32 SCIENCE ABSOLUTE OF SPACE. 



IV. For the circle (as in III) - area G 

 , whence (by 29), integrating, 



dx 



V. For the area CABDC=^ (inclosed by an 

 M N L, form line AB=r, the III to this, 

 CV=j>, and the sects AC=BD=^) 



=y; and ( 24) y re^, and so 



D * 



(integrating) ^=r/ M_^T 



If x increases to infinity, then, in 



FIG. 26. -2* 



S, ^i=^0, 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 space included by^> and the aggregate 

 of axes drawn from the boundaries of p is 

 equal to Y*pi. 



VI. If the angle at the cen- 

 ter of a segment z of a sphere 

 is 2u, and a great circle is^>, 

 and x the arc FC (of the angle 



); (25) 



l:sin ^=/:QBC, 

 and hence OBC=/> sin u. 



Meanwhile *=^, and dx^^- 



2^ 2* 



FIG. 27. 



