

OF MATHEMATICAL PROBLEMS. 



through the other three pass through the centre, the tangeut 

 plane at that point is parallel to the plane through the three 



1171. The equation of a conicoid is 



mnfiy + nlya. + Imafi + IraS + ... + . . . = ; 



prove that it can never be a ruled surface, and that it will be a 

 paraboloid if 



1175. The surface 



I fly + mya + na/3 + 

 will be a cylinder, if 



II' (m + n 1) + mm' 

 and 



+ n'y& = 



nri(l + m n) = 2lmn, 



II' (m r + ri I) + mm' (n +1 m') + nri (I + m' n) 2lm'n. 



1176. If I, m, n, r be respectively the rectangles of segments 

 of chords drawn from four points A, J5, C, D (not in one plane) to 

 meet a certain sphere, and p be the radius of the sphere ; then 

 will 



0, i, 



1, 0, 



1, SA', 



1 fl At 



J ' 1 1 



1, DA\ 



1, l + p a , ra + p 8 , 



1, 1, 



AD 3 , l+p* 

 JSD*, m+p* 



0, CD*, 

 DC*, 0, 

 i + p 8 , r + p a , 



= 0. 



1177. The perpendiculars u, x, y, z let fall from the angular 

 points of a given finite tetrahedron on a plane are connected 

 by the equation 



pu* 



ry* 



2myu + 



+ 2l'uz + Im'xz + Zriyz = ; 



