GENERALIZATION OF PRINCIPLES. 355 



force, and, on the 10th of December, 4 announced to the Royal Society 

 that he had seen Mr. Newton's book, Be Motu Corporum. The feel- 

 ino- that mathematicians were on the brink of discoveries such as are 

 contained in this work was so strong, that Dr. Halley was requested 

 to remind Mr. Newton of his promise of entering them in the Register 

 of the Society, " for securing the invention to himself till such time as 

 he can be at leisure to publish it." The manuscript, with the title 

 Philosophicc Naturalis Principia Mathematica, was presented to the 

 society (to which it was dedicated) on the 28th of April, 1686. Dr. 

 Vincent, who presented it, spoke of the novelty and dignity of the 

 subject ; and the president (Sir J. Hoskins) added, with great truth, 

 " that the method was so much the more to be prized as it was both 

 invented and perfected at the same time." 



The reader will recollect that we are here speaking of the Principia 

 as a Mechanical Treatise only ; we shall afterwards have to consider it 

 as containing the greatest discoveries of Physical Astronomy. As a 

 work on Dynamics, its merit is, that it exhibits a wonderful store of 

 refined and beautiful mathematical artifices, applied to solve all the 

 most general problems which the subject offered. The Principia can 

 hardly be said to contain any new inductive discovery respecting the 

 principles of mechanics ; for though Newton's Axioms or Laws of Mo- 

 tion, which stand at the beginning of the book, are a much clearer and 

 more general statement of the grounds of Mechanics than had yet ap- 

 peared, they do not involve any doctrines which had not been pre- 

 viously stated or taken for granted by other mathematicians. 



The work, however, besides its unrivalled mathematical skill, em- 

 ployed in tracing out, deductively, the consequences of the laws of 

 motion, and its great cosmical discoveries, which we shall hereafter 

 treat of, had great philosophical value in the history of Dynamics, as 

 exhibiting a clear conception of the new character and functions of 

 that science. In his Preface, Newton says, " Rational Mechanics must 

 be the science of the Motions which result from any Forces, and of the 

 Forces which are required for any Motions, accurately propounded and 

 demonstrated. For many things induce me to suspect, that all natural 

 phenomena may depend upon some Forces by which the particles of 

 bodies are either drawn towards each other, and cohere, or repel and 

 recede from each other : and these Forces being hitherto unknown, 

 philosophers have pursued their researches in vain. And I hope 



* Id. p. 184. 



