm, gorge, or ravine between two areas of land. 

  • The topographical boundary dividing two adjacent catchment basins, such as a ridge or a crest. 

  • A thing that divides. 

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. 

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