INDISTINCTNESS OF IDEAS. 189 



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 Archi- 

 medes had been able to demonstrate the properties of the lever, and 

 Stevinus afterwards discovered the true solution of the problem of the 

 inclined plane. The motive to Pappus'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 in- 

 creased as the inclination became greater. Thus his views were vague; 

 he had no clear conception of mechanical action, and he tried a geo- 

 metrical conjecture. This is not the way to real knowledge. 



Pappus (who lived about a. d. 400) was one of the best mathemati- 

 cians of the Alexandrian school ; and, on subjects where his ideas were 

 so indistinct, it is not likely that any much clearer were to be found in 

 the minds of his contemporaries. Accordingly, on all subjects of spec- 

 ulative mechanics, there appears to have been an entire confusion and 

 obscurity of thought till modern times. Men's minds were busy in 

 endeavoring to systematize the distinctions and subtleties of the Aris- 

 totelian school, concerning Motion and Power ; and, being thus em- 

 ployed among doctrines in which there was involved no definite mean- 

 ing capable of real exemplification, they, of course, could not acquire 

 sound physical knowledge. We have already seen that the physical 

 opinions of Aristotle, even as they came from him, had no proper 

 scientific precision. His followers, in their endeavors to perfect and 

 develop his statements, never attempted to introduce clearer ideas than 

 those of their master ; and as they never referred, in any steady man- 

 ner, to facts, the vagueness of their notions was not corrected by any 

 collision with observation. The physical doctrines which they extract- 

 ed from Aristotle were, in the course of time, built up into a regular 

 system; and though these doctrines could not be followed into a 

 practical application without introducing distinctions and changes, 

 such as deprived the terms of all steady signification, the dogmas con- 

 tinued to be repeated, till the world was persuaded that they were self- 

 evident ; and when, at a later period, experimental philosophers, such 

 as Galileo and Boyle, ventured to contradict these current maxims, 

 their new principles sounded in men's ears as strange as they now 

 sound familiar. Thus Boyle promulgated his opinions on the mechan- 

 ics of fluids, as " Hydrostatical Paradoxes, proved and illustrated by 

 experiments." And the opinions which he there opposes, are those 

 which the Aristotelian philosophers habitually propounded as certain 



