74 
LBM LE =D ME 
if namely M'F'\\|\MF and the separation by means of the commas 
indicates the rational angle. In one formula we write 
Tiare Re 
(These angles must not be confounded with those of the tangents). 
Three rationals determine a rational triangle the sides of which 
are the rational distances of the points of intersection. These shall 
be represented as follows: 
2 3 
=P R= A=) ; (). elec. 
zy Y, 
By interchange of the letters the value is reversed. 
Thus holds: 
as) eS) 
P; ’ FP: == (2s ; gl oe ; 
likewise 
Pais: 
If the angles are indicated by w,, w, and w, and if equidistant 
rationals are drawn through the vertices, e.g. P,, Q|||P,;,P,, 
ZE Oe ZO,P,,P, =4,. 
As these are completed by w, to a rational stretched angle, we 
find that: 
A rational right angle is the root out of a rational stretched angle. 
If A, and A, are the director exponents of two rationals, then holds 
for the rational angle formed by these: 
trum (e2:e) | e.(e2,e1); 
so that the condition for a rational angle becomes: 
1+ À, A, ik 
