Moreover, limit or termination is not a positive idea; it is a pure negation. If I have extension and wish to form all the figures possible, I need not conceive any thing new, but only abstract what I have already; I do not add, but take away. Thus in the quadrilateral I obtain the conception of the triangle by abstracting one of the two equal parts into which it is divided by the diagonal. In the same manner I deduce the quadrilateral from a pentagon by abstracting the triangle formed by a line drawn from one of its angles to either of the opposite angles. These observations apply to all geometrical figures. The idea of extension is like an immense ground on which we have only to _draw limits_ in order to obtain whatever we want. It does not follow from this that the understanding cannot proceed by addition or the synthetic method; for, just as the subtraction of one of the parts of the quadrilateral formed a triangle, so also the addition of two triangles with an equal side will produce a quadrilateral. And in the same way points produce lines, lines surfaces, and surfaces solids. In all these cases the idea of figure is that of limited extension, since the quantities which constitute it are merely extension with certain limitations. 15. An observation here presents itself to my mind, which I think must throw great light upon the question which we are now discussing. If we compare the two methods by which the idea of figure is obtained; the synthetic, or that of composition or addition, and the analytic, or that of subtraction or limitation, we shall find that the second is more natural than the other; because that which the analytic method produces is permanent in the figure and essential to it, whilst the synthetic only seems to constitute it, and as soon as it is thus constituted the marks of its formation are obliterated. An example will make this clearer. In order to conceive a rectangle I have only to limit indefinite space by four lines in a rectangular position; that is, to _affirm_ a part, and _deny_ the rest. The lines are nothing in themselves, and represent only the limit beyond which the space included in the rectangle cannot pass. To abstract this limitation or denial of all that is not contained in the surface of the rectangle, would be to destroy the rectangle. Therefore, the denial in which this method consists is always permanent, the manner of the production of the idea is inseparable from the idea itself. But if, on the other hand, I proceed to form the rectangle by addition or by joining the hypotheneuse of two right-angle triangles, the ideas of the two component parts are not necessary to the idea of the rectangle after its formation. I can conceive the rectangle even abstracting the diagonal.