18 SCIENCE ABSOLUTE OF SPACK. 



their intersection (by ^ 7 and 11); and so also 

 rav AP and ray BD intersect. 



Prom this it is evident that Euclid s Axiom 

 A7 and all things which are claimed in geome 

 try and plane trigonometry hold good abso 

 lutely in F, L lines being substituted in place 

 of straights: therefore the trigonometric 

 functions are taken here in the same sense as 

 in I; and the circle of which the L form ra 

 dius = r in F, is = 2~r; and likewise area of 

 Or (in F) = *f* (by understanding J^Ol in F, 

 or the known 3.1415926. . .) 



22. If ray AB were the L of ray AM, and 

 C &amp;lt;&amp;gt;n ray AM; and the ZCAB (formed by the 

 straight ray AM and the L form 

 line ray AB), carried first along 

 the ray AB, then along the ray 

 BA, always forward to infinity: 

 the path *CD of C will be the 

 line L of CM. 



For let D In- any point in line 

 CD (called later L l, let DN be II CM, and B 

 tlu- point of L falling on the- straight DN. We 

 &amp;gt;hall have BN^ AM, and sect AC=sect BD, and 

 * . I)N=*CM, consequently D in L . But if D in 

 L and DN II CM, and B the point of L on the 

 aight DN; we shall have AM^BN and CM 

 whence manifestly sect BD=sect AC, 



