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Difference between Of no consideration and On no consideration

of no consideration—(also: of no account) not important; insignificant in the eyes of others:

  • In our day it seems incredible that the landscape was at one time of no consideration to artists.

on no consideration—(also: on no account) certainly not; in no circumstances:

  • On no consideration will he allow gambling. He has been proof against every inducement to permit it.