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

ANOTHER GEOMETRIC INTREPRETATION 79
Let us next have a look at postulate (I2). But we
must premise some
DEFINITIONS.-A pair of points, A and B, of a pathocircle is a segment AB or BA; A and B are its ends; the
points between them are the segment's points.
A A
FIG. 14. FIG. x5.
FIG. I6.
It is easy to see, Fig. I6, that the Pasch postulate (I2)
is verified. A, B, C are three points not on a same
pathocircle; they determine three segments, AB, BC, CA;
the pathocircle a going through AB, one of the three,
goes through another, BC.