SCIENCE ABSOLUTE OP SPACE. 



23 



The path called CD will be denoted by CD 

 IIIAB. 



28. If BN II ^=AM, and C in ray AM, and 

 AC=x: we shall have ( 23) 



X = sin u : sin v. 

 For if CD and AE are JL BN, 

 iE and BF_L AM; we shall have (as 

 in 27) &quot; 



OBF : ODC = sin u : sin v. 

 ButevidentlyBF=AE: therefore 



OEA : OCD = sin u : sin v. 

 But in the F form surfaces of 

 AM and CM (cutting AMBN in AB and CG) 

 (by 21) 



OEA : ODC=AB : CG-X. 

 Therefore also 



X=sin u 

 29. If ZBAM=rt. 



M 



FIG. 20. 



, and 

 shall 



sin v. 

 and sect 

 BNIIAM, we&quot; 

 have in S 



Y=cotan y 2 u. 

 For, if sect AB= 

 sect AC, and CPU 

 AM (and so BN II ^ 

 CP), and ZPCD- 

 ZQCD; there is given (19) DSj_ray CD, so 

 that DS II CP, and so ( 1) DT II CQ. Moreover, 

 if BE 1 ray DS, then ( 7) DS II BN, and so ( 6) 



FIG. 21 



