# Dropping parallel postulate and infinitude of straight line

I was reading an article about back ground of Killing's work by Thomas Hawkins from Historia mathematica $1980$ (doi: 10.1016/0315-0860(80)90027-0). It was written that Killing stated that if one drop assumptions infinitude of straight line and parallel postulates four possibilities arise, which we can judge. I got only one which is very simple. Lines which has a transverse need not intersect at a point on the side where sum of interior angles is less than two right angles.

Is it correct? Then what are the other possibilities Killing suggests?