36 SCIENCE ABSOLUTE OF SPACE. 



Moreover, we find (from 32) in i\ the area 

 and the volume in III each Pq; from IV 



(from VII) the globe of radius x 

 = $*x*, 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- [eo 

 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 2&amp;lt;&amp;gt;. 



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

 alogous to the plane geometry of - .) 



III. If it were agreed that l exists, nothing 

 more would be unknown in this respect; but 



