alternate vs vary

alternate

verb
  • To vary by turns. 

  • To perform by turns, or in succession; to cause to succeed by turns; to interchange regularly. 

  • To perform an alternation (removal of alternate vertices) on (a polytope or tessellation); to remove vertices (from a face or edge) as part of an alternation. 

  • To happen, succeed, or act by turns; to follow reciprocally in place or time; followed by with. 

noun
  • A substitute; an alternative; one designated to take the place of another, if necessary, in performing some duty. 

  • A replacement of equal or greater value or function. 

  • A proportion derived from another proportion by interchanging the means. 

  • That which alternates with something else; vicissitude. 

  • Figures or tinctures that succeed each other by turns. 

adj
  • Other; alternative. 

  • Distributed singly at different heights of the stem, and at equal intervals as respects angular divergence 

  • Designating the members in a series, which regularly intervene between the members of another series, as the odd or even numbers of the numerals; every other; every second. 

  • Happening by turns; one following the other in succession of time or place; first one and then the other (repeatedly) 

vary

verb
  • To display differences. 

  • To make of different kinds; to make different from one another; to diversity; to variegate. 

  • To embellish; to change fancifully; to present under new aspects, as of form, key, measure, etc. See variation. 

  • To be or act different from the usual. 

  • Not to remain constant: to change with time or a similar parameter. 

  • To institute a change in, from a current state; to modify. 

  • To change with time or a similar parameter. 

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