A new proof of Belyiʼs Theorem

A new proof of Belyiʼs Theorem is given. While Belyiʼs two proofs use different methods to first reduce the branch locus from Q¯ to Q and then from Q to {0,1,∞}{0,1,∞}, our argument uses a single, new method to reduce directly from Q¯ to {0,1,∞}{0,1,∞}.