incompatible vs of a piece

incompatible

adj
  • Of two things: that cannot coexist; not congruous because of differences; unable to function together due to dissimilarities. 

  • Incapable of being together without mutual reaction or decomposition, as certain medicines. 

noun
  • An incompatible substance; one of a group of things that cannot be placed or used together because of a change of chemical composition or opposing medicinal qualities. 

  • A consequent of a contrary. 

of a piece

prep
  • Used other than figuratively or idiomatically: see of, a, piece. 

  • Of the same kind. 

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