As for our assertion that infinity in every direction is impossible, several arguments support it.

First, an infinite extension cannot exist. The proof is that supposing an infinite extension leads to an impossibility; it must therefore itself be impossible. We say that it leads to an impossibility because, if we suppose an infinite extension and another, finite extension parallel to it, and the finite line then moves from parallelism into alignment with it, we say: this entails that there must be a point on the first, infinite line that is the first point of alignment. The finite line was not previously aligned with the infinite line, but then became aligned with it. Thus this alignment came into being at