40 HISTORY OF MECHANICS. 



Sect. 4. Generalization of the Laws of Equili- 

 brium. Principle of Virtual Velocities. 



IT was known, even as early as Aristotle, that the 

 two weights which balance each other on the lever, 

 if they move at all, move with velocities which are 

 in the inverse proportion of the weights. The pecu- 

 liar resources of the Greek language, which could 

 state this relation of inverse proportionality in a 

 single word (avrnreirovQev], fixed it in men's minds, 

 and prompted them to generalize from this property. 

 Such attempts were at first made with indistinct 

 ideas, and on conjecture only ; and had, therefore, 

 no scientific value. This is the judgment which we 

 must pass on the book of Jordanus Nemorarius, 

 which we have already mentioned. Its reasonings 

 are professedly on Aristotelian principles, and 

 exhibit the common Aristotelian absence of all 

 distinct mechanical ideas. But in Varro, whose 

 Tractatus de Motu appeared in 1584, we find the 

 principle, in a general form, not satisfactorily proved 

 indeed, but much more distinctly conceived. This 

 is his first theorem : " Duarum virium connexarum 

 quarum (si moveantur) motus erunt ipsis dvmre- 

 TrovOws proportionales, neutra alteram movebit, sed 

 equilibrium facient." The proof offered of this is, 

 that the resistance to a force is as the motion pro- 

 duced ; and, as we have seen, the theorem is rightly 

 applied in the example of the wedge. From this 

 time it appears to have been usual to prove the 



