36 SCIENCE ABSOLUTE OF SPACE. 



Moreover, we find (from 32) in r, the area 

 and the volume in III each =pq; from IV 



area O#=-^; 

 (from VII) the globe of radius x 



=%xx s , etc. 



The theorems enunciated at the end of VI 

 are manifestly true unconditionally. 



33. It still remains to set forth (as prom- 

 ised in 32) what this theory means. 



I. Whether I or some one S is reality, re- 

 mains undecided. 



II. All things deduced from the hypothesis 

 of the falsity of Axiom XI (always to be un- 

 derstood in the sense of 32) are absolutely 

 true, and so in this sense, depend upon no 

 hypothesis. 



There is therefore a plane trigonometry a 

 priori, in which the system alone really re- 

 mains unknown; and so where remain un- 

 known solely the absolute magnitudes in the 

 expressions, but where a single known case 

 would manifestly fix the whole system. But 

 spherical trigonometry is established abso- 

 lutely in 26. 



(And we have, on F, a geometry^wholly an-" 

 alogous to the plane geometry of J.) 



III. If it were agreed that - exists, nctthing 

 more would be unknown in this respect; but 



