We believe the preceding to be as legitimate a use as can be made of the sufficient-reason principle ; but before statics can be established on axioms, there is another of them required, which we have never been able to satisfy ourselves comes " from within." It must be assumed that the pressure on the pivot is equal to the sum of the pressures on the ends, whatever the length of the arms may be : this we believe we learn from existing matter in quite a different sense from that in which we speak when we say that we learn the conception of pressure or of a straight line from our communication with the exter nal world by our senses : to us it more resembles the assertion that the sea is salt, or that a horse has four legs. It certainly does not arise from the sufficient-reason principle ; for there is a reason why difference of pressures on the pivots may arise in levers which only differ in the arms, namely, that very difference of the arms. in fact, there is a presumption against the truth of the proposition d priori, derived from a principle etc frequent and usual truth of which may as well be called knowledge " from within," as the conception of pressure or of a straight line : this principle " differences generally make differences, buenet necessarily." The beginner in geometry has this in his mind when ho feels that he has learnt something in finding out that the sum of the angles of a triangle is always the same, whatever the triangle may be : he would have expected it to be otherwise.
Triangles of different sides have generally different areas, different per pendiculars], different inscribed and eircumscribedNeircles, and different angle, : why not different sums of angles / In truth it is a constant and Latent assumption throughout the exact sciences that "differences are to be supposed to make differences, except where the contrary is proved." And the assumption that the pressure on the pivot of a lever is independent of the arms, is either in defiance of this general principle, or a result of experience.
Thinking, then, that the sciences of pure mechanics can be founded upon few and incontrovertible postulates, in such a manner as to entitle them to the name of pure sciences, or some other which shall mark the real distinction between them and the other sciences of matter, we cannot yet be of opinion that their postulates are all derived from their own evidence, or obtainable from the sufficient-reason principle. There are, however, many points connected with this part of them which are difficult of exposition for want of acknowledged terms.