SCIENCE ABSOLUTE OF SPACE. 29 



(since HBC manifestly is neither > nor <, and 

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

 termined by y. 



II. It can be demonstrated 



~ 



Hence is found the limit of -, 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; 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 y> CBN (29), whence 



or y 



the equation sought. 

 Hence we get 



ax 



and =1 : sin CBN-X; and so 

 ax 



dy (X 3 -!)^- 

 BH~ l 



