What evidence does the narrator provide for his claim that he is not mad in "The Tell-Tale Heart"?

The evidence that the narrator provides for his claim that he is not mad can be found in the first two paragraph's of Poe's short story, "The Tell-Tale Heart."  First, the narrator claims that if he was mad, he would not be able to tell the story so calmly.  He also says that he was very, very nervous, but not mad.  This nervousness caused him to have sharpened senses, as opposed to dull ones, and that he has a heightened sense of hearing, enabling him to hear all things in Heaven and Hell.  In the second paragraph, the narrator says, "Madmen know nothing," but he calculated and executed the murder so well that he obviously knows quite a bit.