In sight, abstracting extension, there is color, but we cannot discover in it any thing from which we can produce so fruitful an idea as that of extension. Even at first we see that the color itself is not perceptible without extension, and so far from extension being produced by color, it is on the contrary an indispensable condition without which color cannot be perceived. Colors as the objects of sensation are only individual phenomena, which have no connection with one another nor with the general idea of extension. What has been said of them will equally apply to all the impressions of touch. CHAPTER III. SCIENTIFIC FRUITFULNESS OF THE IDEA OF EXTENSION. 13. In order to understand the superiority of the idea of extension over mere sensations; or rather, in order to understand that there is a true idea of extension considered in itself, and that there is no such idea of the direct and immediate objects of sensation, I wish to call attention to the fact that among all the objects of the senses, _extension alone gives origin to a science_. This is a very important fact;--to explain it as it deserves, I shall establish the following propositions: FIRST PROPOSITION. Extension is the basis of geometry. SECOND PROPOSITION. Not only is extension the basis of geometry, but all that we know of the nature of bodies may be reduced to the manifestations, applications, and modifications of extension, with the addition of the ideas of number and time. THIRD PROPOSITION. Whatever we know of sensations that deserves the name of science is included in the modifications of extension. FOURTH PROPOSITION. We can form no fixed idea of corporeal objects, nor make any observation on the sensible world, unless we are guided by the rule of extension. These four propositions are nothing more than the enunciation of certain facts, the mere exposition of which is a sufficient demonstration. 14. Extension is the basis of geometry. This is evident, since geometry treats only of dimensions, and the idea of dimension is essential to extension. When geometry treats of figures, it is still extension which it is treating of; for figures are only extension with certain limitations. The quadrilateral contains two triangles. To distinguish them, it is only necessary to draw their limit, which is the diagonal. The idea of figure is merely the idea of limited extension, and the figure is of this or that kind according to the nature of its limits. Consequently, the idea of figure is nothing new superadded to extension; but merely its application.