By Frater Apollonius 4°=7□


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For whenever there are any three terms, with mutually equal intervals, that are proportionate, we then perceive that, after the manner of an extended string, the middle is to the first, as is the third to it; and this holds true inversely and alternately, interchanging places and order; so that it is impossible to arrange them numerically without producing an equivalence of results. Likewise the world's shape and movement are well arranged; the shape is a sphere self similar on all sides, able to contain all shapes that are similar; the movement endlessly exhibits the change dependent on a circle.

Now as the sphere is on every side equidistant from the centre, it is able to retain its poise whether in movement or at rest; neither leaving its poise, nor assuming another. Its external appearance being exactly smooth, it needs no mortal organs such as are fitted to, and present in all other living beings, because of their wants. The world-soul's element of divinity radiates out from the centre, entirely penetrating the whole world, forming a single mixture of divided substance with undivided form; and this mixture of two forces, the same and the different, became the origin of motion; which indeed was not accomplished in the easiest way, being extremely difficult.

Now all these proportions are combined harmonically according to numbers; which proportions were scientifically divided according to scale which reveals the elements and the means of the soul's combination. Now seeing that the earlier is more powerful in power and time than the later, the deity did not rank the soul after the substance of the body, but made it older, by taking the first of unities, 384 (12 x 16 )[x 2?]. Knowing this first, we can easily reckon the double and the triple and all the terms together, with the complements and eighths, must amount to 114,69 and likewise the divisions (sum of the tone sequences of 36 tones, amounting to 384 x 27, the perfect cube).

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