150 RELATIONS BETWEEN SEVERAL [BOOK I. 



From the equation, which in article 98 follows the second equation, we have, 

 moreover, 



whence readily follows, 



the upper or lower sign taking effect, as 2/ is less or more than 180. 



109. 



If, in the hyperbola, we take the symbols a, C, c, with the same meaning as in 

 article 99, we have, from equations VIII., IX., article 21, 



/ cos v r cos v = (c -- \\G -~\ a 



v /(ee 1); 

 and consequently, 



Let us suppose that y is a quantity determined by the equation 



&amp;gt;+}=&amp;lt;(&amp;lt;&amp;gt;+$ 



since this is evidently satisfied by two values, the reciprocals of each other, we 

 may adopt the one which is greater than 1. In this manner 



Moreover, 



r 

 and thus, 



r 4- ^ + ? = v^r 



