What's the difference between theorem, lemma and corollary? Can anybody explain me what is the basic difference between theorem, lemma and corollary? 
We have been using it for a long time but I never paid any attention. I am just curious to know.

John Playfair, in his 1862 "Elements of Geometry" (textbook) gives a numbered list as follows (I quote): (5) A Theorem is a demonstrative proposition; in which some property is asserted, and the truth of it is required to be proved. ... (10) A Lemma is a preparatory proposition, laid down in order to shorten the demonstration of the main proposition which follows it. (12) A Corollary, ..., is a consequence drawn immediately from some proposition or other premises.
