178 THE GENESIS OF SCIENCE. 



When mechanics had reached the point to which Galileo 

 brought it when the simple laws of force had been dis 

 entangled from the friction and atmospheric resistance by 

 which all their earthly manifestations are disguised when 

 progressing knowledge of physics Lad given a due insight 

 into these disturbing causes when, by an effort of abstrac 

 tion, it was perceived that all motion would be uniform 

 and rectilinear unless interfered with by external forces 

 and when the various consequences of this perception had 

 been worked out ; then it became possible, by the union of 

 geometry and mechanics, to initiate physical astronomy. 

 Geometry and mechanics having diverged from a common 

 root in men s sensible experiences ; having, with occasional 

 inosculations, been separately developed, the one partly in 

 connexion with astronomy, the other solely by analyzing 

 terrestrial movements ; now join in the investigations of 

 Newton to create a true theory of the celestial motions. 

 And here, also, AVC have to notice the important fact that, 

 in the very process of being brought jointly to bear upon 

 astronomical problems, they are themselves raised to a 

 higher phase of development. For- it was in dealing with 

 the questions raised by celestial dynamics that the then 

 incipient infinitesimal calculus was unfolded by Newton and 

 his continental successors ; and it was from inquiries into 

 the mechanics of the solar system that the general theorems 

 of mechanics contained in the &quot; 1 rincipia,&quot; many of them 

 of purely terrestrial application took their rise. Thus, as 

 in the case of Hipparchus, the presentation of a new order 

 of concrete facts to be analyzed, led to the discovery of 

 new abstract facts; and these abstract facts having been 

 laid hold of, gave means of access to endless groups 

 of concrete facts before incapable of quantitative treat 

 ment. 



Meanwhile, physics had been carrying further that pro 

 gress without which, as just shown, rational mechanics 



