32 SCIENCE ABSOLUTE OF SPACE. 



IV. For the circle (as in III) 



, whence (by 29), integrating, 



V. For the area CABDC= (inclosed by an 

 L form line AB=r, the II! to this, 

 =y, and the sects AC=BD=#) 





=y; and ( 24) y=re*&amp;gt; and so 



(integrating) u- 



If x increases to infinity, then, in 



S, 0T^o, and so u=ri. By the size 

 of MABN, in future this limit is understood. 

 In like manner is found, if p is a figure on 

 F, the spare included by/ and the aggregate 

 of axes drawn from the boundaries of P is 

 equal to Y 



VI. If the angle at the cen 

 ter of a segment z of a sphere 

 is IK, and a great circle is /&amp;gt;, 

 and x the arc FC (of the angle 



*); (25)^ 



1 :sin =/:OBC, 



and hence OBC=/&amp;gt; sin u. 

 j** 

 Meanwhile jr= 



