5&amp;lt;&amp;gt; SCIENCE ABSOLUTE &amp;lt;&amp;gt;K SPACE, 



If we put [ , and y, ;- are arcs situated at 

 llu- distances r, / from a, we shall have 



^ = ,jy=Y, -,=^=1, whence Y=ll 

 r r 



He demonstrates afterward i^-2 M that, if u 

 is tin- an&amp;lt;de which a straight makes with the 



ju-riK-ndicular r to its parallel, we have 

 Y=cot A//. 



Therefore, if \ve put Z- -TJ-U, we have 



tan z+ tan \u 



Y^tan (s+ . ,//) = 



1-tan ^ tan i// 



\vlu-nrc we ,uvt, having re.^ard to the value of 

 tan \//=Y~\ 



tan jfe*| (Y-Y- l )=J^-J ? )(30), 



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



A* 



circle-limit 2/ , we prove (.&amp;gt;()) that 



L a n -^ 



constant. 



Representing this constant by /, and making 



y tend toward xer&amp;lt;&amp;gt;. we have 

 ry r 



1, whence 

 2y 



2y 



T ! _1 



2r 2 / tan ^=M - f 



n 



