SOLID GEOMI/i 



fall from on the faces : prove that the distances of from the 

 several faces are proportional respectively to the faces. 



1087. The equation of the cone of revolution which can be 

 lra\vn touching a system of co-ordinate planes is 



(.)*+(*)+ (n.)*= ft 



ratios I : m : n being given by the equations 



m* + n* - 2mn cos a __ f -I- J* - 2nl cos ft F + m* - 2lm cos y 

 sin'a sin*/J sin'y 



where a, fi, y are the angles between the axes. (See question 

 301). 



1088. The inscribed sphere of a tetrahedron ABCD touches 

 UTS in ,(', ff t C', V\ prove that AA' 9 BE, CC', DD' will 



meet in a point, if 



a a b 8 c y 



cos^ cos- = cos 2 cos^ = cos^ oos^; 



o a, a; b, ft ; c, y are pairs of dihedral angles at opposite 

 edge* 



1 1 . Linear Transformations. General Equation of Hie Second 



B following -iinj.lr nn'tliMil ing the c<uul; 



H of revolution is worthy .f notice. 



When the expression r.r 4- 2b'zx + 2c'xy is 



transformed into AX* + BY*+CZ*, we obtain the eocfll- 

 C from the equivalence of the conditions that 



and ^-f-T'+Z 1 )- r f - 



152 



