contract vs engage

contract

verb
  • To make an agreement or contract; to covenant; to agree; to bargain. 

  • To enter into a contract with. 

  • To enter into, with mutual obligations; to make a bargain or covenant for. 

  • To draw together or nearer; to shorten, narrow, or lessen. 

  • To betroth; to affiance. 

  • To shorten by omitting a letter or letters or by reducing two or more vowels or syllables to one. 

  • To bring on; to incur; to acquire. 

  • To gain or acquire (an illness). 

  • To draw together so as to wrinkle; to knit. 

noun
  • An order, usually given to a hired assassin, to kill someone. 

  • An agreement which the law will enforce in some way. A legally binding contract must contain at least one promise, i.e., a commitment or offer, by an offeror to and accepted by an offeree to do something in the future. A contract is thus executory rather than executed. 

  • An agreement between two or more parties, to perform a specific job or work order, often temporary or of fixed duration and usually governed by a written agreement. 

  • The document containing such an agreement. 

  • A part of legal studies dealing with laws and jurisdiction related to contracts. 

  • The declarer's undertaking to win the number of tricks bid with a stated suit as trump. 

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 contract and engage occurred in a corpus of books? (source: Google Ngram Viewer )