NEWTON S PRINOIPIA. 15 



given, to find the curve in which it makes the body move. 

 The connexion between the inquiries which form the 

 main subject of the two first books of the Principia and 

 Physical Astronomy, the subject of the third, is thus 

 explicitly stated ; but a plain indication is also here 

 afforded of the great discovery in which the whole inves 

 tigation is to end. 



The doctrines of dynamics, known previously to his 

 discoveries, are then given in the form of corollaries to 

 the three general Laws of Motion. The first law is 

 that of the vis inertia, already explained ; and it is 

 to be observed here that a steady and clear conception 

 of the tendency of all moving bodies to proceed in a 

 straight line unless deflected from it, is, perhaps, more 

 than anything else, that which distinguished the Newtonian 

 from the immediately preceding doctrines, mixing up as 

 these did more influences than one proceeding from the 

 centre with a view to explain the composite motion of 

 the planets. 



The second law is, that all changes in the motion of any 

 body, or all changes from rest to motion, are in proportion 

 to the moving force impressed, and are in the straight 

 line of that force s direction. 



The third law is, that reaction is always equal and 

 opposite to action ; or that the mutual actions of any 

 two bodies are always equal to one another, and in opposite 

 directions. 



From these laws the six corollaries which are added 

 deduce the fundamental principles of dynamics ; and 

 there is a scholium to the whole, which states the applica 

 tion of those principles to the descent of heavy bodies, 

 and the parabolic motion of projectiles. Of all the prin 

 ciples, the most important is that of the Composition and 

 Resolution of forces. As by the first law a body always 



