to 



tions ; but almost every consequence and application of it 

 was either traced, or plainly sketched out; it was pursued 

 into all the details; a systematic account of its operation 

 was given, symmetrical, and in its main branches complete ; 

 so that, however nearly former inquirers had approached 

 the general law, the distance was prodigious between their 

 conjectures, how learned and happy soever, and the magni 

 ficent work which the genius of Newton had accomplished.* 

 It must be observed, too, that, beside this grand achieve 

 ment, the Principia performed three other most important 

 services to physical and mathematical science. First. It 

 laid a deep and solid foundation for subsequent discoveries 

 in the science of physical astronomy, both by the general 

 principles of dynamics which it unfolded, and by the ap 

 plication which it made of these to the heavenly bodies 

 and their motions. Secondly. It gave a complete system 

 of dynamics applicable to all subjects connected with 

 motion and force and statics a system throughout abound 

 ing in the most important original mathematical truths, 

 expounded and proved with singular beauty, though with ex 

 treme conciseness. Thirdly. It propounded and showed the 

 application of a new calculus, or method of mathematical 

 investigation, that method by the help of which those truths 

 had been discovered ; and by which others, before resting 

 upon an empirical foundation, were demonstrated. Thus 

 it is no exaggeration to say that, even if the great dis- 



* The subsequent discoveries of mathematicians by means of the improve 

 ments in the calculus, have added new illustrations, and traced further 

 consequences of the theory. But there is only one of their improvements 

 which can justly be said to have advanced the evidence of the fundamental 

 principle further than Sir I. Newton had carried it, by supplying any de 

 fect which he had left ; we allude to the reconcilement by Clairaut of the 

 moon s apogeal motion according to the theory with the observations. 

 This is fully explained in the sequel. It forms one of the most interesting 

 passages in the whole history of science. 



