— AB 0 C 0 D : AC 0 A 0 D : AA 0 B 0 D : AA 0 D 0 D : AB 0 D 0 D : AG 0 D 0 D : ABGD 
viz. multiplying the last-mentioned set of terms by A 0 B 0 C 0 D 0 -r- ABGD, in order to 
make the last term equal to unity, we see that the coefficients ^&c. are equal 
, A 0 B 0 G o n 
ABGD 
of the points A, D thereof. And similarly in the six expressions which enter into the 
A. _B G D 
formula of transformation, the coefficients are =—^qjjjy the six (ABCD) 0 — coordinates 
of the 
23’ 23 
o^o^o^o • n ^. () s - x — coordinates respectively of the line AD by means 
line AD in regard to points A, D thereof 
„ BD 
B, D 
„ CD 
C, D „ 
» BG „ 
B, G „ 
„ CA 
C, A „ 
„ AB 
A, B „ 
The foregoing theory of the transformation of coordinates seemed to me interesting 
for its own sake, and I have developed it in preference to the more simple theory 
which might easily be established of the case in which the coordinates are quantitatively 
defined as being equal to 
(z 0 cos /3 — y 0 cos y, x 0 cos y — z 0 cos a, y 0 cos /3 — x 0 cos a, cos a, cos /3, cos 7) 
respectively.