- There exists at least one line.
- There are exactly three points on every line.
- Not all points are on the same line.
- There is exactly one line on any two distinct points.
- For each line
*l*and each point P not on*l*, there exists exactly one line on P which is not on any point of*l*.

**Proposition 1.** For every point, there is a line not on that point.

**Proposition 2.** For every point, there are at least four lines on that point.

**Proposition 3.** For every point, there are exactly four lines on that point.

**Proposition 4.** In Young's geometry, each line is parallel to exactly two lines.

**Proposition 5.** In Young's geometry, there are exactly 12 lines.

**Proposition 6.** In Young's geometry, there are three lines, no two of which intersect.

**Proposition 7.**In Young's geometry, there are exactly 9 points.

**Proposition 8.** Given any three mutually parallel lines in a Young's geometry, every other line
intersects all three.

Len Smiley Last modified: Tue Jan 23 11:02:08 AKST 2001