Id 



JO. A frustum is cut from a right cone by a plane bisect- 



'.\c axis and pornllcl t<> the base; shew that it will rest 



side on a horizontal table if the height of the 



cone bear to the diameter of its base a greater ratio than 



particles of unequal weights be placed at the an- 

 gular point* of a triangular pyramid, and </, be their common 

 centre of gravity; t , 0,, common centres of ei 



fr i-vi-ry }* iblr arr.m-'-m.-iit !' tin- ]articl.-s; .*h.-\v that thr 



centre of gravity of equal particles placed at 0,, , ... is the 



22. If a cone have its base united concentrically to the 



base of a hemisphere of equal radim, fm.l ;ht of the 



cone that the solid may rest ou a horizontal table on any 



iu spherical surface, Result. r\'3. 



any polygon circumscribe a circle, the centre of 

 grav: area of the polygon, the centre of gravity of 



the perimeter 'lygon, and of the circle, are 



in the same straight lino ; also the distance of the first point 

 third is two-thirds of the distance of the second 

 point from the third. 



yhedron circumscribe a F; KJ centre 



volume of the polyhedron, the centre of 



face of the polyhedron, and the centre of 



, are in the same straight line; also the distance 



it trm tli.- third is three-fourths of the distance 

 of the second point from the t! 



; om a right cone the diameter of whose base is equal 



altitude is cut a right cylinder the diameter of whose 



base is equal to its altitude, their axes being in the same 



Straight line and the base of the cylinder lying in the base of 



the cone; from the remaining cone a similar cylinder is cut, 



telv; shew that the distance of the centre of 



.dcrs from the base of the cone is ^ of 



< ight of the cone, and that the distance of the centre of 



remaining portion from the base of the cone 



is J J of the altitude of the 



