There is a traditional distinction between extensive and intensive quantities, which is somewhat misleading when taken seriously. The theory is that extensive quantities are composed of parts and intensive quantities are not. The only truly extensive quantities are numbers and classes. Where finite classes are concerned, the number of their terms may be taken[Pg 117] as a measure of them, and they have parts corresponding to all smaller numbers. But in geometry we are never concerned with quantities which have parts. The number of points in a volume, whether large or small, is always in the usual kinds of geometry; thus magnitude has nothing to do with number. Interval, as we have seen, is a relation, and smaller intervals are not parts of it. If and are equal intervals in a straight line, we say that the interval is double of each, and we think of it as the "sum" of and . But it is only by a convention, though an almost irresistible one, that we assign as the measure of a number double that which we assign as the measure of or of . And to say that is the "sum" of and is to say something very ambiguous, since the word "sum" has many meanings. When and are considered as vectors, we may say that is their sum even when they are not in one straight line. Again, given suitable definitions, we may say that the points between and are the sum (in the logical sense) of the points between and , and between and ; this will only hold if is a straight line. But the distance between and , considered as a relation, is not properly the "sum," in any recognized sense, of the distances , . Thus all geometrical quantities are "intensive." This shows that the distinction of intensive and extensive is unimportant.