By Frater Apollonius 4°=7□


THE EARTH'S CREATION BY GEOMETRIC FIGURES



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THE EARTH'S CREATION BY GEOMETRIC FIGURES

The Earth, fixed at the centre, becomes the hearth of the gods, and the boundary of darkness and day, producing both settings and risings, according to the occultations produced by the things that form the boundary, just as we im prove our sight by making a tube with our closed hand, to exclude refraction. The Earth is the oldest body in the heavens. Water was not produced without Earth, nor air without moisture; nor could fire continue without moisture and the materials that are inflammable; so that the Earth is fixed upon its balance as the root and base of all other substances. Of produced things, the substratum is Matter, while the reason of each shape is abstract Form; of these two the resultance is Earth, and Water, Air and Fire.

This is how they were created. Every body is composed of surfaces, whose elements are triangles; of which one is right-angled, and the other has all unequal sides, with the greater angle thrice the size of the lesser; while its least angle is the third of a right angle, and the middle [one] is double of the least; for it is two parts out of three; while the greatest is a right angle, being one and a half greater than the middle one, and the triple of the least. Now this unequal [sided] triangle is the half of a equilateral triangle, out into two equal parts by a line let down from apex to that base. Now in each of these triangles there is a right angle; but in the one, the two sides about the right angle are equal, and in the other, all the sides are unequal. Now let this be called a scalene triangle; while the other, the half of the square, is the principle of the constitution the Earth. For the square produced from this scalene triangle is composed of four half squares and from such a square is produced the cube, a [body] the most stationary and steady in every way; having six sides and eight angles, and on this account [the]Earth is a body the heaviest and most difficult [to] be moved and its substance is inconvertible because it has no affinity with a triangle of any kind. Only the Earth has as peculiar element [the--] square and this is the element of the three other substances, Fire, Air and Water. For when the half triangle is put together six times, it produces a solid equilateral triangle; the exemplar of the [pyramid], which has four faces with equal angles, which is the form of Fire, as the easiest to be moved and composed of the finest particles. After this ranks the octohedron, with eight faces and six angles, the element of Air, and the third is the icosahedron, with twenty faces and twelve angles, the element of Water, composed of the most numerous and heaviest particles.

These then, as being composed of the same element, are transmuted. But the deity has made the dodecahedron, as being the nearest to the sphere, the image of the Universe. Fire then, by the fineness of its particles, passes through all things; and Air through the rest of things, with the exception of Fire; and Water through the Earth. All things are therefore full, and have no vacuum. They cohere by the revolving movement of the Universe, and are pressed against, and rubbed by, each other in turn, and produce the never-failing change from production to destruction.





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