=164.= It might be objected, to the above argument, that it involves a _petitio principii_. For it has been assumed that the two points and their relation form a figure, to which other figures can be congruent. Now if two points have no intrinsic relation, it would seem that they cannot form such a figure. The argument, therefore, apparently assumes what it had to prove. Why, it may be asked, should not three points be required, before we obtain any relation, which Free Mobility allows us to construct afresh in other parts of space? The answer to this, as to the corresponding question in the first section of this chapter, lies, I think, in the passivity of space, or the mutual independence of its parts. For it follows, from this independence, that any figure, or any assemblage of points, may be discussed without reference to other figures or points. This principle is the basis of infinite divisibility, of the use of quantity in Geometry, and of all possibility of isolating particular figures for discussion. It follows that two points cannot be dependent, as to their relation, on any other points or figures, for if they were so dependent, we should have to suppose some action of such points or figures on the two points considered, which would contradict the mutual independence of different positions. To illustrate by an example: the relation of two given points does not depend on the other points of the straight line on which the given points lie. For only through their relation, _i.e._ through the straight line which they determine, can the other points of the straight line be known to have any peculiar connection with the given pair. =165.= But why, it may be asked, should there be only one such relation between two points? Why not several? The answer to this lies in the fact that points are wholly constituted by relations, and have no intrinsic nature of their own[172]. A point is defined by its relations to other points, and when once the relations necessary for definition have been given, no fresh relations to the points used in definition are possible, since the point defined has no qualities from which such relations could flow. Now one relation to any one other point is as good for definition as more would be, since however many we had, they would all remain unaltered in a combined motion of both points. Hence there can only be one relation determined by any two points. =166.= (2) We have thus established our first proposition--two points have one and only one relation uniquely determined by those two points. This relation we call their distance apart. It remains to consider the conditions of the measurement of distance, _i.e._, how far a unique value for distance involves a curve uniquely determined by the two points.