jn SCIKNVK ABSOLUTK OF SPACE. 



The same is easily extended to the case of 

 the incommensurability of x and y. 



But if q=v x, manifestly O^Y X. 

 It is also manifest that in l\ for any .r, we 

 have X = l, but in S is X&amp;gt;1, and for any ABu 

 and ABE tlu-rr is such a CDFl!! AB, that CDF 

 =AB, whence AMBN^AMEP, though the 

 first be any multiple of the second; which in 

 deed is singular, but evidently does not prove 

 the absurdity of S. 



^ 25. /// un\ rectilineal triangle, the cir 

 cles ic if /i radii equal to its sides are as the 

 .s///( .s (&amp;gt;/&quot;///( of&amp;gt;/&amp;gt;osite angles. 



For take ZABOrt.Z, 

 and AM J_BAC, and BN and 

 CP II AM; we shall have CAB 

 lAMBN, and so ( since CB_I_ 

 BA), CBlAMHN, conse- 

 qttently CPBNiAMBN. 



Suppose the F of ray CI&amp;gt; 

 FiG.17. cuts the straights BX. AM 



r.-pi-ctively in I) and E, and the bands CPBN, 

 CPAM, 1JXAM along the L form lines CD, 

 CE, DE. Then (20) ZCDE= the angle of 

 NDC, XDK. and so =rt.^; and by like reason- 

 in- ZCED=ZCAB. But (by 21) in the L line 

 A CDE (supposing always here the radius =1), 

 KC:DC = l:sin DEC = l:sin CAB. 



