XX. The purely intellectual additions made by Pythagoras to human wisdom seem to have been vast and permanent. By probable testimony, he added largely to mathematical science; and his discoveries in arithmetic, astronomy, music, and geometry, constitute an era in the history of the mind. His metaphysical and moral speculations are not to be separated from the additions or corruptions of his disciples. But we must at least suppose that Pythagoras established the main proposition of the occult properties of NUMBERS, which were held to be the principles of all things. According to this theory, unity is the abstract principle of all perfection, and the ten elementary numbers contain the elements of the perfect system of nature. By numbers the origin and the substance of all things could be explained [244]. Numbers make the mystery of earth and heaven--of the gods themselves. And this part of his system, which long continued to fool mankind, was a sort of monstrous junction between arithmetic and magic--the most certain of sciences with the most fantastic of chimeras. The Pythagoreans supposed the sun, or central fire, to be the seat of Jupiter and the principle of life. The stars were divine. Men, and even animals, were held to have within them a portion of the celestial nature. The soul, emanating from the celestial fire [245]--can combine with any form of matter, and is compelled to pass through various bodies. Adopting the Egyptian doctrine of transmigration, the Pythagoreans coupled it with the notion of future punishment or reward.