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. Contents: Orrin F. Summerell: Introduction - On the Life and Work of Christian August Brandis - Christiani Augusti Brandis: Diatribe de libris Aristotelis deperditis de Ideis et de Bono sive Philosophia - Christian August Brandis: A Study of the Lost Books of Aristotle On the Ideas and On the Good or On Philosophy - Notes on the Text - Edward C. Halper: Plato's Principles of Mathematics.