  Grosseteste identifies two types of demonstration of the highest sort, natural and mathematical. His analysis of natural demonstrations depends on a distinction between formal and material definition, which was interpolated into the text of Posterior Analytics II 9 and seems to come from the James translation of the commentary of Alexander (= Philoponus?). The interpolated text suggests that a formal definition might serve as the middle term in a demonstration, proving the material definition of the subject. For example, one might demonstrate that anger is the boiling of blood around the heart (its material definition), by using as the middle term the formal definition of anger, the desire to do harm to another. Of course, one would have to know a first principle asserting that whatever fits the formal definition must realize the functioning it expresses in that material form, and one would have to know what anger really is, in its own proper form. Again, drawing on Aristotle's example in Posterior Analytics II 8, thunder is a noise made in a cloud (formal definition), and such a noise, in a cloud, is made (only) when fire is extinguished in it, and so thunder is the extinction of fire in a cloud.