Explain how you managing to communicate with someone who has been dead for hundreds of years (or is in the future). If you want to have fun with the exercise, you can try to do this, but it is not part of the assignment that you try to capture voice of the author whose perspective you are inhabiting—feel free to use your own voice and writing style. You should quote the relevant texts some (e.g., “you write in your Politics that ‘…’, however as I make clear in chapter 14 of Leviathan, ‘…’). Quotes should be used to exemplify your points, and so should normally be preceded and/or proceeded by some explanation of the point with your own words; also, it is a short writing assignment, so quotations should be short, and you should not take up too much space with lots of big quotes.
Finally: this is a relatively short writing assignment, so it’s unrealistic for you to capture the full breadth of all the possible ways your two thinkers might overlap and differ. My suggestion is that, before starting the paper, you a) identify what you take to be the most interesting/important issue or issues of common concern, b) sketch out how you see the two overlapping and differing on these issues, c) examine the underlying reasons in their theories that explain those differences, and structure your letter accordingly. Toward the beginning of your letter, you should tell the reader what topics, lines of argument, etc., that you are going to focus on. “