CAUSE OF ITS FAILURE. 89 



tli at by a continuous progression, the last point becomes the first. So 

 that, as was before stated, it is not surprising that the circle should be 

 the principle of all wonderful properties." 



Aristotle afterwards proceeds to explain more specially how he ap 

 plies the properties of the circle in this case. " The reason," he says 

 in his fourth Problem, " why a force, acting at a greater distance 

 from the fulcrum, mot r es a weight more easily, is, that it describes a 

 greater circle." He had already asserted that when a body at the end 

 of a lever is put in motion, it may be considered as having two 

 motions ; one in the direction of the tangent, and one in the direction 

 of the radius ; the former motion is, he says, according to nature, th< 

 latter, contrary to nature. Now in the smaller circle, the motion, con- 

 trary to nature, is more considerable than it is in the larger circle. 

 " Therefore," he adds, " the mover or weight at the larger arm will be 

 transferred further by the same force than the weight moved, which is 

 at the extremity of the shorter arm." 



These loose and inappropriate notions of " natural" and " unnatu- 

 ral" motions, were unfit to lead to any scientific truths ; and, with the 

 habits of thought which dictated these speculations a perception of 

 the true grounds of mechanical properties was impossible. 



7. Thus, in this instance, the error of Aristotle was the neglect of 

 the Idea appropriate to the facts, namely, the Idea of Mechanical 

 Cause, which is Force ; and the substitution of vague or inapplicable 

 notions involving only relations of space or emotions of wonder. The 

 errors of those who failed similarly in other instances, were of the 

 same kind. To detail or classify these would lead us too far into the 

 philosophy of science ; since we should have to enumerate the Ideas 

 which are appropriate, and the various classes of Facts on which the 

 different sciences are founded, a task not to be now lightly under- 

 taken. But it will be perceived, without further explanation, that it 

 is necessary, in order to obtain from facts any general truth, that we 

 should apply to them that appropriate Idea, by which permanent and 

 definite relations are established among them. 



In such Ideas the ancients were very poor, and the stunted and de- 

 formed growth of their physical science was the result of this penury. 

 The Ideas of Space and Time, Number and Motion, they did in- 

 deed possess distinctly ; and so far as these went, their science was 

 tolerably healthy. They also caught a glimpse of the Idea of a Me- 

 dium by which the qualities of bodies, as colors and sounds, are per- 

 ceived. But the idea of Substance remained barren in their hands ; 



