assume vs understand

assume

verb
  • To authenticate by means of belief; to surmise; to suppose to be true, especially without proof 

  • To receive, adopt (a person) 

  • To adopt a feigned quality or manner; to claim without right; to arrogate 

  • To take on a position, duty or form 

  • To adopt (an idea or cause) 

understand

verb
  • To believe, to think one grasps sufficiently despite potentially incomplete knowledge. 

  • To stand underneath, to support. 

  • To grasp a concept fully in one's mind, especially (of words, statements, art, etc.) to be aware of the meaning of and (of people) to be aware of the intent of. 

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