SCIENCE ABSOLUTE OF SPACE. 27 



II. From 27 follows (if ,*M II rN) 



cos :sin t 3=l : sin u; but from 29 

 1 :sin ^=^(A+A- 1 ); 



therefore cos sin /5^^(A4-A- 1 ) = ^ Lf+^r] 

 (equation for , /? and a). 



III. If aa JLr^r* and #? and n- ll ( 27), 

 and ,5 ay J_ ; manifestly (as in 27) 



sin 



, or 

 . l f^ ~ b l 



2 ^i+^i J (^1+07 J 



(equation for &amp;lt;2^ ^ and c). 

 If r r)=rt. ^, and po\_&amp;lt;^ , 



Qc : 0a=l : sin , and 

 O&amp;lt;^ : Q(d=t&amp;lt;r:=l : cos , 



and so (denoting by Qx\ for any x, the product 

 manifestly 



But (by 27 and II) 



), consequently 



- a l 2 f b - b l 3 , f a ~ a 



another equation for a } b and c (the second 



