believe vs deem

believe

verb
  • To have religious faith; to believe in a greater truth. 

  • To accept as true, particularly without absolute certainty (i.e., as opposed to knowing). 

  • To accept that someone is telling the truth. 

  • To opine, think, reckon. 

deem

verb
  • To hold in belief or estimation; to adjudge as a conclusion; to regard as being; to evaluate according to one's beliefs; to account. 

  • To think, judge, or have or hold as an opinion; to decide or believe on consideration; to suppose. 

noun
  • An opinion, a judgment, a surmise. 

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