PRELUDE TO THE EPOCH OF GALILEO. 315 



they must move through equal spaces on the planes ; but on the plane 

 which is more oblique (that is, more nearly horizontal), the vertical 

 descent will be smaller in the same proportion in which the plane is 

 longer. Hence, by the Aristotelian principle, the weight of the body 

 on the longer plane is less ; and, to produce an equality of effect, the 

 body must be greater in the same proportion. "We may observe that 

 the Aristotelian principle is not only false, but is here misapplied ; for 

 its genuine meaning is, that when bodies fall freely by gravity, they 

 move quicker in proportion as they are heavier ; but the rule is here 

 applied to the motions which bodies would have, if they were moved 

 by a force extraneous to their gravity. The proposition was supposed 

 by the Aristotelians to be true of actual velocities ; it is applied by 

 Jordanus to virtual velocities, without his being aware what he was 

 doing. This confusion being made, the result is got at by taking for 

 granted that bodies thus proved to be equally heavy, have equal pow- 

 ers of descent on the inclined planes ; whereas, in the previous part of 

 the reasoning, the weight was supposed to be proportional to the de- 

 scent in the vertical direction. It is obvious, in all this, that though 

 the author had adopted the false Aristotelian principle, he had 

 not settled in his own mind whether the motions of which it spoke 

 were actual or virtual motions : — motions in the direction of the in- 

 clined plane, or of the intercepted parts of the vertical, corresponding 

 to these ; nor whether the " descending force" of a body was something 

 different from its weight. We cannot doubt that, if he had been re- 

 quired to point out, with any exactness, the cases to which his reason- 

 ing applied, he would have been unable to do so ; not possessing any of 

 those clear fundamental Ideas of Pressure and Force, on which alone any 

 real knowledge on such subjects must depend. The whole of Jordanus's 

 reasoning is an example of the confusion of thought of his period, and 

 of nothing more. It no more supplied the want of some man of ge- 

 nius, who should give the subject a real scientific foundation, than 

 Aristotle's knowledge of the proportion of the weights on the lever su- 

 perseded the necessity of Archimedes' proof of it. 



We are not, therefore, to wonder that, though this pretended theo- 

 rem was copied by other writers, as by Tartalea, in his Quesiti et In- 

 ventioni Diversi, published in 1554, no progress was made in the real 

 solution of any one mechanical problem by means of it. Guido Ubaldi, 

 who, in 1517, writes in such a manner as to show that he had taken a 

 good hold of his subject for his time, refers to Pappus's solution of the 

 problem of the Inclined Plane, but makes no mention of that of Jor- 



