Postulate 2: A finite line segment can extend continuously.

Postulate 3: A circle can be drawn at any distance with any point as the center.

Postulate 4: All right angles are equal to each other.

Postulate 5: One straight line and the other two straight lines intersect in the same plane. If the sum of the two internal angles of a certain side is less than the sum of the two right angles, then the two straight lines extend indefinitely and intersect at that side.

Geometry types: Euclidean geometry (plane and space), non-Euclidean geometry (Luo Bachov geometry), analytic geometry, differential geometry, Riemannian geometry and fractal geometry.