What is an Aristotelian analysis?

Aristotelian analysis - or as it also is known, Aristotelian logic - is the set of rules that according to Aristotle must be followed to achieve 'correct reasoning' that leads to knowledge of the truth about anything.

A complete description of those rules and of the way they should according to Aristotle be applied, would lead to an extremely long answer. There are many treatises on the subject to be found on the Internet; one that tries to be understandable to people that are not academically trained philosophers themselves, can be found by clicking the link below.