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One right line may Post Date: Fri, 1 Aug 2008 23:25:37 +0000 26 Although extension is essentially composed of parts, there is in it something fixed, unalterable, and, in some manner, simple. There may be more or less extension, but not different kinds. One right line may be longer or shorter than another, but its length is not of a different species. Autor of the post: Undefined Neither do I abstract its Post Date: Fri, 1 Aug 2008 23:36:19 +0000 One surface may be larger than another, a solid of a certain kind greater than another of the same kind, but not in a different manner. When I say that in the idea of extension objectively considered there is a certain sort of simplicity, I do not mean that there is any thing entirely simple ; for I have just said that its object is essentially composite. Neither do I abstract its essential elements, which are the three di mensions, nor any idea which it involves, as its liinitabi- lity, or capacity to be limited in various ways. Autor of the post: Undefined A right line Post Date: Fri, 1 Aug 2008 23:56:11 +0000 All I wish to show is that in all the different figures these fundamen tal notions are sufficient, that they are never modified, but always present the same thing to the mind. Let us compare a right line with a curve. A right line Is a direction which is always constant ; the curve a direc tion which is always varied. Autor of the post: Undefined The curve is therefore formed Post Date: Sat, 2 Aug 2008 0:10:14 +0000 A direction always varied is a collection of right directions infinitely small. Therefore, the circumference of a circle is considered as a polygon of an infinite number of sides. The curve is therefore formed by the variety of directions reduced to infinitesimal values. Autor of the post: Undefined The lines are Post Date: Sat, 2 Aug 2008 0:22:34 +0000 This theory which explains the difference of the right line and the curve, is evidently applicable to surfaces and solids. Let us compare a quadrilateral with a pentagon ; all that the second has which the first has not is one side more in peri- metre, and in area the space contained in the triangle formed by a line drawn from one of its angles to either of the op- posite angles. The lines are of the same kind, the surfaces differ only in the ways in which they terminate. Autor of the post: Undefined This intrinsical constancy is indispensable Post Date: Sat, 2 Aug 2008 0:34:53 +0000 But ter mination is the same as limitation. Therefore, all that is essential to the idea of extension, that is, direction and limitability, remain always the same and unchangeable. This intrinsical constancy is indispensable to science. Autor of the post: Undefined Is exten- tion any thing Post Date: Sat, 2 Aug 2008 0:45:10 +0000 That which is mutable, may be the object of perception, but not of scientific perception. 27 WE now come to more difficult questions. Is exten- tion any thing in itself, abstracted from the idea of it ? If any thing, what is it ? Is it identified with bodies, or is it confounded with space ? I have proved that extension exists outside of our selves, that it is not an illusion of the senses ; and this solves the first question, whether extension is any thing. Autor of the post: Undefined Whatever idealists may assert, there Post Date: Sat, 2 Aug 2008 0:58:30 +0000 Whatever may be its nature or our ignorance on this point, there is in reality something which corresponds to our idea of extension. Whoever denies this truth must be content to deny every thing except the consciousness of himself, if indeed he does not experience doubts even of this too. Whatever idealists may assert, there is not, nor ever was a man who in his sound judgment seriously doubted; the existence of an external world. Autor of the post: Undefined It either does not exist Post Date: Sat, 2 Aug 2008 1:17:06 +0000 This conviction is foiv man a necessity against which it is vain to contend. This external world is for us inseparable ft Dm that which is represented by the idea of extension. It either does not exist, or else it is extended. Autor of the post: Undefined 28 It is Post Date: Sat, 2 Aug 2008 1:29:48 +0000 If we could be persuaded that it is not 3xtended, it would not be difficult to convince us that it does not exist. For my part, I find it just as diffi cult to imagine the world without extension as without ex istence, and if I could be made to believe its extension an illusion, I should easily believe its existence also an illu sion. 28 It is to be observed that although we confess our ignorance of the internal nature of extension, it is still ne cessary to admit that we know something of it ; its dimen sions, namely, and what serves as the basis of geometry. 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