56 SCIENCE ABSOLUTE OP SPACE. 



If we put ^=d, and r , r r are arcs situated at 

 the distances y, i from , we shall have 

 -=a y =Y, -,=^=1, whence Y=IT 



He demonstrates afterward ( 29) that, if u 

 is the angle which a straight makes with the 

 perpendicular y to its parallel, we have 

 Y=cot \u. 



Therefore, if we put z=-~u, we have 

 Y = tan 



1 tan z tan j 



whence we get, having regard to the value of 

 tan J=Y~ 1 , 



tan z^ (Y-Y^NiJl'-J '] (30). 

 If now jv is the semi-chord of the arc of 



/^ 



circle-limit 2^, we prove ( 30) that - 



tan z 



constant. 



Representing this constant by i, and making 

 y tend toward zero, we have 



=1, whence 



2r 



2y 



T ' _1 



2=2 * tan z=i - - i 



