Many times, mathematicians will only utilize faciendia as a result of the results of previous definitions or demonstradums. An idea of this is expressed within Topics (Aristotle), where he goes over the difference between a proposition and a problem. " For if it be put in this way, "'An animal that walks on two feet" is the definition of man, is it not?' or '"Animal" is the genus of man, is it not?' the result is a proposition: but if thus, 'Is "an animal that walks on two feet" a definition of man or no?' (or 'Is "animal" his genus or no?') the result is a problem." This is parallel to the idea of the difference between a Q.E.D. and a Q.E.F. A proposition (Q.E.D.) like this functions exactly the same way as it does for Euclid: the proposition is intended to prove a particular property, the problem (Q.E.F.) on the other hand requires multiple propositions in order to prove, or even construct an entirely new category. The problems are the dialectic's objective to solve. In a similar fashion, there are many different ways to construct a mathematical system to construct a triangle. There is only one triangle, however, and the triangle has definite properties. In this way, truth is sought within mathematics and philosophy in a congruous way. Euclid's Elements could be thought of as a document whose objective is to construct a dodecahedron and an icosahedron (Propositions 16 and 17 book XIII). Appollonius' On Conics Book I could be thought of as a document whose objective is to construct a pair of hyperbolas from two bisecting lines (Proposition 50 of book I). Propositions have historically been used in logic and mathematics to work towards solving a problem, and these fields both reflect that in their foundations through Euclid and Aristotle.