equibalance vs symmetry

equibalance

noun
  • Equal weight; equiponderance. 

verb
  • To make of equal weight; to counterbalance. 

symmetry

noun
  • The satisfying arrangement of a balanced distribution of the elements of a whole. 

  • Exact correspondence on either side of a dividing line, plane, center or axis. 

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