I'm guessing here, but I would conjecture that the soft pronunciation of an intervocal 'g' in words of Latin origin ('digit' cf 'rigid' and 'frigid') derives from the way classical Latin developed into and beyond the Middle Ages as a continuing spoken language and the lingua franca of Europe for business, the Church and the academic world. The 'i' following the 'g' is crucial: Latin developed into modern Italian with the practice of pronouncing a 'g' as 'hard' as in 'jug' when followed by 'a', 'o' and 'u', and soft as in 'digit' when followed by 'i' or 'e'.