Pythagoras considered _numbers_ as the essence and principle of all things, and attributed to them a real and distinct existence; so that, in his view, they were the elements out of which the universe was constructed. How he conceived this process has never been satisfactorily explained. He traced the various forms and phenomena of the world to numbers as their basis and essence. The “Monad” or _unit_ he regarded as the source of all numbers. The number _Two_ was imperfect, and the cause of increase and division. _Three_ was called the number of the whole because it had a beginning, middle, and end. _Four_, representing the square, is in the highest degree perfect; and _Ten_, as it contains the sum of the four prime numbers, comprehends all musical and arithmetical proportions, and denotes the system of the world. As the numbers proceed from the monad, so he regarded the pure and simple essence of the Deity as the source of all the forms of nature. Gods, demons, and heroes are emanations of the Supreme, and there is a fourth emanation, the human soul. This is immortal, and when freed from the fetters of the body passes to the habitation of the dead, where it remains till it returns to the world, to dwell in some other human or animal body, and at last, when sufficiently purified, it returns to the source from which it proceeded. This doctrine of the transmigration of souls (metempsychosis), which was originally Egyptian and connected with the doctrine of reward and punishment of human actions, was the chief cause why the Pythagoreans killed no animals. Ovid represents Pythagoras addressing his disciples in these words: “Souls never die, but always on quitting one abode pass to another. I myself can remember that in the time of the Trojan war I was Euphorbus, the son of Panthus, and fell by the spear of Menelaus. Lately being in the temple of Juno, at Argos, I recognized my shield hung up there among the trophies. All things change, nothing perishes. The soul passes hither and thither, occupying now this body, now that, passing from the body of a beast into that of a man, and thence to a beast’s again. As wax is stamped with certain figures, then melted, then stamped anew with others, yet is always the same wax, so the soul, being always the same, yet wears, at different times, different forms. Therefore, if the love of kindred is not extinct in your bosoms, forbear, I entreat you, to violate the life of those who may haply be your own relatives.” Shakspeare, in the “Merchant of Venice,” makes Gratiano allude to the metempsychosis, where he says to Shylock: “Thou almost mak’st me waver in my faith, To hold opinion with Pythagoras, That souls of animals infuse themselves Into the trunks of men; thy currish spirit Governed a wolf; who hanged for human slaughter Infused his soul in thee; for thy desires Are wolfish, bloody, starved and ravenous.”