  Aristotle's point about autonomy is that a theorem in arithmetic (even less a theorem in harmonics) cannot be used to prove something in geometry. Here, arithmetic is probably understood as the number theory found in Euclid, Elements vii-ix, and not mere calculation of numbers, which, of course, is used in geometry. This allows the anti-Platonic point that theorems about the beautiful and theorems in mathematics have nothing to do with one another, even if some theorems are beautiful.