H 176-179] Elliptic Motions the Prindpia 223 



to the Royal Society, a tract called Propositioned de Motu, 

 the 1 1 propositions of which contained the results already 

 mentioned and some others relating to the motion of 

 bodies under attraction to a centre. Although the pro- 

 positions were given in an abstract form, it was pointed out 

 that certain of them applied to the case of the planets. 

 Further pressure from Halley persuaded Newton to give 

 his results a more permanent form by embodying them in 

 a larger book. As might have been expected, the subject 

 grew under his hands, and the great treatise which resulted 

 contained an immense quantity of material not contained 

 in the De Motu. By the middle of 1686 the rough draft 

 was finished, and some of it was ready for press. Halley 

 not only undertook to pay the expenses, but superintended 

 the printing and helped Newton to collect the astronomical 

 data which were necessary. After some delay in the press, 

 the book finally appeared early in July 1687, under the 

 title Philosophic^ Naturalis Prindpia Mathematica. 



178. The Prindpia, as it is commonly called, consists of 

 three books in addition to introductory matter: the first 

 book de ,1s generally with problems of the motion of bodies, 

 solved for ihe most part in an abstract form without special 

 reference to astronomy ; the second book deals with the 

 motion of bodies through media which resist their motion, 

 such as ordinary fluids, and is of comparatively small 

 astronomical importance, except that in it some glaring 

 inconsistencies in the Cartesian theory of vortices are 

 pointed out ; the third book applies to the circumstances 

 of the actual solar system the results already obtained, and 

 is in fact an explanation of the motions of the celestial 

 bodies on Newton's mechanical principles. 



179. The introductory portion, consisting of " Definitions " 

 and "Axioms, or Laws of Motion," forms a very notable 

 contribution to dynamics, being in fact the first coherent 

 statement of the fundamental laws according to which the 

 motions of bodies are produced or changed. Newton 

 himself does not appear to have regarded this part of 

 his book as of very great importance, and the chief 

 results embodied in it, being overshadowed as it were by 

 the more striking discoveries in other parts of the book, 

 attracted comparatively little attention. Much of it must be 



