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Describe a cube round Jupiter; the circle including this will be Saturn. Then inscribe in the Earth an icosahedron; the circle described in it will be Venus. Inscribe an octohedron in Venus; the circle inscribed in it will be Mercury."
Now, inscribe in the earth an icosahedron, the sphere inscribed in it will be Venus: inscribe an octahedron in Venus: the circle inscribed in it will be Mercury."
Pythagoras, that the world was formed of five solid figures which are called mathematical; the earth was produced by the cube, the fire by the pyramid, the air by the octahedron, the water by the icosahedron, and the globe of the universe by the dodecahedron. In all these Plato hath the same sentiments with Pythagoras.
After the cube, the octahedron, and the various forms of pyramid and prism have been mastered, may come the more complex regular bodies the dodecahedron and icosahedron to construct which out of single pieces of cardboard, requires considerable ingenuity.
Now Euclid would, with great right, demand of such a philosopher to make Life; in the same sense, I mean, in which Euclid makes an Icosahedron, or a figure of twenty sides, namely, in the understanding or by an intellectual construction. An argument which, of itself, is sufficient to prove the untenable nature of Materialism.
To the earth then, which is the most stable of bodies and the most easily modelled of them, may be assigned the form of a cube; and the remaining forms to the other elements, to fire the pyramid, to air the octahedron, and to water the icosahedron, according to their degrees of lightness or heaviness or power, or want of power, of penetration.
His theory was this: "Around the orbit of the earth describe a dodecahedron the circle comprising it will be that of Mars; around Mars describe a tetrahedron the circle comprising it will be that of Jupiter; around Jupiter describe a cube the circle comprising it will be that of Saturn; now within the earth's orbit inscribe an icosahedron the inscribed circle will be that of Venus; in the orbit of Venus inscribe an octahedron the circle inscribed will be that of Mercury."
These projections would correspond to the network of lines seen in looking through a glass paperweight of the given shape, the lines being formed by the joining of the several faces. The dodecahedron and icosahedron, having more faces, yield more intricate patterns, and there is no limit to the variety of interesting designs obtainable by these direct and simple means.
The second solid is composed of the same triangles, which unite as eight equilateral triangles, and make one solid angle out of four plane angles six of these angles form a regular octahedron. The third solid is a regular icosahedron, having twenty triangular equilateral bases, and therefore 120 rectangular scalene triangles.
Other sages adhered to the mathematical system of squares and triangles; the cube, the pyramid, and the sphere; the tetrahedron, the octahedron, the icosahedron, and the dodecahedron.
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