Mathematical philosophy, a study of fate and freedom; lectures for educated laymen, by Cassius J. Keyser.

NON-GEOMETRIC INTERPRETATION 98
Solving the foregoing equations for x and y, we get
X2 - XlX3
- lXi
for s1: '
Y2 - Xly3
X3 - X2X1
X= -
I-Â2
for s2:
y3- X2yl
2, are respective
YX1-2 X2 '
X- X 3
I - -Xa
for3 S:
X I - XA3
Now let us suppose that Ax+By+C=O is a system s
not containing any of the dyads di, d2, da. The conditions that s shall contain a dyad of each of the systems, S2, is are respec ce tively
_x2+By2+C
Ax + +By3 +C'
xl +Byl +C
Xa =x+By2+C;
We have, as you see, Xi X2X3 =`I; hence none of the X's is
negative or else two (and only two) of then arç negative.
Now suppose that s contains a d in the segment dld2;
then Xa is negative; hence Xi or X2 is negative, and p j