MAGNITUDE. This term is generally used synonymously with quantity, and is sometimes even confounded with number. The dis tinction between the first two terms is not more marked than this : he who answers the question " how much " describes the quantity, and he who answers "how great ? " describes the magnitude. But since magnitude is generally used in our language as applied to amount of space, we may best describe our own idiom by laying down quantity as the general term, and stating magnitude to mean usually the quan tity of space. The term however must be considered, in a mathe matical point of view, as originating with Euclid (whose word is ;areas), and it is used by him, not particularly as applied to space, but also to everything which admits of .the introduction of the notion of greater or less. In this sense, then, we have many magnitudes (all moral qualities, for instance) which are not the object of mathematical reasoning. So necessary is the notion of magnitude to our conception even of things which we cannot measure, that we borrow idioms from subjects within the province of mathematics. Thus we speak of force of mind, and of it being greater in one individual than in another.
According to the definition of magnitude,—namely, " that of which greater or less can be predicated, when two of the same kind are com pared together," it follows that we include both mental as well as material objects of conception. But the mathematics interpose the
postulate that no such object can be made matter of exact reasoning, unless in cases which admit of the comparison being performed accord ing to some method the results of which shall be self-evident, and inseparable from our notion of the thing measured. Let A and is be two magnitudes of the same kind ; they are then, and then only, the objects of mathematical comparison, when other magnitudes equal to A ands can be found, and added together as often as may be desired ; and when, moreover, any collection of A's can be compared with a col lection of B'S, so as to ascertain which is greater or less than the other. Angles furnish an instance of magnitude the conception of which is exceedingly vague in the mind of most beginners, but which takes precision and certainty in the course of mathematical study. Magni tudes, thus capable of comparison, are the objects of the doctrine of