DISCOVERY OF THE LAWS OF MOTION. 37 



Motion of bodies acted upon by variable forces is, 

 of course, a simpler problem than their Curvilinear 

 Motion, to which we have now to proceed. But it 

 may be remarked that Newton, having established 

 the laws of Curvilinear Motion independently, has, 

 in a great part of his Seventh Section, deduced the 

 simpler case of the Rectilinear Motion from the 

 more complex problem, by reasonings of great in- 

 genuity and beauty. 



Sect. 3. Establishment of the Second Law of Motion. 

 Curvilinear Motions. 



A SLIGHT degree of distinctness in men's mecha- 

 nical notions enabled them to perceive, as we have 

 already explained, that a body which traces a 

 curved line must be urged by some force, by which 

 it is constantly made to deviate from that recti- 

 linear path, which it would pursue if acted upon by 

 no force. Thus, when a body is made to describe a 

 circle, as when a stone is whirled round in a sling, 

 we find that the string does exert such a force on 

 the stone ; for the string is stretched by the effort, 

 and if it be too slender, it may thus be broken. 

 This centrifugal force of bodies moving in circles 

 was noticed even by the ancients. The effect of 

 force to produce curvilinear motion also appears in 

 the paths described by projectiles. We have already 

 seen that though Tartalea did not perceive this cor- 

 rectly, Rivius, about the same time, did. 



