258 PHYSICAL SCIENCE IN THE MIDDLE AGES 



The proper elementary Problem is, To find the 

 force which will support 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 

 mechanical 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 absence of those 

 distinct ideas of force and mechanical pressure, on 

 which our perception of the identity or difference of 

 different modes of action must depend; of those 

 ideas by the help of which Archimedes had been able 

 to demonstrate the properties of the lever, and Ste- 

 vinus afterwards discovered the true solution of the 

 problem of the inclined plane. The motive to Pap- 

 pus's assumption was probably no more than this ; 

 he perceived that the additional power, which he 

 thus obtained, vanished when the plane became 

 horizontal, and increased as the inclination became 

 greater. Thus his views were vague; he had no 

 clear conception of mechanical action, and he tried 

 a geometrical conjecture. This is not the way 

 to real knowledge. 



Pappus (who lived about A.D. 400) was one 



