An analogy is the solution of a problem on the basis of a set of relations contracted by the problematic item. Let the problem be what x is. It is solved by observing the following network of relations:

1. x is associated with b.
2. bx shares b with b1.
3. b1 shares 1 with a1.
4. The relation between a1 and a2 consists in the fact that they share a and differ by where the former has 1, the latter has 2.
5. In other words, bx is similar to a2 because it is related to b1 just as a2 is related to a1.

Given this situation, the conclusion is that x must be 2. Thus, analogy is the construction and resolution of a proportion according to the following schema:

a1 : a2 = b1 : bx; x = 2