AS A MENTAL OPERATION 15 



Such positions are the properties of an ellipse (by 

 conic sections). 



. * . the orbit of Mars is an ellipse. 



The most important, however, of all these kinds of 

 physico-mathematical deductions is that from facts to 

 their causes, because man knows more facts than causes, 

 which are, however, the ideal of knowledge and yet are 

 frequently hidden from experience. Newton's Principia 

 is a conspicuous instance of this method. The full title, 

 Philosophiae Naturalis Principia Mathematica, implies 

 a combination of induction and deduction. It is also 

 a combination of analysis and synthesis : it proceeds 

 from facts to causes as well as from causes to facts. It 

 contains, as everybody knows, the discovery that the 

 planets gravitate to the sun with a force varying in- 

 versely to the square of their distance from it, and that 

 all particles of ponderable bodies so gravitate to one 

 another by the same law. But nobody ever experienced 

 a planet gravitating to the sun. How then did Newton 

 make the discovery ? Let us go to the Principia for 

 our answer. 



Newton begins with the three axioms or laws of 

 motion ; the law of inertia of rest and motion, the law 

 of proportion of force to effect, and the law of recipro- 

 city, or equal action and reaction. He gives inductive 

 gL evidence of these three laws. Though we know of no 

 body moving altogether unimpeded, yet there are in our 

 experience many instances of bodies moving straight 

 forward the more freely the less they are impeded, 

 which enable us to induce the law of inertia in the form 

 that every body perseveres in its state of rest or motion 

 so far as it is not affected by an impressed force. 

 Secondly, the proportion of force to effect is obvious to 

 experience. The third law had been already induced 



