XL. These now were his chief opinions. He affirmed that the soul was immortal and clothed in many bodies successively, and that its first principle was number, and that the first principle of the body was geometry. And he defined it as an abstract idea of spirit diffused in every direction. He said also, that it was self-moving and threefold. For that that part of it which was capable of reasoning was situated in the head, that that portion which was affected by passion was seated around the heart, and that which was appetitive was placed around the navel and the liver. And that it is placed in the middle of the body, and embraces it at the same time in all its parts, and that it consists of elements; and that when it is divided according to harmonic intervals it forms two connected circles; of which the inner circle is divided into six portions, and makes in all seven circles; and that this is placed on the left hand of the diameter, and situated in the interior. But the other is on the right hand of the same line; on which account, and because it is one only, it is the superior of the two. For the other is divided internally; and this too, is the circle of that which is always the same; the other, the circle of that which is changeable and different. And the one he says is the motion of the soul, but the other is the motion of the universe and of the planets.
On the other side, the division of the circles from the centre to the extremities, being harmoniously appropriated to the essence of the soul, the one knows existing things and establishes harmony between them, because it is itself composed of harmonious elements. The circle of what is changeable, engenders opinion by its regular movements; but the circle of that which is always the same produces knowledge.
XLI. Plato lays down two primary causes or principles of all things, God and matter, which he also calls mind, and the cause. And he defines matter as something without shape and without limitation, and says that from it all concretions arise. He affirms also that as it was moving about at random, it was brought by God into one settled place, as God thought order better than disorder; and that this nature is divided into four elements, fire, water, air, and earth, of which the world itself and everything in it was made. But he says that the earth is the only thing that is unchangeable, as he considers the cause to be the difference of the figures of which it is composed; for he says that the figures of the others are homogeneous; for that they are all composed equally of scalene triangles. The figure of the earth, however, is peculiar to itself; for the element of fire is a pyramid; of air, an octagon; of water, an eicosagon; and of the earth, a cube; owing to which these things cannot be changed into earth, nor earth into them. He teaches also that these elements are not separated so as to occupy each a peculiar and distinct place; for the spherical motion collects and compresses all the small things towards the centre, and the small things separate the great ones, on which account the species, as they change, do also change their positions.