Davies was educated first at Penzance Grammar School and then by his father, and by Rev Malachy Hitchins, the mathematical astronomer. At the age of 17, at the recommendation of Hitchins, he was sent to Bristol to join the Mathematical Academy of Benjamin Donne where he remained for three years. His sister Philippa simultaneously finished her own schooling with the famous bluestocking Hannah More. He went up to Pembroke College, Oxford in 1786, whence he graduated with a MA on 29 June 1789.