We are able to follow the three moments in the Ionic philosophy: (_α_) The original essence is water; (_β_) Anaximander’s infinite is descriptive of movement, simple going out of and coming back into the simple, universal aspects of form—condensation and rarefaction; (_γ_) the air is compared to the soul. It is now requisite that what is viewed as reality should be brought into the Notion; in so doing we see that the moments of division, condensation, and rarefaction are not in any way antagonistic to the Notion. This transition to Pythagoras, or the manifestation of the real side as the ideal, is Thought breaking free from what is sensuous, and, therefore, it is a separation between the intelligible and the real. B. PYTHAGORAS AND THE PYTHAGOREANS. The later Neo-Pythagoreans have written many extensive biographies of Pythagoras, and are especially diffuse as regards the Pythagorean brotherhood. But it must be taken into consideration that these often distorted statements must not be regarded as historical. The life of Pythagoras thus first comes to us in history through the medium of the ideas belonging to the first centuries after Christ, and more or less in the style in which the life of Christ is written, on the ground of ordinary actuality, and not in a poetic atmosphere; it appears to be the intermingling of many marvellous and extravagant tales, and to take its origin in part from eastern ideas and in part from western. In acknowledging the remarkable nature of his life and genius and of the life which he inculcated on his followers, it was added that his dealings were not with right things, and that he was a magician and one who had intercourse with higher beings. All the ideas of magic, that medley of unnatural and natural, the mysteries which pervade a clouded, miserable imagination, and the wild ideas of distorted brains, have attached themselves to him.