52 SCIENCE ABSOLUTE OP SPACE. 



-sin (cv ITl): si* 1 (#\CT)- And hence 

 1 : sin =sin (vC~l) : sin (avCTl). 



In II becomes 



cos a : sin /5=cos (#VITl) : 1 ; 

 in III becomes 



cos (cv ^i)=cos (a\ D.COS (fa ^i). 

 These, as all the formulas of plane trigonom 

 etry deducible from them, coincide completely 

 with the formulas of spherical trigonometry; 

 except that if, ex. gr., also the sides and the 

 angles opposite them of a right-angled spheri 

 cal triangle and the hypothenuse bear the same 

 names, the sides of the rectilineal triangle are 

 to be divided by v 1 to obtain the formulas for 

 the spherical triangle. 



Obviously we get (clearly as Tom., II., p. 252), 

 from I, 1 : sin =:sin c : sin a; 



from II, 1 : cos a = sin^ : cos &amp;gt;/.; 



from III, cos =cos a cos b. 



Though it be allowable to pass over other 

 things; yet I have learned that the reader 

 may be offended and impeded by the deduc 

 tion omitted, (Tom. I., App., p. 19) [in 32 at 

 end] : it will not be irrelevant to show how, ex. 

 gr., from 



follows 







e l +e 



