114. In this he confounds, I say, the vague imagination with the idea. The limit between the two is strongly marked. When we see an object we have the sensation and intuition of extension. The space perceived or sensed is, in this case, the extension itself perceived. We imagine a multitude of extended objects, and a capacity which contains them all. We imagine this capacity as the immensity of the ethereal regions, a boundless abyss, a dark region beyond the limits of creation. So far there is no idea, there is only an imagination arising from the fact that when we begin to see bodies we do not see the air which surrounds them, and the transparency of the air permits us to see distant objects, and thus from our infancy we are accustomed to imagine an empty capacity in which all bodies are placed, but which is distinct from them. But this is not the idea of space; it is only an imagination of it, a sort of rude, sensible idea, probably common to man and the beasts. The true idea, and the only one deserving the name, is that which our mind possesses when it conceives extension in itself, without any mixture of sensation, and which is, as it were, the seed of the whole science of geometry. 115. It should be observed that the word representation as applied to purely intellectual ideas must be taken in a purely metaphorical sense, unless we eliminate from its meaning all that relates to the sensible order. We know objects by ideas, but they are not represented to us. Representation, properly speaking, occurs only in the imagination which necessarily relates to sensible things. If I demonstrate the properties of a triangle, it is clear that I must know the triangle, that I must have an idea of it; but this idea is not the natural representation which is presented to me like a figure in a painting. All the world, even irrational animals have this representation, yet we cannot say that brutes have the idea of a triangle. This representation has no degrees of perfection, but is equally perfect in all. Any one who imagines three lines with an area enclosed, possesses the representation of a triangle with as much perfection as Archimedes; but the same cannot be said of the idea of a triangle, which is evidently susceptible of various degrees of perfection.