28 ORIGIN AND SIGNIFICANCE OF 



sole form of its scientific method is deduction. Con- 

 clusion is deduced from conclusion, and yet no one 

 of common sense doubts but that these geometrical 

 principles must find their practical application in the 

 real world about us. Land surveying, as well as ar- 

 chitecture, the construction of machinery no less than 

 mathematical physics, are continually calculating re- 

 lations of space of the most varied kind by geometrical 

 principles ; they expect that the success of their con- 

 structions and experiments shall agree with these 

 calculations ; and no case is known in which this ex- 

 pectation has been falsified, provided the calculations 

 were made correctly and with sufficient data. 



Indeed, the fact that geometry exists, and is cap- 

 able of all this, has always been used as a prominent 

 example in the discussion on that question, which 

 forms, as it were, the centre of all antitheses of philo- 

 sophical systems, that there can be a cognition of 

 principles destitute of any bases drawn from ex- 

 perience. In the answer to Kant's celebrated ques- 

 tion, 'How are synthetical principles a priori 

 possible?' geometrical axioms are certainly those 

 examples which appear to show most decisively that 

 synthetical principles are a priori possible at all. 

 The circumstance that such principles exist, and force 

 themselves on our conviction, is regarded as a proof 

 that space is an a priori mode of all external perception, 



