188 PHYSICAL SCIENCE IX THE MIDDLE AGES. 



We may, therefore, consider the prevalence of Collections of the 

 kind just referred to, as indicating a deficiency of philosophical talent 

 in the ages now under review. As evidence of the same character, 

 we may add the long train of publishers of Abstracts, Epitomes, Bibli- 

 ographical Notices, and similar writers. All such writers are worth- 

 less for all purposes of science, and their labors may be considered as 

 dead works ; they have in them no principle of philosophical vitality ; 

 they draw their origin and nutriment from the death of true physical 

 knowledge ; -and resemble the swarms of insects that are born from 

 the perishing carcass of some noble animal. 



2. Indistinctness of Ideas in Mechanics. But the indistinctness of 

 thought which is so fatal a feature in the intellect of the stationary 

 period, may be traced more directly in the works, even of the best 

 authors, of those times. We find that they did' not retain steadily the 

 ideas on which the scientific success of the previous period had de- 

 pended. For instance, it is a remarkable circumstance in the history 

 of the science of Mechanics, that it did not make any advance from 

 the time of Archimedes to that of Stevinus and Galileo. Archimedes 

 had established the doctrine of the lever ; several persons tried, in the 

 intermediate time, to prove the property of the inclined plane, and 

 none of them succeeded. But let us look to the attempts ; for exam- 

 ple, that of Pappus, in the eighth Book of his Mathematical Collec- 

 tions, and we may see the reason of the failure. His Problem shows, 

 in the very terms in which it is propounded, the want of a clear ap- 

 prehension of the subject. " Having given the power which will draw 

 a given weight along the horizontal plane, to find the additional power 

 which will draw the same weight along a given inclined plane." This 

 is proposed without previously defining how Powers, producing such 

 effects, are to be measured ; and as if the speed with which the body 

 were drawn, and the nature of the surface of the plane, were of no 

 consequence. The proper elementary Problem is, To find the force 

 which will stqyport a body on a smooth inclined plane; and no doubt 

 the solution of Pappus has more reference to this problem than to 

 his own. His reasoning is, however, totally at variance with mechan- 

 ical ideas on any view of the problem. He supposes the weight to be 

 formed into a sphere ; and this sphere being placed in contact with 

 the inclined plane, he assumes that the effect will be the same as if the 

 weight were supported on a horizontal lever, the fulcrum being the 

 point of contact of the sphere with the plane, and the power acting at 

 the circumference of the sphere. Such an assumption implies an entire 



