depend one on the other. An alteration in one will bring about an alteration in the other, because of this dependence. Let us call one of the variables , and the other that depends on it .
Suppose we make to vary, that is to say, we either alter it or imagine it to be altered, by adding to it a bit which we call . We are thus causing to become . Then, because has been altered, will have altered also, and will have become . Here the bit may be in some cases positive, in others negative; and it won’t (except by a miracle) be the same size as .
Take two examples.
(1) Let and be respectively the base and the height of a right-angled triangle (Fig. 4), of which
Fig. 4.
the slope of the other side is fixed at . If we suppose this triangle to expand and yet keep its angles the same as at first, then, when the base grows so as to become , the height becomes . Here, increasing results in an increase of . The little triangle, the height of which is , and the base