cession or juxtaposition of our ideas, can ever of itself produce the idea of this relation between them. My first object will be to inquire whether the perception of the equality of two lines is the same with the perception of the contiguity of their extremities: whether the one idea necessarily includes every thing that is contained in the other.
I see two points touch one another, or that there is no sensible interval between them. What possible connection is there between this idea, and that of their being the boundaries of two lines of equal length? It is only by drawing out those points to a certain distance that I get the idea of any lines at all; they must be drawn out to the same distance before they can be equal; and I can have no idea of their being equal without dividing that equal distance into two distinct parts or lines, both of which I must consider at the same time as contained with the same limits. If the ideas merely succeeded one another, or even coexisted as distinct images, they would still be perfectly unconnected with each other, each being absolutely contained within itself, and there being no common act of attention to both to unite them together. Now the question is whether this perception of the equality of these two lines is not properly an idea of comparison (in the sense in which every one uses and feels these words,) an idea which cannot possibly be expressed or defined by any other relation between our ideas; or whether it is only a round-about way of getting at the old idea of the coincidence of their points or ends, which certainly is not an idea of comparison, or of the relation between equal quantities, and simply because there are no quantities to be compared. The one relates to the agreement of the things themselves one with another, the other to their local situation. There is no proving any farther that these ideas are different, but by appealing to every
