belief vs proof

belief

noun
  • Faith or trust in the reality of something; often based upon one's own reasoning, trust in a claim, desire of actuality, and/or evidence considered. 

  • Mental acceptance of a claim as true. 

  • Religious faith. 

  • One's religious or moral convictions. 

  • The quality or state of believing. 

  • Something believed. 

proof

noun
  • The degree of evidence which convinces the mind of any truth or fact, and produces belief; a test by facts or arguments which induce, or tend to induce, certainty of the judgment; conclusive evidence; demonstration. 

  • A process for testing the accuracy of an operation performed. Compare prove, transitive verb, 5. 

  • A sequence of statements consisting of axioms, assumptions, statements already demonstrated in another proof, and statements that logically follow from previous statements in the sequence, and which concludes with a statement that is the object of the proof. 

  • The quality or state of having been proved or tried; firmness or hardness which resists impression, or does not yield to force; impenetrability of physical bodies. 

  • A measure of the alcohol content of liquor. Originally, in Britain, 100 proof was defined as 57.1% by volume (no longer used). In the US, 100 proof means that the alcohol content is 50% of the total volume of the liquid; thus, absolute alcohol would be 200 proof. 

  • A limited-run high-quality strike of a particular coin, originally as a test run, although nowadays mostly for collectors' sets. 

  • A proof sheet; a trial impression, as from type, taken for correction or examination. 

  • An effort, process, or operation designed to establish or discover a fact or truth; an act of testing; a test; a trial. 

adj
  • Firm or successful in resisting. 

  • Being of a certain standard as to alcohol content. 

  • Used in proving or testing. 

verb
  • To make resistant, especially to water. 

  • To test-fire with a load considerably more powerful than the firearm in question's rated maximum chamber pressure, in order to establish the firearm's ability to withstand pressures well in excess of those expected in service without bursting. 

  • To proofread. 

  • To test the activeness of yeast. 

  • To allow yeast-containing dough to rise. 

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