[ 5^7 ] 



fed. of remainder : great circle : : D S* — K S^ ( G N« ) = 

 C N2 — C Si : A C2 ; or fea of remaind. : C N» — C S^ :: great 

 circle : AC* : -circumf. : diameter. 



Now if on the fquare pn C N as a bafe, a cube and pyra- 

 mid of the fame height be conftruded, the difference of the 

 areas of any fedions of the cube and pyramid at the diftance 

 CS from the vertex = C N^ — C S^ . And the folids of equal- 

 heights, whofe fedions at the fame height are always in the 

 fame given ratio, are in the ratio of their bafcs, therefore the 

 remainder of hemifphere : diff. between the cube and pyramid 

 :: circumference : diameter. But the diiference between the 

 cube and pyramid = f of the cube. Hence the remainder of 

 the hemifphere : 4 cube on C N : : circumference : diameter, 

 or remainder of fphere : j- cube on C N = f cube on G^ : :. 

 circumference : diameter. 0,ED. 



Problem. ABC being a quadrant of a great circle of a 

 fphere, the centre of which is C, it is required to find the nature pj^ 2. 

 of the curve E »z « C, fo that the furface of the fphere infill- 

 ing perpendicularly over the area E A « »? C may be algebraically 

 affignable ; and alfo that the folidity infifting perpendicularly on 

 the fame area may be algebraically affignable. 



SOLDTION. 



