Describe the method of inquiry used by Aristotle.

That would be logic.  Aristotle's logic was based largely on the establishment of two statements having an equivocal relationship and their relationship of a possible third statement.  The first two statements were called a "major and minor premise", while the third statement was called a "conclusion."  Here is a simplistic version of Aristotle's logic:

• If B is equal to A


• And C is equal to B


• Then A is equal to C

Aristotle's teachings laid the foundation to the modern method of inquiry, sometimes known as the "Scientific Method".  The scientific method has it's roots largely in Aristotle's logic, where a question is put forth of a scientific nature, seeking an answer.  Often, these questions have no easy answers and are designed to foster the asking of additional questions, all related to the original one.  Aristotle's teachings were the standard used for nearly 1500 years and had tremendous influence upon the philosophy and teaching of this time.