DISCOVERY OF THE LAWS OF MOTION. 43 



are primarily established. It rather serves verbally 

 to conjoin Laws previously known, than to exhibit 

 a connexion in them: it is rather a help for the 

 memory than a proof for the reason. 



The Principle of Virtual Velocities is so far 

 from implying any clear possession of mechanical 

 ideas, that any one who knows the property of the 

 Lever, whether he is capable of seeing the reason 

 for it or not, can see that the greater weight moves 

 slower in the exact proportion of its greater magni- 

 tude. Accordingly, Aristotle, whose entire want 

 of sound mechanical views we have shown, has yet 

 noticed this truth. When Galileo treats of it, 

 instead of offering any reasons which could inde- 

 pendently establish this principle, he gives his 

 readers a number of analogies and illustrations, 

 many of them very loose ones. Thus the raising 

 a great weight by a small force, he illustrates by 

 supposing the weight broken into many small parts, 

 and conceiving these parts raised one by one. By 

 other persons, the analogy, already intimated, of 

 gain and loss is referred to as an argument for the 

 principle in question. Such images may please the 

 fancy, but they cannot be accepted as mechanical 

 reasons. 



Since Galileo neither first enunciated this rule, 

 nor ever proved it as an independent principle of 

 mechanics, we cannot consider the discovery of it 

 as one of his mechanical achievements. Still less 

 can we compare his reference to this principle with 



