SCIENCE ABSOLUTE OF SPACE. 29 



(since HBC manifestly is neither &amp;gt; nor &amp;lt;, and 

 so =rt.^), the tangent at B of BG will be de 

 termined by y. 



II. It can be demonstrated 



~ 



Hence is found the limit of -7-?, and thence, 



ax 



by integration, z (expressed in terms of x. 



And of any line given in the concrete, the 

 equation in S can be found; e. g., of L. For 

 if ray AM be the axis of L&amp;lt;; then any ray CB 

 from ray AM cuts L [since (by 19) any 

 straight from A except the straight AM will 

 cut L] ; but (if BN is axis) 



X=l:sin CBN (28), 

 and Y=cotan ^ CBN (29), whence 



Y=X+VX*-1. 



or 



[16] 



the equation sought. 

 Hence we get 

 dv 



and =l : sin CBN=X; and so 

 dx 



