Question V.

Why, Since Bodies and Figures are Contained Partly by Rectilinears and Partly by Circles, Does he Make Isosceles Triangles and Triangles of Unequal Sides the Principles of Rectilinears; of which the Isosceles Triangle Constitutes the Cube, the Element of the Earth; and a Scalene Triangle Forms the Pyramid, the Octahedron the Seed of Fire, Air and Water Respectively, and the Icosahedron; - While he Passes Over Circulars, Though he Does Mention the Globe, where he Says that Each of the Afore-Reckoned Figures Divides a Round Body that Circumscribes it into Equal Parts. (See "Timaeus," pp. 53-56.)

Is their opinion true who think that he ascribed a dodecahedron to the globe, when he says that God made use of it in delineating the universe? For upon account of the multitude of its bases and the obtuseness of its angles, avoiding all rectitude, it is flexible, and by circumtension, like globes made of twelve skins, it becomes circular and comprehensive. For it has twenty solid angles, each of which is contained by three obtuse planes, and each of these contains one and the fifth part of a right angle. Now it is made up of twelve equilateral and equangular quinquangles (or pentagons), each of which consists of thirty of the first scalene triangles. Therefore it seems to resemble both the Zodiac and the year, it being divided into the same number of parts as these.

Or is a right line in Nature prior to circumference; or is circumference but an accident of rectilinear? For a right line is said to bend; and a circle is described by a centre and distance, which is the place of a right line from which a circumference is measured, this being everywhere equally distant from the middle. And a cone and a cylinder are made by rectilinears; a cone by keeping one side of a triangle fixed and carrying another round with the base - a cylinder, by doing the like with a parallelogram. Further, that is nearest to principle which is less; but a right is the least of all lines, as it is simple; whereas in a circumference one part is convex without, another concave within. Besides, numbers are before figures, as unity is before a point, which is unity in position. But indeed unity is triangular; for every triangular number (Triangular numbers are those of which

equilateral triangles can be formed in this way:

                            . .         . . .       . .          . . .  .     . .        . . .       . . .    . . .      . . .   . . . .   . . . . .

Such are: 3, 6, 10, 15, 21, 28, 36, 45, etc.; that is, numbers formed by adding the digits in regular order. (G.)) taken eight times, by adding unity, becomes quadrate; and this happens to unity. Therefore a triangle is before a circle, whence a right line is before a circumference. Besides, no element is divided into things compounded of itself; indeed there is a dissolution of all other things into the elements. Now a triangle is divided into no circumference, but two diameters cut a circle into four triangles; therefore a rectilinear figure is before a circular, and has more of the nature of an element. And Plato himself shows that a rectilinear is in the first place, and a circular is only consequential and accidental. For when he says the earth consists of cubes, each of which is contained with rectilinear superficies, he says the earth is spherical and round. Therefore there was no need of making a peculiar element for round things, since rectilinears, fitted after a certain manner among themselves, do make up this figure.

Besides, a right line, whether great or little, preserves the same rectitude; but as to the circumference of a circle, the less it is, the crookeder it is; the larger, the straighter. Therefore if a convex surface stands on a plane, it sometimes touches the under plane in a point, sometimes in a line. So that a man may imagine that a circumference is made up of little right lines.

But observe whether this be not true, that no circle or sphere in this world is exactly drawn; but since by the tension and circumtension of the straight lines, or by the minuteness of the parts, the difference is hidden, the figure seems circular and round. Therefore no corruptible body moves circularly, but altogether in a right line. To be truly spherical is not in a sensible body, but is the element of the soul and mind, to which he has given circular motion, as being agreeable to their nature.