332 HISTORY OF MECHANICS, 



tve have already mentioned. Its reasonings are professedly on Aris- 

 totelian 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 satis- 

 factorily proved, indeed, but much more distinctly conceived. This is 

 his first theorem : " Duarum virium connexarum quarum (si moveantur) 

 motus erunt ipsis dvrnreTrovO&s proportionales, neutra alteram move- 

 bit, sed equilibrium facient." The proof offered of this is, that the 

 resistance to a force is as the motion produced ; 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 properties of 

 machines by means of this principle. This is done, for instance, in Les 

 Raisons des Forces Mouvantes, the production of Solomon de Cans, 

 engineer to the Elector Palatine, published at Antwerp in 1616; in 

 which the effect of Toothed- Wheels and of the Screw is determined in 

 this manner, but the Inclined Plane is not treated of. The same is 

 the case in Bishop Wilkins's Mathematical Magic, in 1648. 



When the true doctrine of the Inclined Plane had been established, 

 the laws of equilibrium for all the simple machines or Mechanical 

 Powers, as they had usually been enumerated in books on Mechanics, 

 were brought into view; for it was easy to see that the Wedge and the 

 Screw involved the same principle as the Inclined Plane, and the 

 Pulley could obviously be reduced to the Lever. It was, also, not 

 difficult for a person with clear mechanical ideas to perceive how any 

 other combination of bodies, on which pressure and traction arc 

 exerted, may be reduced to these simple machines, so as to disclose 

 the relation of the forces. Hence by the discovery of Stcvinus, all 

 problems of equilibrium were essentially solved. 



The conjectural generalization of the property of the lever, which 

 we have just mentioned, enabled mathematicians to express the solution 

 of all these problems by means of one proposition. This was done by 

 saying, that in raising a weight by any machine, we lose in Time what 

 we gain in Force ; the weight raised moves as much slower than the 

 power, as it is larger than the power. This was explained with great 

 clearness by Galileo, in the preface to his Treatise on Mechanical 

 Science, published in 1592. 



The motions, however, which we here suppose the parts of the 

 machine to have, are not motions which the forces produce ; for at 

 present we are dealing with the case in which the forces balance each 

 other, and therefore produce no motion. Bat we ascribe to the 



