engage vs mesh

engage

verb
  • To mesh or interlock (of machinery, especially a clutch). 

  • 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 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. 

mesh

verb
  • To connect together by interlocking, as gears do. 

  • To catch in a mesh. 

  • To fit in; to come together harmoniously. 

noun
  • In mesh analysis: a loop in a electric circuit (to which Kirchhoff's voltage law can be applied). 

  • The opening or space enclosed by the threads of a net between knot and knot, or the threads enclosing such a space. 

  • A measure of fineness (particle size) of ground material. A powder that passes through a sieve having 300 openings per linear inch but does not pass 400 openings per linear inch is said to be -300 +400 mesh. 

  • The engagement of the teeth of wheels, or of a wheel and rack. 

  • A structure made of connected strands of metal, fiber, or other flexible/ductile material, with evenly spaced openings between them. 

  • A polygon mesh. 

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