  A demonstration of the highest sort in mathematics does not, of course, work out the mechanism by which some function must be accomplished, so in this case the middle term will be the formal definition of the subject, stated in terms of its parts (so a definition of a triangle will be in terms of the lines making it up, the definition of a number in terms of the units making it up, and so on). The attribute, rather than a material definition, will simply be the property proved of the subject.