72 
of their segments between their common intersection and the sur- 
face will be in a constant ratio, (Geometry, 606.) 
(6) If a general equation of the n" degree between three vari- 
ables be arranged according to the dimensions of one of them, z, 
Cet ay Seta Ao Ad 2 tee ete esa, =O, 
it is evident that a, will be a formula of the first degree between 
and y, Az one of the second degree between these variables, and in 
general a, a formula of the x" degree between them. 
For each system of values of # and y this equation gives n values 
of z, which when real determine as many points of the surface. 
gk 
The sum of these values i If a surface be assumed, repre- 
sented by the equation 
it will have the property of intersecting the ordinate 2, so that the 
sum of the intercepts between it and the surface on the one side 
shall be equal to the sum of the intercepts on the other side. Since 
4, has the form ay + Bx + D, the equation of this surface is 
Ay + Be + ncz +p =0; 
it is therefore a plane. This plane therefore intersects a system of 
parallels to the axis of z, so that the sums of the intercepts between 
it and the surface on each side are equal. Such a plane may be 
called a diametral plane from its analogy to the diameter of a plane 
eurve. 
