principle vs theorem

principle

noun
  • A fundamental assumption or guiding belief. 

  • A fundamental essence, particularly one producing a given quality. 

  • A rule used to choose among solutions to a problem. 

  • A rule or law of nature, or the basic idea on how the laws of nature are applied. 

  • Bernoulli's Principle 

  • An original faculty or endowment. 

  • A source, or origin; that from which anything proceeds; fundamental substance or energy; primordial substance; ultimate element, or cause. 

  • Moral rule or aspect. 

verb
  • To equip with principles; to establish, or fix, in certain principles; to impress with any tenet or rule of conduct. 

theorem

noun
  • A mathematical statement that is expected to be true 

  • A mathematical statement of some importance that has been proven to be true. Minor theorems are often called propositions. Theorems which are not very interesting in themselves but are an essential part of a bigger theorem's proof are called lemmas. 

  • A syntactically correct expression that is deducible from the given axioms of a deductive system. 

verb
  • To formulate into a theorem. 

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