68 ORIGIN AND SIGNIFICANCE OF 



for a priori principles, is a point on which I need 

 not insist. 



To sum up, the final outcome of the whole inquiry 

 may be thus expressed : 



(1.) The axioms of geometry, taken by themselves 

 out of all connection with mechanical propositions, re- 

 present no relations of real things. When thus iso- 

 lated, if we regard them with Kant as forms of 

 intuition transcendentally given, they constitute a 

 form into which any empirical content whatever will 

 fit, and which therefore does not in any way limit or 

 determine beforehand the nature of the content. This 

 is true, however, not only of Euclid's axioms, but also 

 of the axioms of spherical and pseudospherical geo- 

 metry. 



(2.) As soon as certain principles of mechanics are 

 conjoined with the axioms of geometry, we obtain a 

 system of propositions which has real import, and 

 which can be verified or overturned by empirical obser- 

 vations, just as it can be inferred from experience. If 

 such a system were to be taken as a transcendental 

 form of intuition and thought, there must be assumed 

 a pre-established harmony between form and reality. 



