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Fragments of the Lost Writings of Proclus


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Author Topic: Fragments of the Lost Writings of Proclus  (Read 1635 times)
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« on: February 06, 2009, 01:17:42 pm »

place, and is moved from a foreign place, if nothing impedes it; and if this, in a similar manner, happens to fire and the other elements,—it is evident that fire, and each of the elements in a foreign place, will be a sphere or a pyramid, but in its proper place a cube."

In opposition to this ninth argument, Proclus says, "that though the elements are in their proper places, yet such as consist of easily movable figures are not without motion; for pyramids are always moved from the dissimilitude of the vertex to the base. Thus also with respect to air, the elements of it, when it exists in its proper place, are assimilated to things perpetually flowing; and the elements of water love collision. For the summits are adjacent to the bases of their similars, and being impelled, they strike against the whole in the place in which each is contained. But being thus moved, they imitate the motion in a circle, neither being moved from the middle nor to the middle, but revolving about each other in their own place. The elements of earth, however, remain, because they have their summits the same with their bases. But nothing similar acts on the similar, whether they possess similitude according to figures, or according to power, or according to magnitude."

"Farther still," says Aristotle, "if fire heats

p. 22

and burns through its angles, all the elements will impart heat, but one perhaps more than another; since all of them will have angles; as, for instance, the octaedron and the dodecaedron. And according to Democritus, a sphere also burns, as being a certain angle; so that they will differ by the more and the less. This, however, is evidently false."

Proclus, in opposition to this tenth argument, says, "that it is improperly assumed that an angle is calorific, and that a false conclusion is the consequence of this assumption. For Timæus assumes from sense, that sharpness and a power of dividing are certain properties of heat. But that which cuts, cuts not simply by an angle, but by the sharpness of the angle, and tenuity of the side. For thus also the arts make incisive instruments, and nature sharpens the angles of those teeth that are called incisores, and giving breadth to the grinders, has attenuated the sides. An acute angle also is subservient to rapid motion. Hence a power of this kind is not to be ascribed to an angle simply, but to the penetrating acuteness of the angle, the incisive tenuity of the side, and the celerity of the motion. It is likewise necessary that magnitude should be present, as in the pyramid, that it may forcibly enter. If, therefore, in fire alone there is acuteness of

p. 23

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