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Thus no one denies Post Date: Sun, 3 Aug 2008 14:39:27 +0000 Hence motion for us is only the change of the respective position of bodies. If we had not experienced this change, we should have no idea of motion. Thus no one denies that the phenomena of diurnal motion are the same, whether the heavens revolve around us from east to west, or the earth turns on its axis from west to east. Autor of the post: Undefined 87 But one Post Date: Sun, 3 Aug 2008 14:59:11 +0000 Therefore, the motion of only one body is a pure illu sion ; and there is no proof of the argument founded on it which is brought to oppose our doctrine of space. Hence, also, the whole universe considered as only one body, is immovable, motion takes place only in its interior. 87 But one of the strangest results of this theory is the a priori demonstration that the universe can only be termi nated in a certain manner, to the exclusion of a multitude of figures which are essentially repugnant to it. Autor of the post: Undefined This excludes a multitude Post Date: Sun, 3 Aug 2008 15:11:08 +0000 According to the doctrine which we have put forth, if we suppose only one body to exist, it cannot have any part of its surface so disposed that the shortest line from any one point to another shall pass outside of the body. For, as we suppose only one body, outside of it is pure nothing and can, therefore, contain no distances which can be mea sured by lines. This excludes a multitude of irregular fig ures, and thus we find geometrical regularity growing out of a metaphysical idea. Autor of the post: Undefined This distance cannot exist, for Post Date: Sun, 3 Aug 2008 15:28:03 +0000 Hence if only one body were in existence, it would be impossible for it to have any angles entering into it. For, its figure requires that the point A, the vertex of the angle, should be at the distance A D from the point D, the vertex of another angle. This distance cannot exist, for there is no distance where there is no body. Autor of the post: Undefined The observation of nature confirms Post Date: Sun, 3 Aug 2008 15:44:42 +0000 Therefore, the dis tance would exist and not exist at the same time, which is contradictory. It would also be an absurdity, because the capacities marked by the angles would not be filled. The observation of nature confirms the former result, in asmuch as its tendency is always to terminate every thing with curved lines and surfaces. Autor of the post: Undefined 88 Another consequence, as strange Post Date: Sun, 3 Aug 2008 16:00:57 +0000 The orbits of the stars are curves, and the stars themselves terminate in curve surfaces. The great irregularities which are observed in their surfaces might seem to destroy this conclusion, but it must be re membered the limit of the figure is not in these irregulari ties, but in the atmosphere which surrounds them, and which, being a fluid, can have no irregularities of surface. 88 Another consequence, as strange as the former, is, that we are obliged to admit the existence of a perfect geo metrical surface, and this a priori. Autor of the post: Undefined It is evident Post Date: Sun, 3 Aug 2008 16:15:09 +0000 If, where there is no body, distance is metaphysically im possible, this must be just as true in small as in great things, and even in infinitesimals. This is also a reason of the im possibility of vacuum. It is evident that a surface is not perfect when some of its points go farther out than others, so that the less they go out from the surface the more per- feet it becomes. Autor of the post: Undefined The difference is only Post Date: Sun, 3 Aug 2008 16:31:58 +0000 As there are no such points in the last surface of the universe, this surface is the realization of geometrical perfection. We have demonstrated that it is impossible for the sur- fa3e to have any angles entering into it ; it is equally im possible for it to have any, even the least, prominence. The difference is only in greater or less, which does not affect the metaphysical impossibility. Autor of the post: Undefined It is of the greatest Post Date: Sun, 3 Aug 2008 16:42:31 +0000 It is, therefore, demon strated that in the ultimate surface of the universe there is no irregularity, but that its surface is geometrically perfect. 89 I NOW proceed to deduce the last consequence of the principle explained above. It is of the greatest im portance, and seems to deserve the careful attention of all those who unite their metaphysical and physical studies. Autor of the post: Undefined [We abstract here the manner Post Date: Sun, 3 Aug 2008 16:58:28 +0000 The existence of universal gravitation may be demon strated a priori. Universal gravitation is a law of nature by which some bodies are directed to others. [We abstract here the manner. 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