In his groundbreaking study of 1823, here for the first time critically edited as well as translated, the German historian of philosophy Christian August Brandis pieces together the ancient testimonies about the lost books of Aristotle treating the unwritten doctrines of Plato. By systematically documenting the importance of the doctrine of ideal numbers for the Platonic theory of ideas and illuminating its significance, Brandis places the contemporary discussion about the development of Plato’s thought and its criticism by Aristotle on a new footing in a manner still resonating today.