24 



SCIENCE ABSOLUTE OF SPACE. 



BNnES, and (since DT II CG) BQllET; con- 

 sequently (1) ZEBN=ZEBQ. Let BCF be 

 an 1,-line of BN, and FG, DH, CK, EL, L form 

 lines of FT, DT, CQ and ET; evidently (22) 

 HG=DF=DK-HC; therefore, 

 CG=2CH=2z>. 



Likewise it is evident BG=2BL=2^. 

 ButBC=BG-CG; wherefore y=z~v, and 

 so (24) Y=Z:V. 

 Finally ( 28) 



Z = l : sin y 2 u, 

 and V=l : sin (rt.^~X ^)> 

 consequently Y=cotan ^ u. 



30. However, it is easy to see (by 25) 

 that the solution of the problem of Plane 

 Trigonometry, in S, requires 

 the expression of the circle 

 in terms of the radius; but 

 this can by obtained by the 

 rectification of L. 



Let AB, CM, C'M' be _L 

 ray AC, and B anywhere in 

 ray AB; we shall have ( 25) 



sin u : sin v=Qp : Qy, 

 and sin u' : sin v 1 ' =Qp' : 



FIG. 22. 



and so 



sm v 



sin v 



