Let the ratio of the length of segment AB to the length of segment BC be k; 
that is, k = AB/BC. If the length of BC is m, the length of AB must therefore he km. 
Furthermore, let the length of CD be s. Hence, BD = BC + CD = m + s, AD = AB + BC + CD = 
km + m + s, AC = AB + BC = km + m, and the anharmonic ratio is: 
  
BD BC ; m+s m 
A * AB E uis owls (17) 
Dividing the numerator and denominator of the first factor by s, and the numerator and 
denominator of the inverted second factor by m, yields: 
  
  
  
m 
= + 
|l Et a ao 
AM 3 
S 
As point D is moved along line ABCD to point N at infinity, s approaches infinity, and = 
and seus approach zero. Hence, for point N at infinity: 
A-k-t1 (19) 
The image of point N is, of course, the vanishing point, n, of the line. It therefore 
follows from equations (16) and (19) that: 
k+1 = =) be (20) 
an ac 
Figure 5 shows the image, abc, of line ABC ín the photograph coordinate system, 
Xy. Given the ratio k = AB/BC, it is required to locate the vanishing point, n, on the 
line image abc produced. 
The projection, a'b'c'n', of line abcn onto the x-axis has the same anharmonic 
ratio, A = k + 1, as abcn. Hence, from equation (20), 
ts! Y! M x. 7 
pra see 55 = n 2 C X5 (21) 
a'n a'c x - x -x 
n a C a 
y i 
ius ee me am em pcr mem wer mmi e aem n 
Yn-—-——-——— = 
Pd 
- 
  
  
la 1b’ Ic’ jn' x 
Xa Xp Xc Xn 
Figure 5 
  
ZB