48 



and if p be the vertical ordinate of the focus by projection, the equa- 

 tion of the projecting plane is 



y„ — h — '?^ _ ?.'/ + p-?/3 } ,L"') 



X,, — 3« — z„J« Jj; 4" P-^* 



p being determined by the condition that the two planes (K'") (L'"), 

 shall be perpendicular to each other, which gives 



p Sx" 4" ^'/ 



In general, whatever arbitrary position we assign to the rectangu- 

 lar axes, if we represent by x + ap, y -f- (3p, z + yp, the coordi- 

 nates of the focus by projection, those of the given point being x, y, z, 

 and those of the near point O! + ia?, 7/ -\- di/, z + h, we shall find, 

 by a similar process, 



P 



}x" + 3y" + 3«" " Sjp' + ay + ^z' — (.Jar + /Sjy + yJz)'- ' 



i,v', iy', hz, having the same meanings as in the fifth number. And 

 since the equations (C) give, by differentiation and elimination, 



and therefore 



