PHILOSOPHICAL SOCIETY OP WASHINGTON. 



59 



Again, A sin ^ A =- y ; whence from (6) 



a 1 4- tan ^ A 



sin i A 



or — = 



T + 



7 sin^A cos A A 



-, and similarly 



/3 



+ 



7 sin ^ B cos \ B 

 Fig. 2. 



Now sin i B = sin (45° - ^ A) = cosiA--sm|A ^^^ 

 cosiB = cos(45--iA)=^^iiA±^i^M; 



whence 



1 



2 cos ^ A 



y\/2 cos-^A — sin^A cos-^A + sinA 2cos'^-^A — 1' 

 from which we find 



and similarly 





whence 



Since cos i B ::= cos j A +^sin j A ^ 



In this page, and the following, the symbol y (for radius) should read r. 



