26 SCIENCE ABSOLUTE OF SPACE. 



- T =*, and 

 nat. log I 



1=0=2.7182818..., 

 which noted quantity shines forth here also. 



If obviously henceforth i denote that sect of 

 which the 1=0, we shall have 



ri tan z. 

 But ( 21) Gy=2-r/ therefore 



=2* tan z=i T-Y-' = * 



(by 24). 



nat. log Y 



31. For the trigonometric solution of all 

 right-angled rectilineal triangles (whence the 

 resolution of all triangles is easy , in S, three LI 

 equations suffice : indeed (a, b denoting the 

 sides, c the hypothenuse, and , ,3 the angles 

 opposite the sides) an equation expressing the 

 relation 



1st, between a, c, a; 



2d, between a, , ; 



3d, between a, b, c; 

 of course from these equations 

 emerge three others by elim- 

 ination. FIG. 23. 



From 25 and 30 



1 : sin a=(C-C~ l ) : (A-A- ] ) = 



f_^r j (equation for c, a and ). 



