Proposition 30
 

The surface of a figure circumscribed as before about a shpere is greater than four times the great circle of the sphere.

 

From Proposition 21 we have the following :

(BB'+CC'+...)/AA' = A'B/ BA then we have

AB(BB' +CC' + .....) = AA'. A'B

From Proposition 29 we have the following :
(Radius of R) = Sqrt(AA'.A'B) > A'B

we know A'B = 20 P where P is the point in which AB touches the circle ama'm'.
so (radius R) > (diameter of circle ama'm')

finally we get that the surface of the circumscribed solid is greater than 4 times the great circle of the given sphere .