Though some have considered Speusippus as inferior to Aristotle, the world is nevertheless indebted to him for defining and expounding many things that Plato had left obscure in his doctrine of the Sensible and Ideal. His maxim was “The Immaterial is known by means of scientific thought, the Material by scientific perception.”[15] Xenocrates expounded many of the unwritten theories and teachings of his master. He too held the Pythagorean doctrine, and his system of numerals and mathematics in the highest estimation. Recognizing but three degrees of knowledge—_Thought_, _Perception_, and _Envisagement_ (or knowledge by _Intuition_), he made the former busy itself with all {xix} that which is _beyond_ the heavens; Perception with things in the heavens; Intuition with the heavens themselves. We find again these theories, and nearly in the same language in the _Manava-Dharma-Sastra_, when speaking of the creation of man: “He (the Supreme) drew from his own essence the immortal breath which _perisheth not in the being_, and to this soul of the being he gave the Ahancara (conscience of the _ego_) sovereign guide. Then he gave to that soul of the being (man) the intellect formed of _the three qualities_, and the five organs of the outward perception.” These three qualities are Intelligence, Conscience, and Will; answering to the Thought, Perception, and Envisagement of Xenocrates. The relation of numbers to Ideas was developed by him further than by Speusippus, and he surpassed Plato in his definition of the doctrine of Invisible Magnitudes. Reducing them to their ideal primary elements, he demonstrated that every figure and form originated out of the smallest indivisible line. That Xenocrates held the same theories as Plato in relation to the human soul (supposed to be a number) is evident, though Aristotle contradicts this, like every other teaching of this philosopher.[16] This is conclusive evidence that many of Plato’s doctrines were delivered orally, even were it shown that Xenocrates and not Plato was the first to originate the theory of indivisible magnitudes. He derives the Soul from the first Duad, and calls it a self-moved number.[17] Theophrastus remarks that he entered and eliminated this Soul-theory more than any other Platonist. He built upon it the cosmological doctrine, and proved the necessary existence in every part of the universal space of a successive and progressive series of animated and thinking though spiritual beings.[18] The Human Soul with him is a compound of the most spiritual properties of the Monad and the Duad, possessing the highest principles of both. If, like Plato and Prodicus, he refers to the Elements as to Divine Powers, and calls them gods, neither himself nor others connected any anthropomorphic idea with the appellation. Krische remarks that he called them gods only that these elementary powers should not be confounded with the dæmons of the nether world[19] (the Elementary Spirits).