 Brouwer realized (1907: 125–128 [1975: 72–73]) that the hypothetical judgement seems to pose a problem for his view on logic as described above. For what is peculiar to the hypothetical judgement, Brouwer says, is that there the priority of mathematics over logic seems to be reversed. Among the examples he refers to are the proofs found in elementary geometry of the problems of Apollonius. Here is one of them: Given three circles, defined by their centers and their radii, construct a fourth circle that is tangent to each of the given three. The way this is usually solved is first to assume that such a fourth circle exists, then to set up equations that express how it is related to the three given circles, and then, via algebraic manipulations and logic, arrive at explicit definitions of the center and radius of the required circle, and, from there, at corresponding mathematical constructions. So it seems that here one first has to assume the existence of the required circle, then use logic to make various judgements about it, and only thereby arrives at a mathematical construction for it.