What are the two things that the mad man believes will help him in accomplishing his goal of trying to convince the reader that he's sane, not mad?
One has something to do with the content of his story; The other has something to do with his telling of his story. Please give me examples within the text.
The first thing is that the narrator repeatedly tries to convince the reader that he is NOT mad. The way he tells the story illustrates this:
Right at the beginning, we learn that the narrator has been ill:
TRUE! nervous, very, very dreadfully nervous I had been and am; but why WILL you say that I am mad? The disease had sharpened my senses, not destroyed, not dulled them.
From this information, we can surmise that his illness was mental in nature - the "disease" sharpened his senses, not dulled them.
Again, he says:
Now this is the point. You fancy me mad. Madmen know nothing.
He continues to point out how he is NOT mad throughout the story, giving examples that he hopes will convince the reader of his sanity, but his thinking is erratic and confused, so he proves just the opposite. The way he tells the story shows how crazy he really is.
Secondly, he gives minute details about how carefully he planned the murder. This, he hopes, will prove that he is not mad. How could a madman plan something so precisely?
You should have seen how wisely I proceeded -- with what caution -- with what foresight, with what dissimulation, I went to work!
He proceeds to unfold his plan - what he did for seven nights in a row. Finally, on the 8th night, he is ready. He again points out what he did, step by step, hoping again to prove that his careful carrying out of a mad deed proves that he is not mad, when in fact, his rantings illustrate just the opposite. He wants the reader to think he is methodical and therefore perfectly sane. He hopes that by including a lot of detail (content), he will be more convincing.
The narrator tries to convince the reader of his sanity in several different manners. First, he claims that
... the disease had sharpened my senses--not destroyed--not dulled them.
He goes on to say that his own calmness in telling the story is another example of his sanity; his "caution" and "foresight" in planning his evil deed is another claim. He claims to have had no specific reason for killing the old man: He loved him and had no desire for his money. After killing the man, the narrator claims that no madman would proceeded with such
... wise precautions that I took for concealment of the body.
When the police arrive, his "manner" and "ease" is shown as a sane response to his new predicament.