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Nature entirely fulfills these conditions Post Date: Sat, 2 Aug 2008 6:37:31 +0000 Nature goes as far as science ; neither remains behind ; but our means of experience are unable to keep up with them. The mechanician determines the indivisible point in which the centre of gravity is situated, supposing the sur face without thickness, the lines without breadth, and the length divided at a determinate point of space, which has no extension. Nature entirely fulfills these conditions. Autor of the post: Undefined The first, which favors unextencled Post Date: Sat, 2 Aug 2008 6:53:24 +0000 The point exists, and the reality should not be blamed lor the limitation of our experience. The point exists in either of the hypotheses mentioned above. The first, which favors unextencled points, admits the existence of the centre of gravity in all its scientific purity. Autor of the post: Undefined Within this molecule Post Date: Sat, 2 Aug 2008 7:06:09 +0000 The other is not so decided, but it says to us : "Do you see this molecule, this little globe of infinitesimal diameter, the smallness of which the imagination cannot represent ? Make it still smaller, by dividing it for all eternity, in decreasing geometrical progression, and you will always be coming nearer the centre of gravity without ever reach ing it. Nature will never fail ; the limit will ever re tire from you ; but you will know you are approaching it. Within this molecule is what you seek. Autor of the post: Undefined 35 These reflections place beyond Post Date: Sat, 2 Aug 2008 7:23:23 +0000 Continue to ad vance, you will never reach it, but what you want is there." In this case I do not see that the reality falls short of scientific exactness ; no mechanical theory imagined or conceived can go farther. 35 These reflections place beyond all doubt that geom etry with all its exactness, and theories in all their rigor, exist in nature. Autor of the post: Undefined If he could see Post Date: Sat, 2 Aug 2008 7:39:01 +0000 If we could follow it in our experience, we should find the real conformed to the ideal order, and we should discover that when experience is opposed to theory, it is not the latter which is wrong, but the limi tation of our means makes us lay aside the conditions im posed by the theory. The machinist who constructs a system of indented wheels finds himself obliged to correct the rules of theory, on account of friction, and other cir cumstances, proceeding from the material which he em ploys. If he could see with a glance the bosom of nature, he would discover in the friction itself a new system of infinitesimal gearing which would confirm with wonderful exactness those very rules which a rude experience re presents to him as opposed to reality. Autor of the post: Undefined Man in his weakness, un Post Date: Sat, 2 Aug 2008 7:52:34 +0000 36 If the universe is admirable in its masses of gigantic immensity, it is not less so in its smallest parts. We are placed between two infinities. Man in his weakness, un able to reach either one or the other, must content himself with feeling them, hoping that a new existence in another world will clear up the secrets which are now veiled in im penetrable darkness. Autor of the post: Undefined It moves, and its extension Post Date: Sat, 2 Aug 2008 8:05:01 +0000 37 IF extension is something as we have proved ; what is it? We find extension in bodies and also in space because in both we find that which constitutes its essence, which is dimension. Is the extension of bodies the same as the extensi 3n of space ? I see and hold in my hand a pen: it is certainly extended. It moves, and its extension moves with it. Autor of the post: Undefined This seems to have all Post Date: Sat, 2 Aug 2008 8:19:25 +0000 The space in which its motion is executed remains immovable. At the instant A the extension of the pen occupies the point A at the moment B the same extension of the pen occupies the part B of space which is distinct from the part A ; therefore neither the part A of space nor the part B is identified with the extension of the body. This seems to have all the force of a demonstration ; but to make it more clear and more general, I will put it into the form of a syllogism. Autor of the post: Undefined 38 Is the extension Post Date: Sat, 2 Aug 2008 8:30:19 +0000 Things which are separated or may be separated are distinct ; but the extension of bodies may be separated from any part of space ; therefore the extension of bodies and the extension of space are distinct, I said that this reasoning seems to have all the force of a demonstration, but it is nevertheless subject to serious dif ficulties. These difficulties cannot be understood without a profound analysis of the idea of space, and therefore I shall reserve my opinion until this has been treated of in the following chapters. 38 Is the extension of a body the body itself? I can not conceive a body without extension, but this does not prove that extension is the same thing as the body. Autor of the post: Undefined In those beings which we Post Date: Sat, 2 Aug 2008 8:44:18 +0000 My soul has acquired a knowledge of the body by means of the senses. These senses have awakened in me the idea of extension ; but they have told me nothing of the intrinsic nature of the body perceived. In those beings which we call bodies we find the power of producing in us impressions very distinct from that of extension. 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