Aristotle believed that all substances, such as the above, were made up of earth, air, fire, and water in differing proportions. Consider the burning of wood. It breaks down into fire and earth (ash). You can obtain fire from wood, but not wood from fire, so fire must be a component of wood.
He goes to great lengths in On the Heavens to derive the properties of the elements and how they are related to each other. He explains how they are subject to generation and destruction. For example, fire can be destroyed by two methods: by its contrary (water) when quenched and by itself when it burns out.